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NLP Centre, Faculty of Informatics, Masaryk University 14

math_qa__Ts8wwjVf7KTzsm1Y

What is the area of square field whose side of length 20 m? Select A) 200 sq m B) 186 sq m C) 586 sq m D) 287 sq m E) 400 sq m

<gadget id="calculator">20 ** 2</gadget> <output>400</output> <result>E</result>

E

What is the area of square field whose side of length 20 m?

square_area(20)

square_area(n0)|

"20 * 20 = 400 sq m answer : e"

geometry

math_qa__KV2JEoVbtRWQ29ff

In a survey of 345 employees, 104 of them are uninsured, 54 work part time, and 12.5 percent of employees who are uninsured work part time. If a person is to be randomly selected from those surveyed, what is the probability that the person will neither work part time nor be uninsured? Choose the most appropriate option. A) 7 / 12 B) 8 / 41 C) 9 / 348 D) 1 / 8 E) 40 / 69

<gadget id="calculator">12.5 * 104</gadget> <output>1_300</output> <gadget id="calculator">1 * 100</gadget> <output>100</output> <gadget id="calculator">1_300 / 100</gadget> <output>13</output> <gadget id="calculator">54 - 13</gadget> <output>41</output> <gadget id="calculator">41 + 104</gadget> <output>145</output> <gadget id="calculator">345 - 145</gadget> <output>200</output> <gadget id="calculator">200 / 345</gadget> <output>40/69 = around 0.57971</output> <result>E</result>

E

In a survey of 345 employees, 104 of them are uninsured, 54 work part time, and 12.5 percent of employees who are uninsured work part time. If a person is to be randomly selected from those surveyed, what is the probability that the person will neither work part time nor be uninsured?

divide(subtract(345, add(subtract(54, divide(multiply(12.5, 104), multiply(const_1, const_100))), 104)), 345)

multiply(n1,n3)|multiply(const_1,const_100)|divide(#0,#1)|subtract(n2,#2)|add(n1,#3)|subtract(n0,#4)|divide(#5,n0)|

"- - - - - - - - - ui - - - - - - - - - - - - - - - - nui - - - - - - - total pt - - - - ( 12.5 / 100 ) * 104 = 13 - - - - - - - - - - - - - 54 npt - - - 104 - 13 - - - - - - - - - - - - - - x - - - - - - - - 291 total - - 104 - - - - - - - - - - - - - - - - - - - - - - - - - - - - 345 we have to find not part time and not uninsured . in other words not part time and insured = x / 345 = ( 291 - 104 + 13 ) / 345 = 40 / 69 answer is e ."

physics

math_qa__jDNe3RqGDVY8MxHM

Two dogsled teams raced across a 300 mile course in Wyoming. Team A finished the course in 3 fewer hours than team W. If team A's average speed was 5 mph greater than team W's, what was team W's average mph? Pick one: A) 12 B) 15 C) 18 D) 20 E) 25

<gadget id="calculator">300 / 5</gadget> <output>60</output> <gadget id="calculator">60 / 3</gadget> <output>20</output> <result>D</result>

D

Two dogsled teams raced across a 300 mile course in Wyoming. Team A finished the course in 3 fewer hours than team W. If team A's average speed was 5 mph greater than team W's, what was team W's average mph?

divide(divide(300, 5), 3)

divide(n0,n2)|divide(#0,n1)|

"this is a very specific format that has appeared in a handful of real gmat questions , and you may wish to learn to recognize it : here we have a * fixed * distance , and we are given the difference between the times and speeds of two things that have traveled that distance . this is one of the very small number of question formats where backsolving is typically easier than solving directly , since the direct approach normally produces a quadratic equation . say team w ' s speed was s . then team w ' s time is 300 / s . team a ' s speed was then s + 5 , and team a ' s time was then 300 / ( s + 5 ) . we need to find an answer choice for s so that the time of team a is 3 less than the time of team w . that is , we need an answer choice so that 300 / ( s + 5 ) = ( 300 / s ) - 3 . you can now immediately use number properties to zero in on promising answer choices : the times in these questions will always work out to be integers , and we need to divide 300 by s , and by s + 5 . so we want an answer choice s which is a factor of 300 , and for which s + 5 is also a factor of 300 . so you can rule out answers a and c immediately , since s + 5 wo n ' t be a divisor of 300 in those cases ( sometimes using number properties you get to the correct answer without doing any other work , but unfortunately that ' s not the case here ) . testing the other answer choices , if you try answer d , you find the time for team w is 15 hours , and for team a is 12 hours , and since these differ by 3 , as desired , d is correct ."

physics

math_qa__h72V4YGcV7BjqOoa

The ratio of numbers is 3:4 and their H.C.F is 8. Their L.C.M is: Pick one: A) 12 B) 96 C) 24 D) 48 E) 98

<gadget id="calculator">3 * 8</gadget> <output>24</output> <gadget id="calculator">4 * 8</gadget> <output>32</output> <gadget id="calculator">lcm(24, 32)</gadget> <output>96</output> <result>B</result>

B

The ratio of numbers is 3:4 and their H.C.F is 8. Their L.C.M is:

lcm(multiply(3, 8), multiply(4, 8))

multiply(n0,n2)|multiply(n1,n2)|lcm(#0,#1)

let the numbers be 3 x and 4 x . then their h . c . f = x . so , x = 8 . so , the numbers are 24 and 32 . l . c . m of 24 and 32 = 96 . answer : b

other

math_qa__XFLSLIS9b5vYCli5

Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.59000? Choices. A) 81000 B) 81007 C) 74671.875 D) 81066 E) 81022

<gadget id="calculator">1 / 8</gadget> <output>1/8 = around 0.125</output> <gadget id="calculator">(1/8) * 59_000</gadget> <output>7_375</output> <gadget id="calculator">59_000 + 7_375</gadget> <output>66_375</output> <gadget id="calculator">(1/8) * 66_375</gadget> <output>66_375/8 = around 8_296.875</output> <gadget id="calculator">66_375 + (66_375/8)</gadget> <output>597_375/8 = around 74_671.875</output> <result>C</result>

C

Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.59000?

add(add(59000, multiply(divide(1, 8), 59000)), multiply(divide(1, 8), add(59000, multiply(divide(1, 8), 59000))))

divide(n0,n1)|multiply(n2,#0)|add(n2,#1)|multiply(#2,#0)|add(#2,#3)|

"59000 * 9 / 8 * 9 / 8 = 74671.875 answer : c"

general

math_qa__qikq8feC6GD4erSB

A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 30%? Select A) 650 B) 882 C) 772 D) 652 E) 271

<gadget id="calculator">30 / 100</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">500 * (3/10)</gadget> <output>150</output> <gadget id="calculator">500 + 150</gadget> <output>650</output> <result>A</result>

A

A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 30%?

add(500, multiply(500, divide(30, const_100)))

divide(n1,const_100)|multiply(n0,#0)|add(n0,#1)|

"cost price = rs . 500 profit = 30 % of 500 = rs . 150 selling price = cost price + profit = 500 + 150 = 650 answer : a"

gain

math_qa__6YMaH51yTAcjOOVw

If the sum and difference of two numbers are 20 and 8 respectively, then the difference of their square is: Select: A) 12 B) 28 C) 160 D) 180 E) 18

<gadget id="calculator">20 + 8</gadget> <output>28</output> <gadget id="calculator">28 / 2</gadget> <output>14</output> <gadget id="calculator">14 ** 2</gadget> <output>196</output> <gadget id="calculator">20 - 14</gadget> <output>6</output> <gadget id="calculator">6 ** 2</gadget> <output>36</output> <gadget id="calculator">196 - 36</gadget> <output>160</output> <result>C</result>

C

If the sum and difference of two numbers are 20 and 8 respectively, then the difference of their square is:

subtract(power(divide(add(20, 8), const_2), const_2), power(subtract(20, divide(add(20, 8), const_2)), const_2))

add(n0,n1)|divide(#0,const_2)|power(#1,const_2)|subtract(n0,#1)|power(#3,const_2)|subtract(#2,#4)|

"let the numbers be x and y . then , x + y = 20 and x - y = 8 x 2 - y 2 = ( x + y ) ( x - y ) = 20 * 8 = 160 . answer : c"

general

math_qa__ztGEWwbAA1QW3NbF

RAJA complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km. Choose the most appropriate option: A) 200 km B) 250 km C) 224 km D) 255 km E) 260 km

<gadget id="calculator">10 / 2</gadget> <output>5</output> <gadget id="calculator">5 * 24</gadget> <output>120</output> <gadget id="calculator">5 * 21</gadget> <output>105</output> <gadget id="calculator">120 + 105</gadget> <output>225</output> <result>C</result>

C

RAJA complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.

add(multiply(divide(10, const_2), 24), multiply(divide(10, const_2), 21))

divide(n0,const_2)|multiply(n2,#0)|multiply(n1,#0)|add(#1,#2)

consider x - - > ( 1 / 2 ) x / 21 + ( 1 / 2 ) x / 24 = 10 = = > x / 21 + x / 24 = 20 15 x = 168 * 20 = = > 224 km answer c

physics

math_qa__mxOLrTa4MpiWTZKp

The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is: Answers: A) 44 % B) 46 % C) 48 % D) 50 % E) 51 %

<gadget id="calculator">100 + 20</gadget> <output>120</output> <gadget id="calculator">120 / 100</gadget> <output>6/5 = around 1.2</output> <gadget id="calculator">(6/5) * (6/5)</gadget> <output>36/25 = around 1.44</output> <gadget id="calculator">(36/25) - 1</gadget> <output>11/25 = around 0.44</output> <gadget id="calculator">(11/25) * 100</gadget> <output>44</output> <result>A</result>

A

The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:

multiply(subtract(multiply(divide(add(const_100, 20), const_100), divide(add(const_100, 20), const_100)), const_1), const_100)

add(n0,const_100)|divide(#0,const_100)|multiply(#1,#1)|subtract(#2,const_1)|multiply(#3,const_100)|

"let original length = x metres and original breadth = y metres . original area = ( xy ) m 2 . new length = 120 x m = 6 x m . 100 5 new breadth = 120 y m = 6 y m . 100 5 new area = 6 x x 6 y m 2 = 36 xy m 2 . 5 5 25 the difference between the original area = xy and new - area 36 / 25 xy is = ( 36 / 25 ) xy - xy = xy ( 36 / 25 - 1 ) = xy ( 11 / 25 ) or ( 11 / 25 ) xy increase % = 11 xy x 1 x 100 % = 44 % . 25 xy a"

geometry

math_qa__YZTXqvHpulTLGiok

A person travels equal distances with speeds of 2km/hr, 4km/hr, 6km/hr. and takes a total time of 11minutes. Find the total distance ? Choose the correct choice from the following answers: A) 1 km B) 500 mts C) 600 mts D) 2 km E) 250 mts

<gadget id="calculator">11 / 60</gadget> <output>11/60 = around 0.183333</output> <gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">1 / 4</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(1/2) + (1/4)</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">1 / 6</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">(3/4) + (1/6)</gadget> <output>11/12 = around 0.916667</output> <gadget id="calculator">(11/60) / (11/12)</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(1/5) * 3</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">(3/5) * 1_000</gadget> <output>600</output> <result>C</result>

C

A person travels equal distances with speeds of 2km/hr, 4km/hr, 6km/hr. and takes a total time of 11minutes. Find the total distance ?

multiply(multiply(divide(divide(11, const_60), add(add(divide(const_1, 2), divide(const_1, 4)), divide(const_1, 6))), const_3), const_1000)

divide(n3,const_60)|divide(const_1,n0)|divide(const_1,n1)|divide(const_1,n2)|add(#1,#2)|add(#4,#3)|divide(#0,#5)|multiply(#6,const_3)|multiply(#7,const_1000)|

"let the each distance be x km total distance = 3 x then total time , ( x / 2 ) + ( x / 4 ) + ( x / 6 ) = 11 / 60 x = 0.2 total distance = 3 * 0.2 = 0.6 km = 600 meters correct option is c"

physics

math_qa__5xMrQg0zFQAITO1F

The ratio of the radius of two circles is 1: 9, and then the ratio of their areas is? Answers A) 1 : 8 B) 1 : 6 C) 1 : 9 D) 1 : 3 E) 1 : 81

<gadget id="calculator">pi * (1 ** 2)</gadget> <output>pi = around 3.141593</output> <gadget id="calculator">pi * (9 ** 2)</gadget> <output>81*pi = around 254.469005</output> <gadget id="calculator">pi / (81*pi)</gadget> <output>1/81 = around 0.012346</output> <result>E</result>

E

The ratio of the radius of two circles is 1: 9, and then the ratio of their areas is?

divide(circle_area(1), circle_area(9))

circle_area(n0)|circle_area(n1)|divide(#0,#1)|

"r 1 : r 2 = 1 : 9 π r 12 : π r 22 r 12 : r 22 = 1 : 81 answer : e"

geometry

math_qa__rK4tOJ5KN6LkhJ4A

The average salary of all the workers in a workshop is Rs. 9000. The average salary of 6 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is? Select: A) 23 B) 21 C) 52 D) 56 E) 12

<gadget id="calculator">12_000 - 9_000</gadget> <output>3_000</output> <gadget id="calculator">6 * 3_000</gadget> <output>18_000</output> <gadget id="calculator">9_000 - 6_000</gadget> <output>3_000</output> <gadget id="calculator">18_000 / 3_000</gadget> <output>6</output> <gadget id="calculator">6 + 6</gadget> <output>12</output> <result>E</result>

E

The average salary of all the workers in a workshop is Rs. 9000. The average salary of 6 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is?

add(6, divide(multiply(6, subtract(12000, 9000)), subtract(9000, 6000)))

subtract(n2,n0)|subtract(n0,n3)|multiply(n1,#0)|divide(#2,#1)|add(n1,#3)|

"let the total number of workers be x . then , 9000 x = ( 12000 * 6 ) + 6000 ( x - 6 ) = > 3000 x = 36000 = x = 12 . answer : e"

general

math_qa__ltBbq1Jkjatf32aH

the first flight out of phoenix airport had a late departure . if the next 3 flights departed on - time , how many subsequent flights need to depart from phoenix on - time , for the airport ' s on - time departure rate to be higher than 60 % ? i will see what is the quickest way to solve it then i will provide the explanation Select the correct option: A) 6 B) 7 C) 9 D) 4 E) 11

<gadget id="calculator">60 / 100</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">(3/5) * 10</gadget> <output>6</output> <gadget id="calculator">6 + 1</gadget> <output>7</output> <gadget id="calculator">7 - 3</gadget> <output>4</output> <result>D</result>

D

the first flight out of phoenix airport had a late departure . if the next 3 flights departed on - time , how many subsequent flights need to depart from phoenix on - time , for the airport ' s on - time departure rate to be higher than 60 % ? i will see what is the quickest way to solve it then i will provide the explanation

subtract(add(multiply(divide(60, const_100), const_10), const_1), 3)

divide(n1,const_100)|multiply(#0,const_10)|add(#1,const_1)|subtract(#2,n0)

the following approach might be the easiest one and less error prone . we need on - time departure rate to be higher than 6 / 10 , so it should be at least 7 / 11 , which means that 7 out of 11 flights must depart on time . since for now 3 out of 4 flights departed on time then 7 - 3 = 4 subsequent flights need to depart on - time . answer : d

gain

math_qa__lco7XdJG2iE3tvz2

6) A marketing firm determined that , of 300 households surveyed, 80 used neither Brand A nor Brand B soap.60 used only Brand A soap and for every household that used both brands of soap, 3 used only brand B soap.how many of the 200 household surveyed used both brands of soap? Choose the correct choice from the following answers: A) 15 B) 20 C) 30 D) 40 E) 45

