Datasets:

MU-NLPC

/

Calc-math_qa

like 4

Follow

NLP Centre, Faculty of Informatics, Masaryk University 14

math_qa__y0lanmxjfzB9RbQy

If 10 litres of an oil of Rs.40 per litres be mixed with 5 litres of another oil of Rs.66 per litre then what is the rate of mixed oil per litre? Choose the most appropriate option. A) rs . 48.66 B) rs . 51.03 C) rs . 54.17 D) rs . 55.33 E) none of the above

<gadget id="calculator">10 * 40</gadget> <output>400</output> <gadget id="calculator">5 * 66</gadget> <output>330</output> <gadget id="calculator">400 + 330</gadget> <output>730</output> <gadget id="calculator">10 + 5</gadget> <output>15</output> <gadget id="calculator">730 / 15</gadget> <output>146/3 = around 48.666667</output> <result>A</result>

A

If 10 litres of an oil of Rs.40 per litres be mixed with 5 litres of another oil of Rs.66 per litre then what is the rate of mixed oil per litre?

divide(add(multiply(10, 40), multiply(5, 66)), add(10, 5))

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

"40 * 10 = 400 66 * 5 = 330 730 / 15 = 48.66 answer : a"

gain

math_qa__CS4MVwDZTv0fmFD4

Tom wants to buy items costing $25.35, $70.69, and $85.96. He earns $6.50 an hour doing odd jobs. If ten percent of his income is put aside for other purposes, how many hours must he work to earn the money he needs for his purchases? Round your answer to the nearest whole hour. Options. A) 8 hours B) 48 hours C) 31 hours D) 18 hours E) 28 hours

<gadget id="calculator">25.35 + 70.69</gadget> <output>96.04</output> <gadget id="calculator">96.04 + 85.96</gadget> <output>182</output> <gadget id="calculator">1 / 10</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">1 - (1/10)</gadget> <output>9/10 = around 0.9</output> <gadget id="calculator">6.5 * (9/10)</gadget> <output>5.85</output> <gadget id="calculator">182 / 5.85</gadget> <output>31.111111</output> <gadget id="calculator">floor(31.111111)</gadget> <output>31</output> <result>C</result>

C

Tom wants to buy items costing $25.35, $70.69, and $85.96. He earns $6.50 an hour doing odd jobs. If ten percent of his income is put aside for other purposes, how many hours must he work to earn the money he needs for his purchases? Round your answer to the nearest whole hour.

floor(divide(add(add(25.35, 70.69), 85.96), multiply(6.5, subtract(const_1, divide(const_1, const_10)))))

add(n0,n1)|divide(const_1,const_10)|add(n2,#0)|subtract(const_1,#1)|multiply(n3,#3)|divide(#2,#4)|floor(#5)

$ 6.50 x . 10 = $ . 65 is 10 % of his hourly income $ 6.50 - . 65 = $ 5.85 hourly amount available to spend $ 25.35 + $ 70.69 + $ 85.96 = $ 182 total needed $ 182 ÷ $ 5.85 = 31.11 . . . rounds to 31 hours correct answer c

physics

math_qa__dwOpOzK1eyCf3A5v

A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 1.8 kilometer long bridge, at the same speed? Choose the correct choice from the following choices A) 4 min B) 2 min C) 8 min D) 9 min E) 3 min

<gadget id="calculator">1.8 * 1_000</gadget> <output>1_800</output> <gadget id="calculator">600 / 40</gadget> <output>15</output> <gadget id="calculator">1_800 / 15</gadget> <output>120</output> <gadget id="calculator">120 / 60</gadget> <output>2</output> <result>B</result>

B

A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 1.8 kilometer long bridge, at the same speed?

divide(divide(multiply(1.8, const_1000), speed(600, 40)), const_60)

multiply(n2,const_1000)|speed(n0,n1)|divide(#0,#1)|divide(#2,const_60)

s = 600 / 40 = 15 mps s = 1800 / 15 = 120 sec = 2 min . answer : b

physics

math_qa__3kLhXnDu6fp9glkQ

A small college reduced its faculty by approximately 13 percent to 195 professors. What was the original number of faculty members? Choose the correct choice from the following answers: A) 182 B) 208 C) 224 D) 254 E) 302