<gadget id="calculator">300 - 80</gadget> <output>220</output> <gadget id="calculator">220 - 60</gadget> <output>160</output> <gadget id="calculator">160 / 4</gadget> <output>40</output> <result>D</result>

D

6) A marketing firm determined that , of 300 households surveyed, 80 used neither Brand A nor Brand B soap.60 used only Brand A soap and for every household that used both brands of soap, 3 used only brand B soap.how many of the 200 household surveyed used both brands of soap?

divide(subtract(subtract(300, 80), 60), const_4)

subtract(n1,n2)|subtract(#0,n3)|divide(#1,const_4)|

"220 = at least one of soap a or b both brands = x brand b = 3 x = > 60 + x + 3 x = 220 = > 4 x = 160 = > x = 40 answer - d"

other

math_qa__4vLInuLxchBzUcpG

A perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer. How many positive integers n are there such that n is less than 50,000 and at the same time n is a perfect square and a perfect cube? Choose the correct choice from the following answers: A) 3 B) 4 C) 5 D) 6 E) 7

<gadget id="calculator">4 + 2</gadget> <output>6</output> <gadget id="calculator">6 / 1</gadget> <output>6</output> <result>D</result>

D

A perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer. How many positive integers n are there such that n is less than 50,000 and at the same time n is a perfect square and a perfect cube?

divide(add(const_4, const_2), const_1)

add(const_2,const_4)|divide(#0,const_1)

if n is a perfect square and a perfect cube , then n = a ^ 6 for some integer a . the numbers are 1 ^ 6 = 1 , 2 ^ 6 = 64 , 3 ^ 6 = 729 , 4 ^ 6 = 4096 , 5 ^ 6 = 15,625 , 6 ^ = 46,656 . the answer is d .

geometry

math_qa__T6Bes5ycedXxDKLG

At Joel’s bookstore, the current inventory is 40% historical fiction. Of the historical fiction books, 40% are new releases, while 40% of the other books are new releases. What fraction of all new releases are the historical fiction new releases? Choose the correct choice from the following options. A) 4 / 25 B) 8 / 23 C) 2 / 5 D) 8 / 15 E) 2 / 5

<gadget id="calculator">40 * 40</gadget> <output>1_600</output> <gadget id="calculator">1_600 / 100</gadget> <output>16</output> <gadget id="calculator">100 - 40</gadget> <output>60</output> <gadget id="calculator">40 * 60</gadget> <output>2_400</output> <gadget id="calculator">2_400 / 100</gadget> <output>24</output> <gadget id="calculator">16 + 24</gadget> <output>40</output> <gadget id="calculator">16 / 40</gadget> <output>2/5 = around 0.4</output> <result>E</result>

E

At Joel’s bookstore, the current inventory is 40% historical fiction. Of the historical fiction books, 40% are new releases, while 40% of the other books are new releases. What fraction of all new releases are the historical fiction new releases?

divide(divide(multiply(40, 40), const_100), add(divide(multiply(40, 40), const_100), divide(multiply(40, subtract(const_100, 40)), const_100)))

multiply(n0,n1)|subtract(const_100,n0)|divide(#0,const_100)|multiply(n2,#1)|divide(#3,const_100)|add(#2,#4)|divide(#2,#5)|

"let there be 100 books in all historic fiction books = 40 % of total = 40 other books = 60 new historic fiction = 40 % of 40 = 16 other new books = 40 % of 60 = 24 total new books = 24 + 16 = 40 fraction = 16 / 40 = 2 / 5 ans : e"

gain

math_qa__2sElilygpBHoih0v

The price of lunch for 15 people was $209.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity? Select the correct option: A) $ 11.73 B) $ 12.66 C) $ 13.80 D) $ 14.00 E) $ 15.87

<gadget id="calculator">100 + 15</gadget> <output>115</output> <gadget id="calculator">209 / 115</gadget> <output>209/115 = around 1.817391</output> <gadget id="calculator">(209/115) * 100</gadget> <output>4_180/23 = around 181.73913</output> <gadget id="calculator">1 / 15</gadget> <output>1/15 = around 0.066667</output> <gadget id="calculator">(4_180/23) * (1/15)</gadget> <output>836/69 = around 12.115942</output> <result>B</result>

B

The price of lunch for 15 people was $209.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity?

multiply(multiply(divide(209.00, add(const_100, 15)), const_100), divide(const_1, 15))

add(n0,const_100)|divide(const_1,n0)|divide(n1,#0)|multiply(#2,const_100)|multiply(#1,#3)|

"take the initial price before the gratuity is 100 the gratuity is calculated on the final price , so as we assumed the final bill before adding gratuity is 100 so gratuity is 15 % of 100 is 15 so the total price of meals is 115 so the given amount i . e 209 is for 115 then we have to calculate for 100 for 115 209 for 100 x so by cross multiplication we get 115 x = 100 * 209 = > x = 100 * 209 / 110 by simplifying we get x as 190 which is the price of lunch before gratuity so the gratuity is 19 so as the question ask the average price person excluding gratuity is 190 / 15 = 12.66 so our answer is b )"

general

math_qa__mzRPLzoTYDhV3oCL

The average of 50 numbers id 44. If two numbers, namely 45 and 55 are discarded, the average of the remaining numbers is : Choose one A) 22.35 B) 33.25 C) 22.25 D) 11.35 E) 43.75

<gadget id="calculator">50 * 44</gadget> <output>2_200</output> <gadget id="calculator">45 + 55</gadget> <output>100</output> <gadget id="calculator">2_200 - 100</gadget> <output>2_100</output> <gadget id="calculator">50 - 2</gadget> <output>48</output> <gadget id="calculator">2_100 / 48</gadget> <output>175/4 = around 43.75</output> <result>E</result>

E

The average of 50 numbers id 44. If two numbers, namely 45 and 55 are discarded, the average of the remaining numbers is :

divide(subtract(multiply(50, 44), add(45, 55)), subtract(50, const_2))

add(n2,n3)|multiply(n0,n1)|subtract(n0,const_2)|subtract(#1,#0)|divide(#3,#2)|

"explanation : total of 50 numbers = ( 50 × 44 ) = 2200 total of 48 numbers = ( 2200 - ( 45 + 55 ) ] = 2100 required average = 2100 / 48 = 43.75 answer : e"

general

math_qa__63xl2SduD02Ixae2

6 persons in an organization including a and b were to be divided in two groups of 3 members each . the total number of groups containing both a and b is what fraction of the total number of groups which can be formed ? Select the correct option A) 3 / 10 B) 1 / 70 C) 3 / 14 D) 1 / 10 E) 11 / 14

<gadget id="calculator">6 ** 2</gadget> <output>36</output> <gadget id="calculator">6 - 1</gadget> <output>5</output> <gadget id="calculator">6 * 5</gadget> <output>30</output> <gadget id="calculator">5 - 1</gadget> <output>4</output> <gadget id="calculator">30 * 4</gadget> <output>120</output> <gadget id="calculator">36 / 120</gadget> <output>3/10 = around 0.3</output> <result>A</result>

A

6 persons in an organization including a and b were to be divided in two groups of 3 members each . the total number of groups containing both a and b is what fraction of the total number of groups which can be formed ?

divide(power(6, const_2), multiply(multiply(6, subtract(6, const_1)), subtract(subtract(6, const_1), const_1)))

power(n0,const_2)|subtract(n0,const_1)|multiply(n0,#1)|subtract(#1,const_1)|multiply(#2,#3)|divide(#0,#4)

the fraction is nothing but the probability . . number to choose 3 out of 6 = 6 c 3 number to choose a and b and 2 from remaining 4 = 4 c 2 . . prob of a and b choosen = 4 c 2 / 6 c 3 = 3 / 10 answer : a

general

math_qa__IEthdNbMU1O83RHa

What number has a 5:1 ratio to the number 11? Choose the correct choice from the following options. A) 22 B) 50 C) 55 D) 52 E) 12

<gadget id="calculator">11 * 5</gadget> <output>55</output> <result>C</result>

C

What number has a 5:1 ratio to the number 11?

multiply(11, 5)

multiply(n0,n2)|

"5 : 1 = x : 10 x = 55 answer : c"

other

math_qa__u33sb2UOU2cfdqku

In a class, if 50% of the boys were girls, then there would be 50% more girls than boys. What percentage of the overall class is girls? Choose the correct choice from the following answers: A) 25 % B) 33.33 % C) 40 % D) 20 % E) 10 %

<gadget id="calculator">50 / 100</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">1 + (1/2)</gadget> <output>3/2 = around 1.5</output> <gadget id="calculator">(3/2) * (1/2)</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">(3/4) - (1/2)</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(1/4) + 1</gadget> <output>5/4 = around 1.25</output> <gadget id="calculator">(1/4) / (5/4)</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(1/5) * 100</gadget> <output>20</output> <result>D</result>

D

In a class, if 50% of the boys were girls, then there would be 50% more girls than boys. What percentage of the overall class is girls?

multiply(divide(subtract(multiply(add(const_1, divide(50, const_100)), divide(50, const_100)), divide(50, const_100)), add(subtract(multiply(add(const_1, divide(50, const_100)), divide(50, const_100)), divide(50, const_100)), const_1)), const_100)

divide(n0,const_100)|add(#0,const_1)|multiply(#1,#0)|subtract(#2,#0)|add(#3,const_1)|divide(#3,#4)|multiply(#5,const_100)

detailed solution for questions of this type , it is best to go from the final step . in the final state , the number of girls should be 1.5 * the number of boys . when 50 % of the boys are taken as girls , let the number of boys = x number of girls = 1.5 x total number of students = 2.5 x original number of boys = 2 x ( 50 % of boys = x ) original number of girls = 0.5 x girls form 20 % of the overall class . correct answer d .

gain

math_qa__tvNUpZWkxQdnAqdu

A man can row downstream at the rate of 30 Kmph and upstream at 10 Kmph. Find the man’s rate in still water and rate of current? Choose the most appropriate option: A) 10 B) 8.0 C) 9.5 D) 9.0 E) 8.25

<gadget id="calculator">30 - 10</gadget> <output>20</output> <gadget id="calculator">20 / 2</gadget> <output>10</output> <result>A</result>

A

A man can row downstream at the rate of 30 Kmph and upstream at 10 Kmph. Find the man’s rate in still water and rate of current?

divide(subtract(30, 10), const_2)

subtract(n0,n1)|divide(#0,const_2)|

"rate of still water = 1 / 2 ( down stream + upstream ) = 1 / 2 ( 30 + 10 ) = 20 kmph rate of current = 1 / 2 ( down stream - upstream ) = 1 / 2 ( 30 - 10 ) = 1 / 2 ( 20 ) = 10 kmph answer is a ."

gain

math_qa__8dm8YDpmA29eYkCN

The cost of a one-family home was $ 120,000 in 1980. In 1988, the price had increased to $ 192,000. What was the percent increase in the cost of the home? Choose the correct answer. A) 60 % B) 50 % C) 55 % D) 40 % E) 33.3 %

<gadget id="calculator">4 * 4</gadget> <output>16</output> <gadget id="calculator">12 * 16</gadget> <output>192</output> <gadget id="calculator">192 * 1_000</gadget> <output>192_000</output> <gadget id="calculator">12 * 1_000</gadget> <output>12_000</output> <gadget id="calculator">12_000 * 10</gadget> <output>120_000</output> <gadget id="calculator">192_000 - 120_000</gadget> <output>72_000</output> <gadget id="calculator">72_000 / 120_000</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">(3/5) * 100</gadget> <output>60</output> <result>A</result>

A

The cost of a one-family home was $ 120,000 in 1980. In 1988, the price had increased to $ 192,000. What was the percent increase in the cost of the home?

multiply(divide(subtract(multiply(multiply(const_12, multiply(const_4, const_4)), const_1000), multiply(multiply(const_12, const_1000), const_10)), multiply(multiply(const_12, const_1000), const_10)), const_100)

multiply(const_4,const_4)|multiply(const_1000,const_12)|multiply(#0,const_12)|multiply(#1,const_10)|multiply(#2,const_1000)|subtract(#4,#3)|divide(#5,#3)|multiply(#6,const_100)

increase = 192000 - 120000 = 72000 % increase = 72000 * 100 / 120000 = 60 % answer : option a

general

math_qa__Ta0md8104lzb2Lwb

A dishonest dealer professes to sell goods at the cost price but uses a weight of 900 grams per kg, what is his percent? Select the correct option: A) 11.11 % B) 25 % C) 22 % D) 29 % E) 45 %

<gadget id="calculator">100 / 900</gadget> <output>1/9 = around 0.111111</output> <gadget id="calculator">3 + 2</gadget> <output>5</output> <gadget id="calculator">5 * 2</gadget> <output>10</output> <gadget id="calculator">100 * 10</gadget> <output>1_000</output> <gadget id="calculator">(1/9) * 1_000</gadget> <output>1_000/9 = around 111.111111</output> <gadget id="calculator">(1_000/9) - 100</gadget> <output>100/9 = around 11.111111</output> <result>A</result>

A

A dishonest dealer professes to sell goods at the cost price but uses a weight of 900 grams per kg, what is his percent?

subtract(multiply(divide(const_100, 900), multiply(const_100, multiply(add(const_3, const_2), const_2))), const_100)

add(const_2,const_3)|divide(const_100,n0)|multiply(#0,const_2)|multiply(#2,const_100)|multiply(#1,#3)|subtract(#4,const_100)|

"900 - - - 100 100 - - - ? = > 11.11 % answer : a"

gain

math_qa__bteOpXtVUbIm1lkn

In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of thesportformulation contains 5 ounces of corn syrup, how many ounces of water does it contain? Answers: A) 45 B) 50 C) 55 D) 60 E) 75

<gadget id="calculator">1 / 12</gadget> <output>1/12 = around 0.083333</output> <gadget id="calculator">(1/12) * 3</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">1 / 30</gadget> <output>1/30 = around 0.033333</output> <gadget id="calculator">(1/30) / 2</gadget> <output>1/60 = around 0.016667</output> <gadget id="calculator">(1/4) / (1/60)</gadget> <output>15</output> <gadget id="calculator">15 * 5</gadget> <output>75</output> <result>E</result>

E

In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of thesportformulation contains 5 ounces of corn syrup, how many ounces of water does it contain?

multiply(divide(multiply(divide(1, 12), const_3), divide(divide(1, 30), const_2)), 5)

divide(n0,n1)|divide(n0,n2)|divide(#1,const_2)|multiply(#0,const_3)|divide(#3,#2)|multiply(n3,#4)|

"f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 5 * 180 / 12 = 75 ounces of water e"

other

math_qa__bU8LSlljutbnfjO7

A batsman in his 19th inning makes a score of 100 and their by increasing his average by 2. What is his average after the 19th inning? Choose the correct choice from the following answers: A) 58 B) 60 C) 62 D) 64 E) 66

<gadget id="calculator">2 * 19</gadget> <output>38</output> <gadget id="calculator">100 - 38</gadget> <output>62</output> <gadget id="calculator">62 + 2</gadget> <output>64</output> <result>D</result>

D

A batsman in his 19th inning makes a score of 100 and their by increasing his average by 2. What is his average after the 19th inning?

add(subtract(100, multiply(2, 19)), 2)

multiply(n0,n2)|subtract(n1,#0)|add(n2,#1)|

"18 x + 100 = 19 ( x + 2 ) x = 62 + 2 = 64 answer : d"

general

math_qa__pqc6wm0c9CTuzPYQ

B takes 12 more days than A to finish a task. B and A start this task and A leaves the task 12 days before the task is finished. B completes 60% of the overall task. How long would B have taken to finish the task if he had worked independently? Choose one. A) 48 days B) 36 days C) 28 days D) 32 days E) 22 days

<gadget id="calculator">12 * 10</gadget> <output>120</output> <gadget id="calculator">4 + 1</gadget> <output>5</output> <gadget id="calculator">120 / 5</gadget> <output>24</output> <gadget id="calculator">24 + 12</gadget> <output>36</output> <result>B</result>

B

B takes 12 more days than A to finish a task. B and A start this task and A leaves the task 12 days before the task is finished. B completes 60% of the overall task. How long would B have taken to finish the task if he had worked independently?

add(divide(multiply(12, const_10), add(const_4, const_1)), 12)

add(const_1,const_4)|multiply(n0,const_10)|divide(#1,#0)|add(n0,#2)

detailed solution let us say a and b split their share of the task and started doing their respective shares simultaneously . let ’ s say a takes a days to finish the task . therefore , b takes a + 12 days to finish the entire task . a has to finish 40 % of the task , since b is doing the rest . so a will only take 2 a / 5 number of days . b only has to finish 60 % of the task , so b will take ( 3 ( a + 12 ) / 5 ) number of days . but as we know , b starts working along with a and finishes 12 days after a stops working . so , ( 3 ( a + 12 ) / 5 ) = ( ( 2 a ) / 5 + 12 ) 3 a + 36 = 2 a + 60 a = 24 ; b = 36 days . answer choice b

physics

math_qa__p7kKLgLGYBQXMHBR

An error 19% in excess is made while measuring the side of a square. Now What is the percentage of error in the calculated area of the square? Choose the correct choice from the following answers A) 6.64 % B) 41.61 % C) 45.64 % D) 46.64 % E) 10.64 %

<gadget id="calculator">100 + 19</gadget> <output>119</output> <gadget id="calculator">119 ** 2</gadget> <output>14_161</output> <gadget id="calculator">100 ** 2</gadget> <output>10_000</output> <gadget id="calculator">14_161 - 10_000</gadget> <output>4_161</output> <gadget id="calculator">4_161 * 100</gadget> <output>416_100</output> <gadget id="calculator">416_100 / 10_000</gadget> <output>4_161/100 = around 41.61</output> <result>B</result>

B

An error 19% in excess is made while measuring the side of a square. Now What is the percentage of error in the calculated area of the square?

divide(multiply(subtract(square_area(add(const_100, 19)), square_area(const_100)), const_100), square_area(const_100))

add(n0,const_100)|square_area(const_100)|square_area(#0)|subtract(#2,#1)|multiply(#3,const_100)|divide(#4,#1)|

"percentage error in calculated area = ( 19 + 19 + ( 19 ã — 19 ) / 100 ) % = 41.61 % answer : b"

gain

math_qa__y3RxZnhl8ySBjBUm

In the first 20 overs of a cricket game, the run rate was only 4.2. What should be the run rate in the remaining 30 Overs to reach the target of 324 runs? Choose the correct choice from the following options A) 7.25 B) 8.5 C) 8 D) 9.15 E) 10

<gadget id="calculator">20 * 4.2</gadget> <output>84</output> <gadget id="calculator">324 - 84</gadget> <output>240</output> <gadget id="calculator">240 / 30</gadget> <output>8</output> <result>C</result>

C

In the first 20 overs of a cricket game, the run rate was only 4.2. What should be the run rate in the remaining 30 Overs to reach the target of 324 runs?

divide(subtract(324, multiply(20, 4.2)), 30)

multiply(n0,n1)|subtract(n3,#0)|divide(#1,n2)|

"explanation : required run rate = ( 324 - 4.2 20 ) = 240 / 30 = 8 . answer : c"

gain

math_qa__2HMlsGnVK23bvmsU

x and y are integers. a+ b< 11 , and a> 6. What is the smallest possible value of a- b? Choose the correct choice from the following choices: A) 1 B) 2 C) 4 D) - 2 E) - 4

<gadget id="calculator">11 + 6</gadget> <output>17</output> <gadget id="calculator">17 - 4</gadget> <output>13</output> <gadget id="calculator">13 + 1</gadget> <output>14</output> <gadget id="calculator">14 / 2</gadget> <output>7</output> <gadget id="calculator">7 - 3</gadget> <output>4</output> <result>C</result>

C

x and y are integers. a+ b< 11 , and a> 6. What is the smallest possible value of a- b?

subtract(divide(add(subtract(add(11, 6), const_4), const_1), const_2), const_3)

add(n0,n1)|subtract(#0,const_4)|add(#1,const_1)|divide(#2,const_2)|subtract(#3,const_3)

focus on the transition points and plug in the values . a > 6 so a could be 7 , 8 , 9 , 10 , 11 etc look at a = 7 7 + b < 11 b < 4 b could be 3 , 2 , 1 , 0 , - 1 etc when b is 3 , we get a - b = 4 this must be the smallest value because as a increases , b reduces so a - b increases . take another example . a = 11 so b < 0 . a - b will give a value greater than 11 . answer ( c ) .

general

math_qa__t2msxkVSayMlN9KX

A mobile battery in 1 hour charges to 20 percent.How much time (in minute) will it require more to charge to 65 percent. Answers: A) 145 B) 150 C) 195 D) 160 E) 130

<gadget id="calculator">65 / 20</gadget> <output>13/4 = around 3.25</output> <gadget id="calculator">(13/4) * 60</gadget> <output>195</output> <result>C</result>

C

A mobile battery in 1 hour charges to 20 percent.How much time (in minute) will it require more to charge to 65 percent.

multiply(divide(65, 20), const_60)

divide(n2,n1)|multiply(#0,const_60)

1 hr = 20 percent . thus 15 min = 5 percent . now to charge 65 percent 195 min . answer : c

physics

math_qa__jgEb6wrcMM82WuaO

If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x = 2^i * 3^k * 5^m * 7^p, then i + k + m + p = Answers. A) 4 B) 7 C) 8 D) 11 E) 12

<gadget id="calculator">7 + 2</gadget> <output>9</output> <gadget id="calculator">5 / 5</gadget> <output>1</output> <gadget id="calculator">9 + 1</gadget> <output>10</output> <gadget id="calculator">3 / 3</gadget> <output>1</output> <gadget id="calculator">10 + 1</gadget> <output>11</output> <result>D</result>

D

If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x = 2^i * 3^k * 5^m * 7^p, then i + k + m + p =

add(add(add(7, 2), divide(5, 5)), divide(3, 3))

add(n2,n5)|divide(n4,n4)|divide(n3,n3)|add(#0,#1)|add(#3,#2)

given that x = 8 ! = 2 ^ 7 ∗ 3 ^ 2 ∗ 5 ∗ 7 x . hence , x = 2 ^ 7 ∗ 3 ^ 2 ∗ 5 ^ 1 ∗ 7 ^ 1 = 2 ^ i ∗ 3 ^ k ∗ 5 ^ m ∗ 7 p , since i , k , m , and p are positive integers , then we can equate the exponents , so we have that i = 7 , k = 2 , m = 1 , and p = 1 therefore , i + k + m + p = 7 + 2 + 1 + 1 = 11 answer : d .

general

math_qa__WdvWEalUoFkSLycY

Find the base K of the number system, if (524)8 = (664)K ? Choose the most appropriate option. A) 4 B) 5 C) 6 D) 7 E) 8

<gadget id="calculator">2 * 8</gadget> <output>16</output> <gadget id="calculator">8 ** 2</gadget> <output>64</output> <gadget id="calculator">10 / 2</gadget> <output>5</output> <gadget id="calculator">64 * 5</gadget> <output>320</output> <gadget id="calculator">16 + 320</gadget> <output>336</output> <gadget id="calculator">4 + 336</gadget> <output>340</output> <gadget id="calculator">4 - 340</gadget> <output>-336</output> <gadget id="calculator">(-336) / 3</gadget> <output>-112</output> <gadget id="calculator">(-112) / 2</gadget> <output>-56</output> <gadget id="calculator">4 * (-56)</gadget> <output>-224</output> <gadget id="calculator">1 - (-224)</gadget> <output>225</output> <gadget id="calculator">225 ** (1/2)</gadget> <output>15</output> <gadget id="calculator">15 - 1</gadget> <output>14</output> <gadget id="calculator">14 / 2</gadget> <output>7</output> <result>D</result>

D

Find the base K of the number system, if (524)8 = (664)K ?

divide(subtract(sqrt(subtract(const_1, multiply(const_4, divide(divide(subtract(const_4, add(const_4, add(multiply(const_2, 8), multiply(power(8, const_2), divide(const_10, const_2))))), const_3), const_2)))), const_1), const_2)

divide(const_10,const_2)|multiply(n1,const_2)|power(n1,const_2)|multiply(#0,#2)|add(#1,#3)|add(#4,const_4)|subtract(const_4,#5)|divide(#6,const_3)|divide(#7,const_2)|multiply(#8,const_4)|subtract(const_1,#9)|sqrt(#10)|subtract(#11,const_1)|divide(#12,const_2)

5 * 8 ^ 2 + 2 * 8 ^ 1 + 4 * 8 ^ 0 = 6 * k ^ 2 + 6 * k ^ 1 + 4 * k ^ 0 320 + 16 + 4 = 6 ( k ^ 2 ) + 6 k + 4 340 = 6 ( k ^ 2 ) + 6 k + 4 6 ( k ^ 2 ) + 6 k + 4 - 340 = 0 6 ( k ^ 2 ) + 6 k - 336 = 0 dividing by 6 ; ( k ^ 2 ) + k - 56 = 0 solving this quadratic equation we get , k = 7 and k = - 8 thus k = 7 answer : d

geometry

math_qa__iPgsBuKeHgvVgIDi

If N is the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case.What is the sum of the digits of N ? Choose the correct choice from the following answers: A) 1 B) 2 C) 3 D) 5 E) 4

<gadget id="calculator">6_905 - 1_305</gadget> <output>5_600</output> <gadget id="calculator">4_665 - 1_305</gadget> <output>3_360</output> <gadget id="calculator">6_905 - 4_665</gadget> <output>2_240</output> <gadget id="calculator">gcd(3_360, 2_240)</gadget> <output>1_120</output> <gadget id="calculator">gcd(5_600, 1_120)</gadget> <output>1_120</output> <gadget id="calculator">1_120 / 10</gadget> <output>112</output> <gadget id="calculator">112 / 10</gadget> <output>56/5 = around 11.2</output> <gadget id="calculator">(56/5) / 10</gadget> <output>28/25 = around 1.12</output> <gadget id="calculator">floor(28/25)</gadget> <output>1</output> <gadget id="calculator">10 * 100</gadget> <output>1_000</output> <gadget id="calculator">1 * 1_000</gadget> <output>1_000</output> <gadget id="calculator">1_120 - 1_000</gadget> <output>120</output> <gadget id="calculator">120 / 100</gadget> <output>6/5 = around 1.2</output> <gadget id="calculator">floor(6/5)</gadget> <output>1</output> <gadget id="calculator">1 + 1</gadget> <output>2</output> <gadget id="calculator">floor(56/5)</gadget> <output>11</output> <gadget id="calculator">11 * 100</gadget> <output>1_100</output> <gadget id="calculator">1_120 - 1_100</gadget> <output>20</output> <gadget id="calculator">20 / 10</gadget> <output>2</output> <gadget id="calculator">floor(2)</gadget> <output>2</output> <gadget id="calculator">2 + 2</gadget> <output>4</output> <gadget id="calculator">floor(112)</gadget> <output>112</output> <gadget id="calculator">112 * 10</gadget> <output>1_120</output> <gadget id="calculator">1_120 - 1_120</gadget> <output>0</output> <gadget id="calculator">4 + 0</gadget> <output>4</output> <result>E</result>

E

If N is the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case.What is the sum of the digits of N ?

add(add(add(floor(divide(divide(divide(gcd(subtract(6905, 1305), gcd(subtract(4665, 1305), subtract(6905, 4665))), const_10), const_10), const_10)), floor(divide(subtract(gcd(subtract(4665, 1305), subtract(6905, 4665)), multiply(floor(divide(divide(divide(gcd(subtract(6905, 1305), gcd(subtract(4665, 1305), subtract(6905, 4665))), const_10), const_10), const_10)), multiply(const_10, const_100))), const_100))), floor(divide(subtract(gcd(subtract(4665, 1305), subtract(6905, 4665)), multiply(floor(divide(divide(gcd(subtract(6905, 1305), gcd(subtract(4665, 1305), subtract(6905, 4665))), const_10), const_10)), const_100)), const_10))), subtract(gcd(subtract(4665, 1305), subtract(6905, 4665)), multiply(floor(divide(gcd(subtract(6905, 1305), gcd(subtract(4665, 1305), subtract(6905, 4665))), const_10)), const_10)))

multiply(const_10,const_100)|subtract(n1,n0)|subtract(n2,n1)|subtract(n2,n0)|gcd(#1,#2)|gcd(#4,#3)|divide(#5,const_10)|divide(#6,const_10)|floor(#6)|divide(#7,const_10)|floor(#7)|multiply(#8,const_10)|floor(#9)|multiply(#10,const_100)|subtract(#4,#11)|multiply(#12,#0)|subtract(#4,#13)|divide(#16,const_10)|subtract(#4,#15)|divide(#18,const_100)|floor(#17)|floor(#19)|add(#12,#21)|add(#22,#20)|add(#23,#14)

n = h . c . f . of ( 4665 - 1305 ) , ( 6905 - 4665 ) and ( 6905 - 1305 ) = h . c . f . of 3360 , 2240 and 5600 = 1120 . sum of digits in n = ( 1 + 1 + 2 + 0 ) = 4 answer : e

general

math_qa__jfP23WXJ5bTuW7nZ

An area of a circularplace is 17 hectares. Find the cost of fencing it at the rate of Rs. 3 permeter approximately. Choose the most appropriate option: A) rs . 4000 B) rs . 4450 C) rs . 4457 D) rs . 4560 E) rs . 5457

<gadget id="calculator">17 / pi</gadget> <output>17/pi = around 5.411268</output> <gadget id="calculator">(17/pi) ** (1/2)</gadget> <output>sqrt(17)/sqrt(pi) = around 2.326213</output> <gadget id="calculator">(sqrt(17)/sqrt(pi)) * 100</gadget> <output>100*sqrt(17)/sqrt(pi) = around 232.621325</output> <gadget id="calculator">2 * pi * (100*sqrt(17)/sqrt(pi))</gadget> <output>200*sqrt(17)*sqrt(pi) = around 1_461.602889</output> <gadget id="calculator">(200*sqrt(17)*sqrt(pi)) * 3</gadget> <output>600*sqrt(17)*sqrt(pi) = around 4_384.808666</output> <result>C</result>

C

An area of a circularplace is 17 hectares. Find the cost of fencing it at the rate of Rs. 3 permeter approximately.

multiply(circumface(multiply(sqrt(divide(17, const_pi)), const_100)), 3)

divide(n0,const_pi)|sqrt(#0)|multiply(#1,const_100)|circumface(#2)|multiply(n1,#3)

area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 3 ) = rs . 4457 . c

geometry

math_qa__k2XFeESLfOC6iQ7V

Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.90 at the candy store. What is John’s weekly allowance? Choose the most appropriate option A) $ 2.40 B) $ 3.00 C) $ 3.40 D) $ 3.60 E) $ 4.80

<gadget id="calculator">3 / 5</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">1 / 3</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">1 - (3/5)</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">(1/3) * (2/5)</gadget> <output>2/15 = around 0.133333</output> <gadget id="calculator">(3/5) + (2/15)</gadget> <output>11/15 = around 0.733333</output> <gadget id="calculator">1 - (11/15)</gadget> <output>4/15 = around 0.266667</output> <gadget id="calculator">0.9 / (4/15)</gadget> <output>3.375</output> <result>C</result>

C

Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.90 at the candy store. What is John’s weekly allowance?

divide(0.90, subtract(const_1, add(divide(3, 5), multiply(divide(const_1, 3), subtract(const_1, divide(3, 5))))))

divide(n0,n1)|divide(const_1,n0)|subtract(const_1,#0)|multiply(#1,#2)|add(#0,#3)|subtract(const_1,#4)|divide(n2,#5)|

"total allowance = x amount spent at the arcade = 3 / 5 x amount remaining = 2 / 5 x amount spent at the toy store = 2 / 5 * 1 / 3 x = 2 / 15 x amount remaining = 2 / 5 x - 2 / 15 x = 4 / 15 x now , 4 / 15 x = $ 0.9 therefore , x = $ 3.40 . answer c"

general

math_qa__cx2oDJJscJxJ11eo

If a tire rotates at 400 revolutions per minute when the car is traveling 96km/h, what is the circumference of the tire? Choose the correct choice from the following options A) 7 meters B) 9 meters C) 4 meters D) 5 meters E) 3 meters

<gadget id="calculator">2 * 3</gadget> <output>6</output> <gadget id="calculator">6 * 10</gadget> <output>60</output> <gadget id="calculator">60 * 400</gadget> <output>24_000</output> <gadget id="calculator">96 / 24_000</gadget> <output>1/250 = around 0.004</output> <gadget id="calculator">(1/250) * 1_000</gadget> <output>4</output> <result>C</result>

C

If a tire rotates at 400 revolutions per minute when the car is traveling 96km/h, what is the circumference of the tire?

multiply(divide(96, multiply(multiply(multiply(const_2, const_3), const_10), 400)), const_1000)

multiply(const_2,const_3)|multiply(#0,const_10)|multiply(n0,#1)|divide(n1,#2)|multiply(#3,const_1000)|

"400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 96,000 m : c is the circumference c = 4 meters correct answer c"

physics

math_qa__Dj7jDZtkewg0kJd7

A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68% of the distribution lies one standard deviation f of the mean, what percent of the distribution is less than m+f? Choices: A) 16 % B) 32 % C) 48 % D) 84 % E) 92 %

<gadget id="calculator">100 - 68</gadget> <output>32</output> <gadget id="calculator">32 / 2</gadget> <output>16</output> <gadget id="calculator">100 - 16</gadget> <output>84</output> <result>D</result>

D

A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68% of the distribution lies one standard deviation f of the mean, what percent of the distribution is less than m+f?

subtract(const_100, divide(subtract(const_100, 68), const_2))

subtract(const_100,n0)|divide(#0,const_2)|subtract(const_100,#1)|

"16 % ________________________________________________ m + f 34 % ________________________________________________ m 34 % ________________________________________________ m - f 16 % since 68 % lies one standard deviation from mean m , = > 50 % of 68 % lies on either side as it is symmetric about m . thus 16 % lie below m - f and 16 % lie above m + f now below m + f = 16 + 34 + 34 = 84 % hence d"

general

math_qa__0pX7dl0buygP1Jvb

The result when a number subtracted from 100 is the same as the number added to 40. what is the number? Select A) 70 B) 65 C) 80 D) 140 E) 60

<gadget id="calculator">100 - 40</gadget> <output>60</output> <gadget id="calculator">60 / 2</gadget> <output>30</output> <gadget id="calculator">30 + 40</gadget> <output>70</output> <result>A</result>

A

The result when a number subtracted from 100 is the same as the number added to 40. what is the number?

add(divide(subtract(100, 40), const_2), 40)

subtract(n0,n1)|divide(#0,const_2)|add(n1,#1)|

"answer let the number be x . then , x - 40 = 100 - x â ‡ ’ 2 x = 100 + 40 = 140 â ‡ ’ 2 x = 140 â ˆ ´ x = 70 correct option : a"

general

math_qa__erql7fBgP0hRntPj

If a/b = 6/5, Then (5a + 4b) / (5a - 4b) = ? Pick. A) 4 B) 7 C) 5 D) 3 E) 6

<gadget id="calculator">5 * 6</gadget> <output>30</output> <gadget id="calculator">4 * 5</gadget> <output>20</output> <gadget id="calculator">30 + 20</gadget> <output>50</output> <gadget id="calculator">30 - 20</gadget> <output>10</output> <gadget id="calculator">50 / 10</gadget> <output>5</output> <result>C</result>

C

If a/b = 6/5, Then (5a + 4b) / (5a - 4b) = ?

divide(add(multiply(5, 6), multiply(4, 5)), subtract(multiply(5, 6), multiply(4, 5)))

multiply(n0,n1)|multiply(n1,n3)|add(#0,#1)|subtract(#0,#1)|divide(#2,#3)|

"answer dividing numerator as well as denominator by b , we get given exp . = ( 5 a + 4 b ) / ( 5 a - 4 b ) = ( 5 a / b + 4 ) / ( 5 a / b - 4 ) since a / b = 6 / 5 this implies that = [ ( 5 * 6 ) / 5 + 4 ] / [ ( 5 * 6 ) / 5 - 4 ) ] = ( 6 + 4 ) / ( 6 - 4 ) = 5 option : c"

general

math_qa__SX4wQf0Mdg6puibp

Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 1w widgets. Pick: A) 4 B) 6 C) 8 D) 10 E) 12

<gadget id="calculator">1 * 2</gadget> <output>2</output> <gadget id="calculator">2 * 3</gadget> <output>6</output> <result>B</result>

B

Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 1w widgets.

multiply(multiply(1, 2), 3)

multiply(n0,n4)|multiply(n3,#0)|

"i am getting 12 . e . hope havent done any calculation errors . . approach . . let y = no . of days taken by y to do w widgets . then x will take y + 2 days . 1 / ( y + 2 ) + 1 / y = 5 / 12 ( 5 / 12 is because ( 5 / 4 ) w widgets are done in 3 days . so , x widgets will be done in 12 / 5 days or 5 / 12 th of a widget in a day ) solving , we have y = 4 = > x takes 6 days to doing x widgets . answer : b"

general

math_qa__qo0jmXUYXGNObkqQ

If the number 761 * 829 is completely divisible by 9, then the smallest whole number in place of * will b Choose the correct choice. A) 4 B) 5 C) 3 D) 8 E) 9

<gadget id="calculator">4 + 3</gadget> <output>7</output> <gadget id="calculator">3 + 3</gadget> <output>6</output> <gadget id="calculator">7 + 6</gadget> <output>13</output> <gadget id="calculator">13 + 1</gadget> <output>14</output> <gadget id="calculator">4 + 4</gadget> <output>8</output> <gadget id="calculator">14 + 8</gadget> <output>22</output> <gadget id="calculator">22 + 2</gadget> <output>24</output> <gadget id="calculator">24 + 9</gadget> <output>33</output> <gadget id="calculator">33 + 3</gadget> <output>36</output> <gadget id="calculator">36 - 33</gadget> <output>3</output> <result>C</result>

C

If the number 761 * 829 is completely divisible by 9, then the smallest whole number in place of * will b

subtract(add(add(add(add(add(add(add(const_4, const_3), add(const_3, const_3)), const_1), add(const_4, const_4)), const_2), 9), const_3), add(add(add(add(add(add(const_4, const_3), add(const_3, const_3)), const_1), add(const_4, const_4)), const_2), 9))

add(const_3,const_4)|add(const_3,const_3)|add(const_4,const_4)|add(#0,#1)|add(#3,const_1)|add(#4,#2)|add(#5,const_2)|add(n2,#6)|add(#7,const_3)|subtract(#8,#7)

sum of digits = ( 7 + 6 + 1 + x + 8 + 2 + 9 ) = ( 33 + x ) , which must be divisible by 9 . x = 3 . c )

general

math_qa__DYTNkCpqxAVYgsMO

Teas worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs 157 per Kg , the price of the third variety per Kg will be? Choose the correct choice from the following answers A) rs . 147.50 B) rs . 785.50 C) rs . 179.50 D) rs . 258.50 E) none of these

<gadget id="calculator">1 + 1</gadget> <output>2</output> <gadget id="calculator">2 + 2</gadget> <output>4</output> <gadget id="calculator">157 * 4</gadget> <output>628</output> <gadget id="calculator">126 + 135</gadget> <output>261</output> <gadget id="calculator">628 - 261</gadget> <output>367</output> <gadget id="calculator">367 / 2</gadget> <output>367/2 = around 183.5</output> <result>C</result>

C

Teas worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs 157 per Kg , the price of the third variety per Kg will be?

divide(subtract(multiply(157, add(add(1, 1), 2)), add(126, 135)), 2)

add(n2,n2)|add(n0,n1)|add(n4,#0)|multiply(n5,#2)|subtract(#3,#1)|divide(#4,n4)

explanation : since first and second varieties are mixed in equal proportions . so , their average price = rs . ( 126 + 135 ) / 2 . = > rs . 130.50 . so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . by the rule of alligation , we have : cost of 1 kg cost of 1 kg of 1 st kind of 2 nd kind ( rs . 130.50 ) ( rs . x ) \ / mean price ( rs . 157 ) / \ x â ˆ ’ 157 22.50 = > x â ˆ ’ ( 157 / 22.50 ) = 1 . = > x â ˆ ’ 157 = 22.50 . = > x = 179.50 rs . answer : c

other

math_qa__AwnOAb9KAO5mwz5L

The sub-duplicate ratio of 9:25 is Choose the correct choice. A) 4 : 3 B) 1 : 2 C) 3 : 5 D) 1 : 4 E) 2 : 3

<gadget id="calculator">9 ** (1/2)</gadget> <output>3</output> <gadget id="calculator">25 ** (1/2)</gadget> <output>5</output> <gadget id="calculator">3 / 5</gadget> <output>3/5 = around 0.6</output> <result>C</result>

C

The sub-duplicate ratio of 9:25 is

divide(sqrt(9), sqrt(25))

sqrt(n0)|sqrt(n1)|divide(#0,#1)

root ( 9 ) : root ( 25 ) = 3 : 5 answer : c

other

math_qa__C99nTYdx6Hiu2Kb5

A train moves past a post and a platform 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train? Choose one A) 79.2 km / hr B) 69 km / hr C) 74 km / hr D) 61 km / hr E) none of these

<gadget id="calculator">264 / 8</gadget> <output>33</output> <gadget id="calculator">33 * 2</gadget> <output>66</output> <result>B</result>

B

A train moves past a post and a platform 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?

multiply(speed(264, 8), const_2)

speed(n0,n1)|multiply(#0,const_2)

let x is the length of the train and v is the speed time taken to move the post = 8 s = > x / v = 8 = > x = 8 v - - - ( 1 ) time taken to cross the platform 264 m long = 20 s ( x + 264 ) / v = 20 = > x + 264 = 20 v - - - ( 2 ) substituting equation 1 in equation 2 , we get 8 v + 264 = 20 v = > v = 264 / 12 = 22 m / s = 22 × 36 / 10 km / hr = 79.2 km / hr answer : b

physics

math_qa__sryrpwkg39kmT4yb

n a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m? Choose the correct answer A) 127.6 B) 127.5 C) 127.0 D) 127.2 E) 127.3

<gadget id="calculator">1_000 - 100</gadget> <output>900</output> <gadget id="calculator">900 * 600</gadget> <output>540_000</output> <gadget id="calculator">540_000 / 1_000</gadget> <output>540</output> <gadget id="calculator">800 - 100</gadget> <output>700</output> <gadget id="calculator">540 * 700</gadget> <output>378_000</output> <gadget id="calculator">378_000 / 800</gadget> <output>945/2 = around 472.5</output> <gadget id="calculator">600 - (945/2)</gadget> <output>255/2 = around 127.5</output> <result>B</result>

B

n a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?

subtract(600, divide(multiply(divide(multiply(subtract(1000, 100), 600), 1000), subtract(800, 100)), 800))

subtract(n0,n1)|subtract(n2,n1)|multiply(n4,#0)|divide(#2,n0)|multiply(#3,#1)|divide(#4,n2)|subtract(n4,#5)

when a runs 1000 m , b runs 900 m and when b runs 800 m , c runs 700 m . when b runs 900 m , distance that c runs = ( 900 * 700 ) / 800 = 6300 / 8 = 787.5 m . in a race of 1000 m , a beats c by ( 1000 - 787.5 ) = 212.5 m to c . in a race of 600 m , the number of meters by which a beats c = ( 600 * 212.5 ) / 1000 = 127.5 m . answer : ob

physics

math_qa__2fDsM9rvfRp2ylRX

nd the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 14 cm? Choose the correct choice from the following choices A) 235 cm 2 B) 260 cm 2 C) 266 cm 2 D) 270 cm 2 E) 280 cm 2

<gadget id="calculator">20 + 18</gadget> <output>38</output> <gadget id="calculator">14 * 38</gadget> <output>532</output> <gadget id="calculator">532 / 2</gadget> <output>266</output> <result>C</result>

C

nd the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 14 cm?

divide(multiply(14, add(20, 18)), const_2)

add(n0,n1)|multiply(n2,#0)|divide(#1,const_2)|

"area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 14 ) = 266 cm 2 answer : c"

physics

math_qa__b193AXchrH9VQIRX

A “palindromic integer” is an integer that remains the same when its digits are reversed. So, for example, 43334 and 516615 are both examples of palindromic integers. How many 6-digit palindromic integers are both even and greater than 600,000? Pick one: A) 150 B) 200 C) 240 D) 300 E) 480

<gadget id="calculator">6 - 4</gadget> <output>2</output> <gadget id="calculator">2 * 10</gadget> <output>20</output> <gadget id="calculator">20 * 10</gadget> <output>200</output> <result>B</result>

B

A “palindromic integer” is an integer that remains the same when its digits are reversed. So, for example, 43334 and 516615 are both examples of palindromic integers. How many 6-digit palindromic integers are both even and greater than 600,000?

multiply(multiply(subtract(6, const_4), const_10), const_10)

subtract(n2,const_4)|multiply(#0,const_10)|multiply(#1,const_10)|

"the first digit and last digit are the same so the 2 possibilities are 6 or 8 . the second and third digits can be any number from 0 to 9 . the total number of palindromic integers is 2 * 10 * 10 = 200 the answer is b ."

general

math_qa__SvYaYXCM6JnxGin2

If p and q are prime numbers, how many divisors does the product p^6 * q^7 have? Choose the most appropriate option: A) 40 B) 56 C) 60 D) 62 E) 70

<gadget id="calculator">6 + 1</gadget> <output>7</output> <gadget id="calculator">7 + 1</gadget> <output>8</output> <gadget id="calculator">7 * 8</gadget> <output>56</output> <result>B</result>

B

If p and q are prime numbers, how many divisors does the product p^6 * q^7 have?

multiply(add(6, const_1), add(7, const_1))

add(n0,const_1)|add(n1,const_1)|multiply(#0,#1)|

"when a number n = a ^ x * b ^ y , where a and b are prime numbers , and x , y are positive integers , the number of divisors of n = ( x + 1 ) ( y + 1 ) therefore , the answer is b . 7 * 8 = 56"

general

math_qa__IVnXLFKg8391INeP

If there is an equal probability of a child being born a boy or a girl, what is the probability that a couple who have 4 children have two children of the same sex and one of the opposite sex? Choose the correct answer. A) 1 / 3 B) 2 / 3 C) 1 / 4 D) 1 / 2 E) 3 / 5

<gadget id="calculator">2 / 4</gadget> <output>1/2 = around 0.5</output> <result>D</result>

D

If there is an equal probability of a child being born a boy or a girl, what is the probability that a couple who have 4 children have two children of the same sex and one of the opposite sex?

divide(const_2, 4)

divide(const_2,n0)

no of ways of selecting a gender - 2 c 1 no of ways of selecting any 2 children out of 4 = 4 c 2 total possible outcomes - 2 ^ 4 ( each child can be either a girl or a boy ) probability = 2 c 1 * 4 c 2 / 2 ^ 4 = 2 * 4 / 2 * 2 * 2 * 2 = 8 / 16 = 1 / 2 ans = d

general

math_qa__cXdEC9KggyjNdrBf

When a certain number X is divided by 72, the remainder is 19. What is the remainder when X is divided by 8? Select: A) 3 B) 2 C) 4 D) 1 E) 5

<gadget id="calculator">19 % 8</gadget> <output>3</output> <result>A</result>

A

When a certain number X is divided by 72, the remainder is 19. What is the remainder when X is divided by 8?

reminder(19, 8)

reminder(n1,n2)|

"let possible value of x is 91 least possible value of x / 8 is 91 / 8 = > 11 quotient with remainder 3 thus answer is ( a ) 3"

general

math_qa__Z4yE1Xi45HbJ6wvg

In a tournament prize of 1st, 2nd, and 3rd is given in same interval.If total amount of prize Rs 4800 and prize of 1st is Rs 2000, find the interval?? Choose the correct choice from the following choices A) 600 B) 450 C) 350 D) 550 E) 400

<gadget id="calculator">2_000 * 3</gadget> <output>6_000</output> <gadget id="calculator">6_000 - 4_800</gadget> <output>1_200</output> <gadget id="calculator">1_200 / 3</gadget> <output>400</output> <result>E</result>

E

In a tournament prize of 1st, 2nd, and 3rd is given in same interval.If total amount of prize Rs 4800 and prize of 1st is Rs 2000, find the interval??

divide(subtract(multiply(2000, 3), 4800), const_3)

multiply(n2,n5)|subtract(#0,n3)|divide(#1,const_3)

let the interval is x . prize of 2 nd and 3 rd is 2000 - x and 2000 - 2 x 2000 + 2000 - x + 2000 - 2 x = 4800 x = 400 answer : e

general

math_qa__ICgDXygg5txdZow0

$600 will become $720 in 4 years find the rate of interest? Choose the correct choice from the following answers: A) 10 % B) 15 % C) 5 % D) 7 % E) 20 %

<gadget id="calculator">720 - 600</gadget> <output>120</output> <gadget id="calculator">4 / 100</gadget> <output>1/25 = around 0.04</output> <gadget id="calculator">600 * (1/25)</gadget> <output>24</output> <gadget id="calculator">120 / 24</gadget> <output>5</output> <result>C</result>

C

$600 will become $720 in 4 years find the rate of interest?

divide(subtract(720, 600), multiply(600, divide(4, const_100)))

divide(n2,const_100)|subtract(n1,n0)|multiply(n0,#0)|divide(#1,#2)|

"si = simple interest = a - p = 720 - 600 = $ 120 r = 100 si / pt = 100 * 120 / 600 * 4 = 5 % answer is c"

gain

math_qa__GVvfugxdKG8WFWo2

The area of a circle is increased by 300%. By what percent has the diameter of the circle increased? Answers. A) 400 % B) 200 % C) 300 % D) 100 % E) 800 %

<gadget id="calculator">2 / 2</gadget> <output>1</output> <gadget id="calculator">100 * 1</gadget> <output>100</output> <result>D</result>

D

The area of a circle is increased by 300%. By what percent has the diameter of the circle increased?

multiply(const_100, divide(const_2, const_2))

divide(const_2,const_2)|multiply(#0,const_100)

the area of the circle is increased by 300 % , thus the area is increased 4 times . the area of a circle it proportional to the square of the diameter ( area = π d ^ 2 / 4 ) , therefore the diameter must increase 2 times ( diameter increase 2 times = area increase 4 times ) , which is increase by 100 % . answer : d .

geometry

math_qa__PvMieHAXl2sSgngc

18 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men? Pick one. A) 32 B) 87 C) 36 D) 99 E) 77

<gadget id="calculator">21 * 8</gadget> <output>168</output> <gadget id="calculator">18 * 3</gadget> <output>54</output> <gadget id="calculator">168 * 54</gadget> <output>9_072</output> <gadget id="calculator">21 * 2</gadget> <output>42</output> <gadget id="calculator">42 * 6</gadget> <output>252</output> <gadget id="calculator">9_072 / 252</gadget> <output>36</output> <gadget id="calculator">floor(36)</gadget> <output>36</output> <gadget id="calculator">36 + 1</gadget> <output>37</output> <result>C</result>

C

18 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men?

add(floor(divide(multiply(multiply(21, 8), multiply(18, 3)), multiply(multiply(21, 2), 6))), const_1)

multiply(n1,n2)|multiply(n0,n5)|multiply(n4,n6)|multiply(#0,#1)|multiply(n3,#2)|divide(#3,#4)|floor(#5)|add(#6,const_1)|

"3 w = 2 m 18 m - - - - - - 21 * 8 hours 21 w - - - - - - x * 6 hours 14 m - - - - - - x * 6 18 * 21 * 8 = 14 * x * 6 x = 36 answer : c"

physics

math_qa__XlpV02oTCzcU2w7O

a school has 9 English 7 history and 6 geography teachers each teacher can teach 2 subjects max what is he minimum number of teachers required Choose the correct choice: A) 7 B) 8 C) 9 D) 10 E) 11

<gadget id="calculator">9 + 7</gadget> <output>16</output> <gadget id="calculator">16 + 6</gadget> <output>22</output> <gadget id="calculator">22 / 2</gadget> <output>11</output> <result>E</result>

E

a school has 9 English 7 history and 6 geography teachers each teacher can teach 2 subjects max what is he minimum number of teachers required

divide(add(add(9, 7), 6), 2)

add(n0,n1)|add(n2,#0)|divide(#1,n3)

total subjects = 9 + 7 + 6 = 22 max subjects by 1 teacher = 2 so , min of teachers required = 22 / 2 = 11 answer : e

general

math_qa__tH1rext0E2V3Dmzw

If in a certain code "RANGE" is coded as 12345 and "RANDOM" is coded as 123678. Then the code for the word "RAND" would be Choose the correct answer: A) 1236 B) 1365 C) 1200 D) 1526 E) 1325

<gadget id="calculator">123_678 % 100</gadget> <output>78</output> <gadget id="calculator">123_678 - 78</gadget> <output>123_600</output> <gadget id="calculator">123_600 / 100</gadget> <output>1_236</output> <result>A</result>

A

If in a certain code "RANGE" is coded as 12345 and "RANDOM" is coded as 123678. Then the code for the word "RAND" would be

divide(subtract(123678, reminder(123678, const_100)), const_100)

reminder(n1,const_100)|subtract(n1,#0)|divide(#1,const_100)

r - 1 a - 2 n - 3 d - 6 so for mango the code is 1236 answer : a

general

math_qa__bQZQDHGMEQYSq6bO

A goods train runs at the speed of 72 kmph and crosses a 230 m long platform in 26 seconds. What is the length of the goods train? Choices A) 230 m B) 270 m C) 643 m D) 832 m E) 290 m

<gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">(5/18) * 72</gadget> <output>20</output> <gadget id="calculator">230 / 20</gadget> <output>23/2 = around 11.5</output> <gadget id="calculator">26 - (23/2)</gadget> <output>29/2 = around 14.5</output> <gadget id="calculator">(29/2) * 20</gadget> <output>290</output> <result>E</result>

E

A goods train runs at the speed of 72 kmph and crosses a 230 m long platform in 26 seconds. What is the length of the goods train?

multiply(subtract(26, divide(230, multiply(const_0_2778, 72))), multiply(const_0_2778, 72))

multiply(n0,const_0_2778)|divide(n1,#0)|subtract(n2,#1)|multiply(#0,#2)|

"speed = ( 72 x 5 / 18 ) m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , x + 230 / 26 = 20 x + 230 = 520 x = 290 . answer : e"

physics

math_qa__Rcp4fw1TaSjefoTL

The distance from the x-axis to point P is half the distance from the y-axis to point P. If the coordinates of P are (x,-9), how many units is P from the y-axis? Choose one. A) 18 B) 12 C) 9 D) 4.5 E) 3

<gadget id="calculator">9 * 2</gadget> <output>18</output> <result>A</result>

A

The distance from the x-axis to point P is half the distance from the y-axis to point P. If the coordinates of P are (x,-9), how many units is P from the y-axis?

multiply(9, const_2)

multiply(n0,const_2)|

"the x - axis is 9 units from the point p . thus the y - axis is 18 units from the point p . the answer is a ."

general

math_qa__s80LJbRH9CD1KOS5

If A's height is 45% less than that of B, how much percent B's height is more than that of A? Answers. A) 66.66 % B) 81.81 % C) 66.766 % D) 86.66 % E) 66.65 %

<gadget id="calculator">100 - 45</gadget> <output>55</output> <gadget id="calculator">45 / 55</gadget> <output>9/11 = around 0.818182</output> <gadget id="calculator">(9/11) * 100</gadget> <output>900/11 = around 81.818182</output> <result>B</result>

B

If A's height is 45% less than that of B, how much percent B's height is more than that of A?

multiply(divide(45, subtract(const_100, 45)), const_100)

subtract(const_100,n0)|divide(n0,#0)|multiply(#1,const_100)|

"excess of b ' s height over a ' s = [ ( 45 / ( 100 - 45 ) ] x 100 % = 81.81 % answer : b )"

general

math_qa__ZvWHALzvoLGZtk0L

Arnold and Danny are two twin brothers that are celebrating their birthday. The product of their ages today is smaller by 9 from the product of their ages a year from today. What is their age today? Choose the correct choice from the following: A) 2 . B) 4 . C) 5 . D) 7 E) 9 .

<gadget id="calculator">9 - 1</gadget> <output>8</output> <gadget id="calculator">8 / 2</gadget> <output>4</output> <result>B</result>

B

Arnold and Danny are two twin brothers that are celebrating their birthday. The product of their ages today is smaller by 9 from the product of their ages a year from today. What is their age today?

divide(subtract(9, const_1), const_2)

subtract(n0,const_1)|divide(#0,const_2)|

"ad = ( a + 1 ) ( d + 1 ) - 9 0 = a + d - 8 a + d = 8 a = d ( as they are twin brothers ) a = d = 4 b is the answer"

general

math_qa__Ju2UruLw9BPc7IpW

There were two candidates in an election. Winner candidate received 60% of votes and won the election by 240 votes. Find the number of votes casted to the winning candidate? Pick. A) 228 B) 720 C) 255 D) 199 E) 231

<gadget id="calculator">100 - 60</gadget> <output>40</output> <gadget id="calculator">60 - 40</gadget> <output>20</output> <gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">240 / (1/5)</gadget> <output>1_200</output> <gadget id="calculator">1_200 * 60</gadget> <output>72_000</output> <gadget id="calculator">72_000 / 100</gadget> <output>720</output> <result>B</result>

B

There were two candidates in an election. Winner candidate received 60% of votes and won the election by 240 votes. Find the number of votes casted to the winning candidate?

divide(multiply(divide(240, divide(subtract(60, subtract(const_100, 60)), const_100)), 60), const_100)

subtract(const_100,n0)|subtract(n0,#0)|divide(#1,const_100)|divide(n1,#2)|multiply(n0,#3)|divide(#4,const_100)|

"w = 60 % l = 40 % 60 % - 40 % = 20 % 20 % - - - - - - - - 240 60 % - - - - - - - - ? = > 720 answer : b"

gain

math_qa__4mAZcjoADenoFbfs

What least number should be subtracted from 997 so that the remainder when divided by 5, 9, and 11 will leave in each case the same remainder 3 ? Choices. A) 1 B) 2 C) 3 D) 4 E) 5

<gadget id="calculator">5 * 9</gadget> <output>45</output> <gadget id="calculator">45 * 11</gadget> <output>495</output> <gadget id="calculator">495 * 2</gadget> <output>990</output> <gadget id="calculator">990 + 3</gadget> <output>993</output> <gadget id="calculator">997 - 993</gadget> <output>4</output> <result>D</result>

D

What least number should be subtracted from 997 so that the remainder when divided by 5, 9, and 11 will leave in each case the same remainder 3 ?

subtract(997, add(multiply(multiply(multiply(5, 9), 11), const_2), 3))

multiply(n1,n2)|multiply(n3,#0)|multiply(#1,const_2)|add(n4,#2)|subtract(n0,#3)

the lcm of 5,9 and 11 is 495 . the next multiple is 2 * 495 = 990 . 990 + { remainder } = 990 + 3 = 993 , which is 4 less than 997 . answer : d .

general

math_qa__xiPofn95s6AH7cDB

A garden center sells a certain grass seed in 5-pound bags at $13.82 per bag, 10-pound bags at $20.43 per bag, and 25-pound bags $32.25 per bag. If a customer is to buy at least 65 pounds of the grass seed, but no more than 80 pounds, what is the least possible cost of the grass seed that the customer will buy? Choose the correct choice from the following: A) $ 94.03 B) $ 96.75 C) $ 98.75 D) $ 102.07 E) $ 105.3

<gadget id="calculator">2 * 32.25</gadget> <output>64.5</output> <gadget id="calculator">1 * 20.43</gadget> <output>20.43</output> <gadget id="calculator">64.5 + 20.43</gadget> <output>84.93</output> <gadget id="calculator">1 * 13.82</gadget> <output>13.82</output> <gadget id="calculator">84.93 + 13.82</gadget> <output>98.75</output> <result>C</result>

C

A garden center sells a certain grass seed in 5-pound bags at $13.82 per bag, 10-pound bags at $20.43 per bag, and 25-pound bags $32.25 per bag. If a customer is to buy at least 65 pounds of the grass seed, but no more than 80 pounds, what is the least possible cost of the grass seed that the customer will buy?

add(add(multiply(const_2, 32.25), multiply(const_1, 20.43)), multiply(const_1, 13.82))

multiply(n5,const_2)|multiply(n3,const_1)|multiply(n1,const_1)|add(#0,#1)|add(#3,#2)|

"there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.75 or 2 ) 25 + 25 + 25 = $ 96.75 c"

general

math_qa__JPOCR5qMC6JUgCdB

In a group of cows and chickens, the number of legs was 14 more than twice the number of heads. The number of cows was: Pick. A) 3 B) 5 C) 9 D) 7 E) 8

<gadget id="calculator">4 - 2</gadget> <output>2</output> <gadget id="calculator">14 / 2</gadget> <output>7</output> <result>D</result>

D

In a group of cows and chickens, the number of legs was 14 more than twice the number of heads. The number of cows was:

divide(14, subtract(const_4, const_2))

subtract(const_4,const_2)|divide(n0,#0)

d 7 let the number of cows be x and their legs be 4 x . let the number of chicken be y and their legs be 2 x . total number of legs = 4 x + 2 y . total number of heads = x + y . the number of legs was 14 more than twice the number of heads . therefore , 2 × ( x + y ) + 14 = 4 x + 2 y . or , 2 x + 2 y + 14 = 4 x + 2 y . or , 2 x + 14 = 4 x [ subtracting 2 y from both sides ] . or , 14 = 4 x – 2 x [ subtracting 2 x from both sides ] . or , 14 = 2 x . or , x = 7 [ dividing by 2 on both sides ] . therefore , the number of cows = 7 .

general

math_qa__9f9EmadMbFV291k5

What least number should be subtracted from 13604 such that the remainder is divisible by 87 ? Choose the correct option. A) 32 B) 29 C) 28 D) 30 E) 31

<gadget id="calculator">13_604 % 87</gadget> <output>32</output> <result>A</result>

A

What least number should be subtracted from 13604 such that the remainder is divisible by 87 ?

reminder(13604, 87)

reminder(n0,n1)|

"13604 ÷ 87 = 156 , remainder = 32 hence 32 is the least number which can be subtracted from 13604 such that the remainder is divisible by 87 answer is a"

general

math_qa__qFCch9jrRDZSCS8z

2: 5 = 4/3: x. The value of x is? Answers: A) 10 / 3 B) 2 C) 3 D) 4 E) 5

<gadget id="calculator">4 / 3</gadget> <output>4/3 = around 1.333333</output> <gadget id="calculator">2 / 5</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">(4/3) / (2/5)</gadget> <output>10/3 = around 3.333333</output> <result>A</result>

A

2: 5 = 4/3: x. The value of x is?

divide(divide(4, 3), divide(2, 5))

divide(n2,n3)|divide(n0,n1)|divide(#0,#1)

x * 2 = 5 * 4 / 3 x * 2 = 20 / 3 x = 10 / 3 answer : a

general

math_qa__sqYXHfeJsbnjJmKF

How many even integers n, such that 20<=n<=200 are of the form 3k+4, where k is any natural number? Select A) 26 B) 30 C) 34 D) 38 E) 42

<gadget id="calculator">200 - 2</gadget> <output>198</output> <gadget id="calculator">20 + 2</gadget> <output>22</output> <gadget id="calculator">198 - 22</gadget> <output>176</output> <gadget id="calculator">2 + 4</gadget> <output>6</output> <gadget id="calculator">176 / 6</gadget> <output>88/3 = around 29.333333</output> <gadget id="calculator">(88/3) + 1</gadget> <output>91/3 = around 30.333333</output> <result>B</result>

B

How many even integers n, such that 20<=n<=200 are of the form 3k+4, where k is any natural number?

add(divide(subtract(subtract(200, const_2), add(20, const_2)), add(const_2, 4)), const_1)

add(n0,const_2)|add(const_2,n3)|subtract(n1,const_2)|subtract(#2,#0)|divide(#3,#1)|add(#4,const_1)|

"the first number is 22 = 16 + 6 ( 1 ) . we can continue adding 6 to make a list : 22 , 28 , 34 , . . . the last number is 196 = 16 + 6 ( 30 ) there are 30 numbers in the list . the answer is b ."

general

math_qa__vnhXn20M2wRj4Xi2

How many seconds will a 750 meter long train moving with a speed of 63 km/hr take to cross a man walking with a speed of 3 km/hr in the direction of the train ? Choose the correct choice. A) 48 B) 36 C) 26 D) 11 E) 45

<gadget id="calculator">63 - 3</gadget> <output>60</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">60 * (5/18)</gadget> <output>50/3 = around 16.666667</output> <gadget id="calculator">750 / (50/3)</gadget> <output>45</output> <result>E</result>

E

How many seconds will a 750 meter long train moving with a speed of 63 km/hr take to cross a man walking with a speed of 3 km/hr in the direction of the train ?

divide(750, multiply(subtract(63, 3), const_0_2778))

subtract(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)|

"explanation : here distance d = 750 mts speed s = 63 - 3 = 60 kmph = 60 x 5 / 18 m / s time t = = 45 sec . answer : e"

physics

math_qa__RPAqCAv5ootXXwWg

A certain country had a total annual expenditure of $7.2 x 10^11 last year. If the population of the country was 240 million last year, what was the per capita expenditure? Choose one: A) $ 500 B) $ 1,000 C) $ 2,000 D) $ 3,000 E) $ 5,000

<gadget id="calculator">10 ** 11</gadget> <output>100_000_000_000</output> <gadget id="calculator">7.2 * 100_000_000_000</gadget> <output>720_000_000_000</output> <gadget id="calculator">4 + 2</gadget> <output>6</output> <gadget id="calculator">10 ** 6</gadget> <output>1_000_000</output> <gadget id="calculator">240 * 1_000_000</gadget> <output>240_000_000</output> <gadget id="calculator">720_000_000_000 / 240_000_000</gadget> <output>3_000</output> <result>D</result>

D

A certain country had a total annual expenditure of $7.2 x 10^11 last year. If the population of the country was 240 million last year, what was the per capita expenditure?

divide(multiply(7.2, power(10, 11)), multiply(240, power(10, add(const_4, const_2))))

add(const_2,const_4)|power(n1,n2)|multiply(n0,#1)|power(n1,#0)|multiply(n3,#3)|divide(#2,#4)|

"total expenditure / population = per capita expenditure hence , ( 7,2 x 10 ^ 11 ) / 240 000 000 = ( 7,2 x 10 ^ 11 ) / ( 2,4 x 10 ^ 8 ) = 3 x 10 ^ ( 11 - 8 ) = 3 x 10 ^ 3 = 3000 . answer is d ."

general

math_qa__GPEhoy31go4shFNH

The average of 17 numbers is 59. Average of the first 9 of them is 56 and that of the last 9 is 63. Find the 9th number? Choose the correct option A) 64 B) 68 C) 65 D) 66 E) 67

<gadget id="calculator">9 * 63</gadget> <output>567</output> <gadget id="calculator">17 * 59</gadget> <output>1_003</output> <gadget id="calculator">56 * 9</gadget> <output>504</output> <gadget id="calculator">1_003 - 504</gadget> <output>499</output> <gadget id="calculator">567 - 499</gadget> <output>68</output> <result>B</result>

B

The average of 17 numbers is 59. Average of the first 9 of them is 56 and that of the last 9 is 63. Find the 9th number?

subtract(multiply(9, 63), subtract(multiply(17, 59), multiply(56, 9)))

multiply(n5,n6)|multiply(n0,n1)|multiply(n2,n3)|subtract(#1,#2)|subtract(#0,#3)|

sum of all the 17 numbers = 17 * 59 = 1,003 sum of the first 9 of them = 9 * 56 = 504 sum of the last 9 of them = 9 * 63 = 567 so , the 8 th number = 504 + 567 - 1,003 = 68 . answer : b

general

math_qa__jwN3wzFOCceLQVDP

A boat can travel with a speed of 24 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 56 km downstream Choose one. A) 2 hours B) 4 hours C) 5 hours D) 6 hours E) 7 hours

<gadget id="calculator">24 + 4</gadget> <output>28</output> <gadget id="calculator">56 / 28</gadget> <output>2</output> <result>A</result>

A

A boat can travel with a speed of 24 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 56 km downstream

divide(56, add(24, 4))

add(n0,n1)|divide(n2,#0)|

"explanation : speed of the boat in still water = 24 km / hr speed of the stream = 4 km / hr speed downstream = ( 22 + 5 ) = 28 km / hr distance travelled downstream = 56 km time taken = distance / speed = 56 / 28 = 2 hours answer : option a"

physics

math_qa__dJrv7rllhD8CvwRZ

Carl is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken. The bank charges him a quarterly compound rate of 7%. What is the approximate interest he pays annually? Pick one A) 1000 B) 1500 C) 3000 D) 2500 E) 2400

<gadget id="calculator">100 * 100</gadget> <output>10_000</output> <gadget id="calculator">7 / 100</gadget> <output>7/100 = around 0.07</output> <gadget id="calculator">1 + (7/100)</gadget> <output>107/100 = around 1.07</output> <gadget id="calculator">(107/100) ** 4</gadget> <output>131_079_601/100_000_000 = around 1.310796</output> <gadget id="calculator">10_000 * (131_079_601/100_000_000)</gadget> <output>131_079_601/10_000 = around 13_107.9601</output> <gadget id="calculator">(131_079_601/10_000) - 10_000</gadget> <output>31_079_601/10_000 = around 3_107.9601</output> <result>C</result>

C

Carl is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken. The bank charges him a quarterly compound rate of 7%. What is the approximate interest he pays annually?

subtract(multiply(multiply(const_100, const_100), power(add(const_1, divide(7, const_100)), const_4)), multiply(const_100, const_100))

divide(n1,const_100)|multiply(const_100,const_100)|add(#0,const_1)|power(#2,const_4)|multiply(#1,#3)|subtract(#4,#1)|

"an easy way too attempt this is by approximation : for the first quarter , he pays 7 % of 10,000 which is $ 700 . so for the four quarters in the year , he will approximately play 700 * 4 = 2800 over the entire year . because of compound interest it will be more than 2800 . approx . option c is correct . answer : c"

gain

math_qa__aoufABcuYVGfPV4e

A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C? Choose one: A) rs . 450 B) rs . 600 C) rs . 800 D) rs . 375 E) rs . 400

<gadget id="calculator">1 / 3</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">1 / 8</gadget> <output>1/8 = around 0.125</output> <gadget id="calculator">1 / 6</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">(1/8) + (1/6)</gadget> <output>7/24 = around 0.291667</output> <gadget id="calculator">(1/3) - (7/24)</gadget> <output>1/24 = around 0.041667</output> <gadget id="calculator">(1/24) * 3_200</gadget> <output>400/3 = around 133.333333</output> <gadget id="calculator">(400/3) * 3</gadget> <output>400</output> <result>E</result>

E

A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

multiply(multiply(subtract(inverse(3), add(inverse(8), inverse(6))), 3200), 3)

inverse(n3)|inverse(n1)|inverse(n0)|add(#1,#2)|subtract(#0,#3)|multiply(n2,#4)|multiply(n3,#5)|

"c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 24 . a ' s wages : b ' s wages : c ' s wages = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . c ' s share ( for 3 days ) = rs . ( 3 x 1 / 24 x 3200 ) = rs . 400 . correct option ` ` e ' ' ."

physics

math_qa__uP52YQ2QhH67Eyey

Mariah has decided to hire three workers. To determine whom she will hire, she has selected a group of 20 candidates. She plans to have one working interview with 3 of the 20 candidates every day to see how well they work together. How many days will it take her to have working interviews with all the different combinations of job candidates? Choose the correct choice from the following answers: A) 520 B) 120 C) 300 D) 30 E) 333

<gadget id="calculator">factorial(20)</gadget> <output>2_432_902_008_176_640_000</output> <gadget id="calculator">20 - 3</gadget> <output>17</output> <gadget id="calculator">factorial(17)</gadget> <output>355_687_428_096_000</output> <gadget id="calculator">2_432_902_008_176_640_000 / 355_687_428_096_000</gadget> <output>6_840</output> <gadget id="calculator">factorial(3)</gadget> <output>6</output> <gadget id="calculator">6_840 / 6</gadget> <output>1_140</output> <gadget id="calculator">1_140 / 2</gadget> <output>570</output> <gadget id="calculator">570 - 20</gadget> <output>550</output> <gadget id="calculator">550 - 20</gadget> <output>530</output> <gadget id="calculator">530 - 10</gadget> <output>520</output> <result>A</result>

A

Mariah has decided to hire three workers. To determine whom she will hire, she has selected a group of 20 candidates. She plans to have one working interview with 3 of the 20 candidates every day to see how well they work together. How many days will it take her to have working interviews with all the different combinations of job candidates?

subtract(subtract(subtract(divide(divide(divide(factorial(20), factorial(subtract(20, 3))), factorial(3)), const_2), 20), 20), const_10)

factorial(n0)|factorial(n1)|subtract(n0,n1)|factorial(#2)|divide(#0,#3)|divide(#4,#1)|divide(#5,const_2)|subtract(#6,n0)|subtract(#7,n0)|subtract(#8,const_10)

520 . answer a

physics

math_qa__XEZMxV1fOaDfmevZ

The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square? Pick one. A) 802 B) 800 C) 829 D) 389 E) 245

<gadget id="calculator">125 * 64</gadget> <output>8_000</output> <gadget id="calculator">10 / 2</gadget> <output>5</output> <gadget id="calculator">8_000 * 5</gadget> <output>40_000</output> <gadget id="calculator">40_000 ** (1/2)</gadget> <output>200</output> <gadget id="calculator">200 * 4</gadget> <output>800</output> <result>B</result>

B

The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?

multiply(sqrt(multiply(rectangle_area(125, 64), divide(const_10, const_2))), const_4)

divide(const_10,const_2)|rectangle_area(n0,n1)|multiply(#0,#1)|sqrt(#2)|multiply(#3,const_4)|

"area of the square = s * s = 5 ( 125 * 64 ) = > s = 25 * 8 = 200 cm perimeter of the square = 4 * 200 = 800 cm . answer : b"

geometry

math_qa__FRIBifrcxxHM6cLe

When positive integer x is divided by 10, the quotient is y and the remainder is 3. When 2x is divided by 7, the quotient is 3y and the remainder is 1. What is the value of 11y – x? Select. A) 2 B) - 2 C) 3 D) - 3 E) 4

<gadget id="calculator">2 * 3</gadget> <output>6</output> <gadget id="calculator">6 - 1</gadget> <output>5</output> <gadget id="calculator">7 * 3</gadget> <output>21</output> <gadget id="calculator">2 * 10</gadget> <output>20</output> <gadget id="calculator">21 - 20</gadget> <output>1</output> <gadget id="calculator">5 / 1</gadget> <output>5</output> <gadget id="calculator">11 * 5</gadget> <output>55</output> <gadget id="calculator">10 * 5</gadget> <output>50</output> <gadget id="calculator">50 + 3</gadget> <output>53</output> <gadget id="calculator">55 - 53</gadget> <output>2</output> <result>A</result>

A

When positive integer x is divided by 10, the quotient is y and the remainder is 3. When 2x is divided by 7, the quotient is 3y and the remainder is 1. What is the value of 11y – x?

subtract(multiply(11, divide(subtract(multiply(2, 3), 1), subtract(multiply(7, 3), multiply(2, 10)))), add(multiply(10, divide(subtract(multiply(2, 3), 1), subtract(multiply(7, 3), multiply(2, 10)))), 3))

multiply(n1,n2)|multiply(n3,n4)|multiply(n0,n2)|subtract(#0,n5)|subtract(#1,#2)|divide(#3,#4)|multiply(n6,#5)|multiply(n0,#5)|add(n1,#7)|subtract(#6,#8)|

"( 1 ) x = 10 y + 3 ( 2 ) 2 x = 21 y + 1 ( 2 ) - ( 1 ) : x = 11 y - 2 11 y - x = 2 the answer is a ."

general

math_qa__zdpHzGgKUGU1AYR7

At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes, and one cola for $120. At the same place it would cost $160.50 for 4 burgers, 10 shakes, and one cola. How much would it cost for a meal of one burger, one shake, and one cola? Choose the correct choice from the following answers A) $ 21 B) $ 27 C) $ 31 D) $ 39 E) it can not be determined

<gadget id="calculator">160.5 - 120</gadget> <output>40.5</output> <gadget id="calculator">120 + 40.5</gadget> <output>160.5</output> <gadget id="calculator">40.5 * 3</gadget> <output>121.5</output> <gadget id="calculator">160.5 - 121.5</gadget> <output>39</output> <result>D</result>

D

At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes, and one cola for $120. At the same place it would cost $160.50 for 4 burgers, 10 shakes, and one cola. How much would it cost for a meal of one burger, one shake, and one cola?

subtract(add(120, subtract(160.50, 120)), multiply(subtract(160.50, 120), 3))

subtract(n3,n2)|add(n2,#0)|multiply(#0,n0)|subtract(#1,#2)|

"let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 120 4 b + 10 s + c = 160.5 subtracting the first equation from the second gives us b + 3 s = 40.5 now if we subtract the new equation two times from first or 3 times from second we will get b + s + c = 39 . in any case , there is no necessity to know each item ' s price , just the sum . answer : d"

general

math_qa__pFCwiS2fcTErwFjv

Find the fraction which has the same ratio to 1/13 that 5/34 has to 7/48. Choose the correct choice from the following choices A) 110 / 1547 B) 120 / 1547 C) 140 / 1547 D) 160 / 1547 E) 220 / 1547

<gadget id="calculator">5 / 34</gadget> <output>5/34 = around 0.147059</output> <gadget id="calculator">7 / 48</gadget> <output>7/48 = around 0.145833</output> <gadget id="calculator">(5/34) / (7/48)</gadget> <output>120/119 = around 1.008403</output> <gadget id="calculator">1 / 13</gadget> <output>1/13 = around 0.076923</output> <gadget id="calculator">(120/119) * (1/13)</gadget> <output>120/1_547 = around 0.077569</output> <result>B</result>

B

Find the fraction which has the same ratio to 1/13 that 5/34 has to 7/48.

multiply(divide(divide(5, 34), divide(7, 48)), divide(1, 13))

divide(n2,n3)|divide(n4,n5)|divide(n0,n1)|divide(#0,#1)|multiply(#3,#2)

p : 1 / 13 = 5 / 34 : 7 / 48 as the product of the means is equal to the product of the extremes . p * 7 / 48 = 1 / 13 * 5 / 34 p * 7 / 48 = 5 / 442 p = 240 / 3094 = > p = 120 / 1547 answer : b

other

math_qa__8vvGArwvNZwqpScw

Two numbers are such that the square of one is 224 less than 8 times the square of the other. If the numbers be in the ratio of 3 : 4, the numbers are Choose the correct option: A) 6 , 8 B) 9 , 12 C) 12 , 16 D) 16 , 20 E) none

<gadget id="calculator">3 ** 2</gadget> <output>9</output> <gadget id="calculator">9 * 224</gadget> <output>2_016</output> <gadget id="calculator">8 * 9</gadget> <output>72</output> <gadget id="calculator">4 ** 2</gadget> <output>16</output> <gadget id="calculator">72 - 16</gadget> <output>56</output> <gadget id="calculator">gcd(2_016, 56)</gadget> <output>56</output> <gadget id="calculator">2_016 / 56</gadget> <output>36</output> <gadget id="calculator">36 ** (1/2)</gadget> <output>6</output> <result>A</result>

A

Two numbers are such that the square of one is 224 less than 8 times the square of the other. If the numbers be in the ratio of 3 : 4, the numbers are

sqrt(divide(multiply(power(3, const_2), 224), gcd(multiply(power(3, const_2), 224), subtract(multiply(8, power(3, const_2)), power(4, const_2)))))

power(n2,const_2)|power(n3,const_2)|multiply(n0,#0)|multiply(n1,#0)|subtract(#3,#1)|gcd(#2,#4)|divide(#2,#5)|sqrt(#6)

solution let the numbers be 3 x and 4 x . then , ( 4 x ) 2 = 8 x ( 3 x ) 2 - 224 ‹ = › 16 x 2 = 72 x 2 - 224 ‹ = › 56 x 2 = 224 . ‹ = › x 2 = 4 . ‹ = › x = 2 . so , the numbers are 6 and 8 . answer a

general

math_qa__1cAua838N77dhzAy

A and B invests Rs.3500 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit? Pick. A) 21 : 5 B) 21 : 16 C) 21 : 2 D) 9 : 9 E) 21 : 11

<gadget id="calculator">3_500 * 6</gadget> <output>21_000</output> <gadget id="calculator">3_500 * 2</gadget> <output>7_000</output> <gadget id="calculator">7_000 * 6</gadget> <output>42_000</output> <gadget id="calculator">21_000 + 42_000</gadget> <output>63_000</output> <gadget id="calculator">6 + 6</gadget> <output>12</output> <gadget id="calculator">4_000 * 12</gadget> <output>48_000</output> <gadget id="calculator">63_000 / 48_000</gadget> <output>21/16 = around 1.3125</output> <result>B</result>

B

A and B invests Rs.3500 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?

divide(add(multiply(3500, 6), multiply(multiply(3500, const_2), 6)), multiply(4000, add(6, 6)))

add(n2,n2)|multiply(n0,n2)|multiply(n0,const_2)|multiply(n2,#2)|multiply(n1,#0)|add(#1,#3)|divide(#5,#4)|

"( 3.5 * 6 + 7 * 6 ) : ( 4 * 12 ) 63 : 48 = > 21 : 16 answer : b"

gain

math_qa__j9WSJHChNPqJ8m4K

A searchlight on top of the watchtower makes 2 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 10 seconds? Choices: A) 5 / 6 B) 3 / 4 C) 2 / 3 D) 1 / 2 E) 3 / 5

<gadget id="calculator">10 * 3</gadget> <output>30</output> <gadget id="calculator">10 / 30</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">1 - (1/3)</gadget> <output>2/3 = around 0.666667</output> <result>C</result>

C

A searchlight on top of the watchtower makes 2 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 10 seconds?

subtract(const_1, divide(10, multiply(10, const_3)))

multiply(n1,const_3)|divide(n1,#0)|subtract(const_1,#1)|

"the searchlight completes one revolution every 30 seconds . the probability that the man ' s area will be lit up is 10 / 30 = 1 / 3 . the probability that he will stay in the dark is 1 - 1 / 3 = 2 / 3 the answer is c ."

physics

math_qa__lFnZOxeStfgS9Vhc

The distance from City A to City B is 30 miles. While driving from City A to City B, Bob drives at a constant speed of 40 miles per hour. Alice leaves City A 30 minutes after Bob. What is the minimum constant speed in miles per hour that Alice must exceed in order to arrive in City B before Bob? Answers: A) 45 B) 88 C) 120 D) 152 E) 154

<gadget id="calculator">30 / 40</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">30 / 60</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">(3/4) - (1/2)</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">30 / (1/4)</gadget> <output>120</output> <result>C</result>

C

The distance from City A to City B is 30 miles. While driving from City A to City B, Bob drives at a constant speed of 40 miles per hour. Alice leaves City A 30 minutes after Bob. What is the minimum constant speed in miles per hour that Alice must exceed in order to arrive in City B before Bob?

divide(30, subtract(divide(30, 40), divide(30, const_60)))

divide(n0,n1)|divide(n2,const_60)|subtract(#0,#1)|divide(n0,#2)|

"the time it takes bob to drive to city b is 30 / 40 = 0.75 hours . alice needs to take less than 0.25 hours for the trip . alice needs to exceed a constant speed of 30 / 0.25 = 120 miles per hour . the answer is c ."

physics

math_qa__1Nu9aFJETviT9YlE

If x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $83. If $2,000 is the total amount invested, how much is invested at 8 percent? Options. A) $ 550 B) $ 650 C) $ 750 D) $ 850 E) $ 950

<gadget id="calculator">100 * 10</gadget> <output>1_000</output> <gadget id="calculator">1_000 * 2</gadget> <output>2_000</output> <gadget id="calculator">10 * 8</gadget> <output>80</output> <gadget id="calculator">80 * 2</gadget> <output>160</output> <gadget id="calculator">160 + 83</gadget> <output>243</output> <gadget id="calculator">10 / 100</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">8 / 100</gadget> <output>2/25 = around 0.08</output> <gadget id="calculator">(1/10) + (2/25)</gadget> <output>9/50 = around 0.18</output> <gadget id="calculator">243 / (9/50)</gadget> <output>1_350</output> <gadget id="calculator">2_000 - 1_350</gadget> <output>650</output> <result>B</result>

B

If x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $83. If $2,000 is the total amount invested, how much is invested at 8 percent?

subtract(multiply(multiply(const_100, 10), const_2), divide(add(multiply(multiply(10, 8), const_2), 83), add(divide(10, const_100), divide(8, const_100))))

divide(n0,const_100)|divide(n1,const_100)|multiply(n0,const_100)|multiply(n0,n1)|add(#0,#1)|multiply(#2,const_2)|multiply(#3,const_2)|add(n4,#6)|divide(#7,#4)|subtract(#5,#8)|

"0.1 x = 0.08 ( 2000 - x ) + 83 0.18 x = 243 x = 1350 then the amount invested at 8 % is $ 2000 - $ 1350 = $ 650 the answer is b ."

general

math_qa__i8znmt6Qlta7sAwX

Line Q has the equation 5y – 3x = 90. If Line S is perpendicular to Q, has an integer for its y-intercept, and intersects Q in the second quadrant, then how many possible Line S’s exist? (Note: Intersections on one of the axes do not count.) Answers. A) 58 B) 61 C) 64 D) 67 E) 70

<gadget id="calculator">90 / 5</gadget> <output>18</output> <gadget id="calculator">18 - 2</gadget> <output>16</output> <gadget id="calculator">90 / 3</gadget> <output>30</output> <gadget id="calculator">30 + 18</gadget> <output>48</output> <gadget id="calculator">16 + 48</gadget> <output>64</output> <result>D</result>

D

Line Q has the equation 5y – 3x = 90. If Line S is perpendicular to Q, has an integer for its y-intercept, and intersects Q in the second quadrant, then how many possible Line S’s exist? (Note: Intersections on one of the axes do not count.)

add(subtract(divide(90, 5), const_2), add(divide(90, 3), divide(90, 5)))

divide(n2,n1)|divide(n2,n0)|add(#0,#1)|subtract(#1,const_2)|add(#2,#3)

5 y - 3 x = 90 and so y = 3 x / 5 + 18 when x = 0 , then y = 18 . when y = 0 , then x = - 30 the slope is 3 / 5 , so the slope of line s is - 5 / 3 . through the point ( - 30 , 0 ) , 0 = - 5 ( - 30 ) / 3 + c the y - intercept is c = - 50 . thus the perpendicular line s can have y - intercepts from - 49 up to 17 . the number of possible lines is 49 + 17 + 1 = 67 the answer is d .

general

math_qa__l98f1EVGmhI4EOG2

The ratio of expenditure and savings is 3 : 2 . If the income increases by 15% and the savings increases by 6% , then by how much percent should his expenditure increases? Choose the correct choice from the following answers A) 22 B) 21 C) 88 D) 76 E) 29

<gadget id="calculator">15 - 6</gadget> <output>9</output> <gadget id="calculator">9 * 2</gadget> <output>18</output> <gadget id="calculator">15 * 3</gadget> <output>45</output> <gadget id="calculator">18 + 45</gadget> <output>63</output> <gadget id="calculator">63 / 3</gadget> <output>21</output> <result>B</result>

B

The ratio of expenditure and savings is 3 : 2 . If the income increases by 15% and the savings increases by 6% , then by how much percent should his expenditure increases?

divide(add(multiply(subtract(15, 6), 2), multiply(15, 3)), const_3)

multiply(n0,n2)|subtract(n2,n3)|multiply(n1,#1)|add(#2,#0)|divide(#3,const_3)

answer : b ) 21

general

math_qa__KYYvER3rjDonGhMF

In an election between the two candidates, the candidates who gets 70% of votes polled is winned by 160 vote’s majority. What is the total number of votes polled? Options. A) 750 B) 400 C) 800 D) 850 E) none of these

<gadget id="calculator">100 * 160</gadget> <output>16_000</output> <gadget id="calculator">100 - 70</gadget> <output>30</output> <gadget id="calculator">70 - 30</gadget> <output>40</output> <gadget id="calculator">16_000 / 40</gadget> <output>400</output> <result>B</result>

B

In an election between the two candidates, the candidates who gets 70% of votes polled is winned by 160 vote’s majority. What is the total number of votes polled?

divide(multiply(const_100, 160), subtract(70, subtract(const_100, 70)))

multiply(n1,const_100)|subtract(const_100,n0)|subtract(n0,#1)|divide(#0,#2)|

"explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 160 ( 40 * 4 = 160 ) 100 % - - - - - > 400 ( 100 * 4 = 400 ) answer : option b"

gain

math_qa__pLxCNjPjD4WI4tMF

If a train, travelling at a speed of 80 kmph, crosses a pole in 5 sec, then the length of train is? Choose the correct option. A) 110.111 m B) 121.111 m C) 111.11 m D) 141.111 m E) 181.111 m

<gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">80 * (5/18)</gadget> <output>200/9 = around 22.222222</output> <gadget id="calculator">(200/9) * 5</gadget> <output>1_000/9 = around 111.111111</output> <result>C</result>

C

If a train, travelling at a speed of 80 kmph, crosses a pole in 5 sec, then the length of train is?

multiply(multiply(80, const_0_2778), 5)

multiply(n0,const_0_2778)|multiply(n1,#0)|

"d = 80 * 5 / 18 * 5 = 111.11 m answer : c"

physics

math_qa__2DpHgS3C1gyVaC9B

If an integer n is to be selected at random from 1 to 99, inclusive, what is probability n(n+1) will be divisible by 3? Choose the correct answer: A) 1 / 4 B) 1 / 3 C) 1 / 2 D) 2 / 3 E) 3 / 4

<gadget id="calculator">2 / 3</gadget> <output>2/3 = around 0.666667</output> <result>D</result>

D

If an integer n is to be selected at random from 1 to 99, inclusive, what is probability n(n+1) will be divisible by 3?

divide(const_2, 3)

divide(const_2,n3)|

"for n ( n + 1 ) to be a multiple of 3 , either n or n + 1 has to be a multiple of 3 . thus n must be of the form 3 k or 3 k - 1 , but not 3 k + 1 . the probability is 2 / 3 . the answer is d ."

general

math_qa__927AXz13al9LAaKe

A sum of money deposited at C.I. amounts to Rs.2420 in 2 years and to Rs.3267 in 3 years. Find the rate percent? Choose the correct choice from the following choices A) 11 B) 10 C) 28 D) 24 E) 35

<gadget id="calculator">3_267 - 2_420</gadget> <output>847</output> <gadget id="calculator">847 / 2_420</gadget> <output>7/20 = around 0.35</output> <gadget id="calculator">(7/20) * 100</gadget> <output>35</output> <result>E</result>

E

A sum of money deposited at C.I. amounts to Rs.2420 in 2 years and to Rs.3267 in 3 years. Find the rate percent?

multiply(divide(subtract(3267, 2420), 2420), const_100)

subtract(n2,n0)|divide(#0,n0)|multiply(#1,const_100)|

"explanation : 2420 - - - 847 100 - - - ? = > 35 % answer : option e"

gain

math_qa__eERMneMoCD712Cwj

workers in a factory store products inside two different sized boxes. The bigger of the boxes can store 50 products while the smaller box can store 40 products. If a fresh batch of products numbering 212 in total were to be stored, what is the least number of products that will not be boxed? Choose the correct choice from the following. A) 23 B) 11 C) 2 D) 10 E) 12

<gadget id="calculator">50 * 4</gadget> <output>200</output> <gadget id="calculator">212 - 200</gadget> <output>12</output> <result>E</result>

E

workers in a factory store products inside two different sized boxes. The bigger of the boxes can store 50 products while the smaller box can store 40 products. If a fresh batch of products numbering 212 in total were to be stored, what is the least number of products that will not be boxed?

subtract(212, multiply(50, const_4))

multiply(n0,const_4)|subtract(n2,#0)

total products to be stored 212 the big box can store 50 small box can store 40 storing 212 products in big box 212 / 50 = 4 r 12 least number of toys that will be left unboxed = 12 answer : e

general

math_qa__RwUFYMM0m14Svpg9

A recipe requires 2 1/2 (mixed number) cups of flour 2 3/4 (mixed number) cups of sugar and 1 1/3 (mixed number) cups of milk to make one cake. Victor has 15 cups if flour, 16 cups of sugar and 8 cups of milk. What is the greatest number of cakes William can make using this recipe? Choose the correct answer: A) 5 B) 6 C) 7 D) 8 E) 9

<gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">2 + (1/2)</gadget> <output>5/2 = around 2.5</output> <gadget id="calculator">15 / (5/2)</gadget> <output>6</output> <gadget id="calculator">3 / 4</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">(3/4) + 2</gadget> <output>11/4 = around 2.75</output> <gadget id="calculator">16 / (11/4)</gadget> <output>64/11 = around 5.818182</output> <gadget id="calculator">floor(64/11)</gadget> <output>5</output> <gadget id="calculator">min(6, 5)</gadget> <output>5</output> <gadget id="calculator">1 / 3</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">(1/3) + 1</gadget> <output>4/3 = around 1.333333</output> <gadget id="calculator">8 / (4/3)</gadget> <output>6</output> <gadget id="calculator">min(5, 6)</gadget> <output>5</output> <result>A</result>

A

A recipe requires 2 1/2 (mixed number) cups of flour 2 3/4 (mixed number) cups of sugar and 1 1/3 (mixed number) cups of milk to make one cake. Victor has 15 cups if flour, 16 cups of sugar and 8 cups of milk. What is the greatest number of cakes William can make using this recipe?

min(min(divide(15, add(2, divide(1, 2))), floor(divide(16, add(divide(3, 4), 2)))), divide(8, add(divide(1, 3), 1)))

divide(n1,n4)|divide(n1,n0)|divide(n4,n5)|add(n1,#0)|add(n0,#1)|add(n0,#2)|divide(n11,#3)|divide(n9,#4)|divide(n10,#5)|floor(#8)|min(#7,#9)|min(#6,#10)|

"less work up front : go through each item and see what the greatest number of cakes you can make with each . the lowest of these will be the right answer . flour : 15 cups , we need 2.5 cups each . just keep going up the line to see how many cakes we can make : that means i can make 2 cakes with 5 cups , so 6 cakes overall with 15 cups . i ' ve already got the answer narrowed to either a or b . sugar : 16 cups , we need 2.75 cups each . same principle . i can make 2 cups with 5.5 cups , so to make 6 cakes i ' d need 16.5 cups . i do n ' t have that much sugar , so we ' re limited to 5 cakes . no need to even do milk because we ' re already at 5 . sugar will be the limiting factor . answer is a"

general

math_qa__gEhosrG19cgMOiFd

In a hostel, the number of students decreased by 5% and the price of food increased by 20% over the previous year. If each student consumes the same amount of food then By how much should the consumption of food be cut short by every student, so that the total cost of the food remains the same as that of the previous year? Select the correct option. A) 19 % B) 12.3 % C) 25 % D) 40 % E) 9.4 %

<gadget id="calculator">100 * 100</gadget> <output>10_000</output> <gadget id="calculator">100 - 5</gadget> <output>95</output> <gadget id="calculator">100 + 20</gadget> <output>120</output> <gadget id="calculator">95 * 120</gadget> <output>11_400</output> <gadget id="calculator">10_000 / 11_400</gadget> <output>50/57 = around 0.877193</output> <gadget id="calculator">1 - (50/57)</gadget> <output>7/57 = around 0.122807</output> <gadget id="calculator">(7/57) * 100</gadget> <output>700/57 = around 12.280702</output> <result>B</result>

B

In a hostel, the number of students decreased by 5% and the price of food increased by 20% over the previous year. If each student consumes the same amount of food then By how much should the consumption of food be cut short by every student, so that the total cost of the food remains the same as that of the previous year?

multiply(subtract(const_1, divide(multiply(const_100, const_100), multiply(subtract(const_100, 5), add(const_100, 20)))), const_100)

add(n1,const_100)|multiply(const_100,const_100)|subtract(const_100,n0)|multiply(#0,#2)|divide(#1,#3)|subtract(const_1,#4)|multiply(#5,const_100)

cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 5 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.95 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.95 * 1.2 ) = > f ( new ) = 0.877 f therefore the new cost of food must be 87.7 % of the old cost , or the cost of food must decrease by 12.28 % ( optionb )

general

math_qa__A4kZDx0hSaVNZnSm

At 15:00 there were 21 students in the computer lab. At 15:03 and every three minutes after that, 3 students entered the lab. If at 15:10 and every ten minutes after that 8 students left the lab, how many students were in the computer lab at 15:44 ? Choose the correct choice from the following options A) 7 B) 14 C) 25 D) 27 E) 30

<gadget id="calculator">44 / 3</gadget> <output>44/3 = around 14.666667</output> <gadget id="calculator">floor(44/3)</gadget> <output>14</output> <gadget id="calculator">14 * 3</gadget> <output>42</output> <gadget id="calculator">42 + 21</gadget> <output>63</output> <gadget id="calculator">44 / 8</gadget> <output>11/2 = around 5.5</output> <gadget id="calculator">floor(11/2)</gadget> <output>5</output> <gadget id="calculator">5 * 8</gadget> <output>40</output> <gadget id="calculator">63 - 40</gadget> <output>23</output> <gadget id="calculator">23 + 3</gadget> <output>26</output> <result>D</result>

D

At 15:00 there were 21 students in the computer lab. At 15:03 and every three minutes after that, 3 students entered the lab. If at 15:10 and every ten minutes after that 8 students left the lab, how many students were in the computer lab at 15:44 ?

add(subtract(add(multiply(floor(divide(44, 3)), 3), 21), multiply(floor(divide(44, 8)), 8)), 3)

divide(n10,n4)|divide(n10,n8)|floor(#0)|floor(#1)|multiply(n4,#2)|multiply(n8,#3)|add(n2,#4)|subtract(#6,#5)|add(n4,#7)

initial no of students + 3 * ( 1 + no of possible 3 minute intervals between 15 : 03 and 15 : 44 ) - 8 * ( 1 + no of possible 10 minute intervals between 15 : 10 and 15 : 44 ) 20 + 3 * 14 - 8 * 4 = 27 d

physics

math_qa__S4R6CJcTE2xxtsvZ

A boy wants to make cuboids of dimension 5m, 6m and 7m from small cubes of .03 m3. Later he realized he can make same cuboids by making it hollow. Then it takes some cubes less. What is the number of the cubes to be removed? Choose the most appropriate option: A) 1000 B) 2000 C) 3000 D) 4000 E) 5000

<gadget id="calculator">3 / 100</gadget> <output>3/100 = around 0.03</output> <gadget id="calculator">(3/100) ** (1/3)</gadget> <output>30**(1/3)/10 = around 0.310723</output> <gadget id="calculator">(30**(1/3)/10) * 2</gadget> <output>30**(1/3)/5 = around 0.621447</output> <gadget id="calculator">7 - (30**(1/3)/5)</gadget> <output>7 - 30**(1/3)/5 = around 6.378553</output> <gadget id="calculator">5 - (30**(1/3)/5)</gadget> <output>5 - 30**(1/3)/5 = around 4.378553</output> <gadget id="calculator">6 - (30**(1/3)/5)</gadget> <output>6 - 30**(1/3)/5 = around 5.378553</output> <gadget id="calculator">(5 - 30**(1/3)/5) * (6 - 30**(1/3)/5)</gadget> <output>(5 - 30**(1/3)/5)*(6 - 30**(1/3)/5) = around 23.550284</output> <gadget id="calculator">(7 - 30**(1/3)/5) * ((5 - 30**(1/3)/5)*(6 - 30**(1/3)/5))</gadget> <output>(5 - 30**(1/3)/5)*(6 - 30**(1/3)/5)*(7 - 30**(1/3)/5) = around 150.216748</output> <gadget id="calculator">((5 - 30**(1/3)/5)*(6 - 30**(1/3)/5)*(7 - 30**(1/3)/5)) / (3/100)</gadget> <output>100*(5 - 30**(1/3)/5)*(6 - 30**(1/3)/5)*(7 - 30**(1/3)/5)/3 = around 5_007.224931</output> <result>E</result>

E

A boy wants to make cuboids of dimension 5m, 6m and 7m from small cubes of .03 m3. Later he realized he can make same cuboids by making it hollow. Then it takes some cubes less. What is the number of the cubes to be removed?

divide(multiply(subtract(7, multiply(cube_edge_by_volume(divide(3, const_100)), const_2)), multiply(subtract(5, multiply(cube_edge_by_volume(divide(3, const_100)), const_2)), subtract(6, multiply(cube_edge_by_volume(divide(3, const_100)), const_2)))), divide(3, const_100))

divide(n3,const_100)|cube_edge_by_volume(#0)|multiply(#1,const_2)|subtract(n0,#2)|subtract(n1,#2)|subtract(n2,#2)|multiply(#3,#4)|multiply(#6,#5)|divide(#7,#0)

volume of the small cube = 0.03 m ^ 3 so side of this cube = cubic root of 0.03 m ^ 3 = . 312 m so after removing the outermost layer the dimensions for the inner cuboid will be ( 5 - 2 * 0.312 ) , ( 6 - 2 * 0.312 ) , ( 7 - 2 * 0.312 ) so total volume will be ( 4.376 ) * ( 5.376 ) * ( 6.376 ) = 150 m ^ 3 so no of cubes will be 150 / 0.03 = 5000 so we can remove 5000 inner cubes answer : e

physics

math_qa__rc5BopvYyXhbnrtO

If A speaks the truth 70% of the times, B speaks the truth 60% of the times. What is the probability that they tell the truth at the same time Pick one A) 0.49 B) 0.48 C) 0.41 D) 0.42 E) 0.411

<gadget id="calculator">4 * 5</gadget> <output>20</output> <gadget id="calculator">20 * 5</gadget> <output>100</output> <gadget id="calculator">70 / 100</gadget> <output>7/10 = around 0.7</output> <gadget id="calculator">60 / 100</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">(7/10) * (3/5)</gadget> <output>21/50 = around 0.42</output> <result>D</result>

D

If A speaks the truth 70% of the times, B speaks the truth 60% of the times. What is the probability that they tell the truth at the same time

multiply(divide(70, multiply(multiply(const_4, const_5), const_5)), divide(60, multiply(multiply(const_4, const_5), const_5)))

multiply(const_4,const_5)|multiply(#0,const_5)|divide(n0,#1)|divide(n1,#1)|multiply(#2,#3)|

"explanation : probability that a speaks truth is 70 / 100 = 0.7 probability that b speaks truth is 60 / 100 = 0.6 since both a and b are independent of each other so probability of a intersection b is p ( a ) × p ( b ) = 0.7 × 0.6 = 0.42 answer : d"

gain

math_qa__OnYAp9FWhBXBgIqs

Find the curved surface area, if the radius of a cone is 21 m and slant height is 15 m? Select: A) 660 B) 770 C) 880 D) 900 E) 990

<gadget id="calculator">21 * 15</gadget> <output>315</output> <gadget id="calculator">pi * 315</gadget> <output>315*pi = around 989.601686</output> <result>E</result>

E

Find the curved surface area, if the radius of a cone is 21 m and slant height is 15 m?

multiply(const_pi, multiply(21, 15))

multiply(n0,n1)|multiply(#0,const_pi)

cone curved surface area = ï € rl 22 / 7 ã — 21 ã — 15 = 66 ã — 15 = 990 m ( power 2 ) answer is e .

geometry

math_qa__XLxmvPKDwTbOTpXO

Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 130 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond? Choose the correct choice from the following answers: A) 280 B) 400 C) 540 D) 650 E) 840

<gadget id="calculator">3 / 5</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">1 - (3/5)</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">130 / (2/5)</gadget> <output>325</output> <gadget id="calculator">3 / 4</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">325 / (3/4)</gadget> <output>1_300/3 = around 433.333333</output> <gadget id="calculator">2 / 3</gadget> <output>2/3 = around 0.666667</output> <gadget id="calculator">(1_300/3) / (2/3)</gadget> <output>650</output> <result>D</result>

D

Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 130 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?

divide(divide(divide(130, subtract(const_1, divide(3, 5))), divide(3, 4)), divide(2, 3))

divide(n1,n5)|divide(n1,n3)|divide(n0,n1)|subtract(const_1,#0)|divide(n6,#3)|divide(#4,#1)|divide(#5,#2)|

"of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month : 2 / 3 * 3 / 4 = 1 / 2 survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year : ( 1 - 3 / 5 ) * 1 / 2 = 1 / 5 survived the first year . 130 geese survived the first year : 1 / 5 * ( total ) = 130 - - > ( total ) = 650 . answer : d ."

general

math_qa__UXunF8JBZAt6dEaM

A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 22 sec. What is the length of the goods train? Choose the correct answer: A) 299 B) 190 C) 276 D) 270 E) 281

<gadget id="calculator">72 / 3_600</gadget> <output>1/50 = around 0.02</output> <gadget id="calculator">(1/50) * 1_000</gadget> <output>20</output> <gadget id="calculator">20 * 22</gadget> <output>440</output> <gadget id="calculator">440 - 250</gadget> <output>190</output> <result>B</result>

B

A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 22 sec. What is the length of the goods train?

subtract(multiply(multiply(divide(72, const_3600), const_1000), 22), 250)

divide(n0,const_3600)|multiply(#0,const_1000)|multiply(n2,#1)|subtract(#2,n1)|

"speed = 72 * 5 / 18 = 20 m / sec . time = 22 sec . let the length of the train be x meters . then , ( x + 250 ) / 22 = 20 x = 190 m . answer : b"

physics

math_qa__CiuDxhioZjCZdENO

John was thrice as old as Tom 6 years ago. John will be 9/7 times as old as Tom in 6 years. How old is Tom today? Pick: A) 6 B) 8 C) 10 D) 12 E) 14

<gadget id="calculator">9 / 7</gadget> <output>9/7 = around 1.285714</output> <gadget id="calculator">6 * (9/7)</gadget> <output>54/7 = around 7.714286</output> <result>B</result>

B

John was thrice as old as Tom 6 years ago. John will be 9/7 times as old as Tom in 6 years. How old is Tom today?

multiply(6, divide(9, 7))

divide(n1,n2)|multiply(n0,#0)|

"j - 6 = 3 ( t - 6 ) , so j = 3 t - 12 j + 6 = 9 / 7 * ( t + 6 ) 7 j + 42 = 9 t + 54 7 ( 3 t - 12 ) + 42 = 9 t + 54 12 t = 96 t = 8 the answer is b ."

general