<gadget id="calculator">100 - 13</gadget> <output>87</output> <gadget id="calculator">87 / 100</gadget> <output>87/100 = around 0.87</output> <gadget id="calculator">195 / (87/100)</gadget> <output>6_500/29 = around 224.137931</output> <result>C</result>

C

A small college reduced its faculty by approximately 13 percent to 195 professors. What was the original number of faculty members?

divide(195, divide(subtract(const_100, 13), const_100))

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

"f x is the original number of faculty members , then after 13 % reduction in faculty members number is . 87 x but we are given . 87 x = 195 x = 224 so the original number of faculty members is 224 correct answer - c"

gain

math_qa__h1vKczCUlmGRtZdC

A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (Assume that the order of the colors in a pair does not matter.) Choose the correct choice from the following choices. A) 4 B) 5 C) 6 D) 12 E) 24

<gadget id="calculator">12 / 2</gadget> <output>6</output> <gadget id="calculator">6 - 1</gadget> <output>5</output> <gadget id="calculator">factorial(5)</gadget> <output>120</output> <gadget id="calculator">factorial(3)</gadget> <output>6</output> <gadget id="calculator">factorial(2)</gadget> <output>2</output> <gadget id="calculator">6 * 2</gadget> <output>12</output> <gadget id="calculator">120 / 12</gadget> <output>10</output> <gadget id="calculator">10 - 5</gadget> <output>5</output> <result>B</result>

B

A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (Assume that the order of the colors in a pair does not matter.)

subtract(divide(factorial(subtract(divide(12, const_2), const_1)), multiply(factorial(const_3), factorial(const_2))), subtract(divide(12, const_2), const_1))

divide(n0,const_2)|factorial(const_3)|factorial(const_2)|multiply(#1,#2)|subtract(#0,const_1)|factorial(#4)|divide(#5,#3)|subtract(#6,#4)|

"let ' s start with 4 minimum number of colors so single color code we can make 4 nos . now if we need to make 2 color combination out of 4 we can do so in 4 ! / 2 ! * 2 ! or 4 * 3 / 2 or 6 so total we can make 4 + 6 = 10 color combinations but we have 12 boxes so let ' s look at 5 we get 5 single color codes and out 5 color choices , we can choose 2 in 5 ! / 2 ! * 3 ! ways or 10 ways . so total we can have 5 + 10 = 15 color combinations . so , minimum number we need will be 5 ans is b . . . . . . ."

general

math_qa__aD9I2ugZ6z9Fqp5t

The present worth of a sum due sometime hence is Rs.576 and the banker’s gain is Rs.16.The true discount is Answers. A) rs . 36 B) rs . 72 C) rs . 48 D) rs . 96 E) none

<gadget id="calculator">576 * 16</gadget> <output>9_216</output> <gadget id="calculator">9_216 ** (1/2)</gadget> <output>96</output> <result>D</result>

D

The present worth of a sum due sometime hence is Rs.576 and the banker’s gain is Rs.16.The true discount is

sqrt(multiply(576, 16))

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

solution t . d = √ p . w xb . g = √ 576 x 16 = 96 . answer d

gain

math_qa__SD4BSWSSGBgJ4PeB

The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. If its present value is Rs. 8748, its purchase price was : Options: A) 12003 B) 12000 C) 12002 D) 12289 E) 12019

<gadget id="calculator">10 / 100</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">(1/10) * 3</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">1 - (3/10)</gadget> <output>7/10 = around 0.7</output> <gadget id="calculator">8_748 / (7/10)</gadget> <output>87_480/7 = around 12_497.142857</output> <result>B</result>

B

The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. If its present value is Rs. 8748, its purchase price was :

divide(8748, subtract(const_1, multiply(divide(10, const_100), 3)))

divide(n0,const_100)|multiply(n1,#0)|subtract(const_1,#1)|divide(n2,#2)|

"explanation : = rs . 12000 answer : b ) 12000"

gain

math_qa__GTL9HejlWkB4qcyK

There are 6 more women than there are men on a local co-ed softball team. If there are a total of 16 players on the team, what is the ratio of men to women? Choose the correct choice from the following options: A) 10 / 16 B) 6 / 16 C) 4 / 16 D) 5 / 11 E) 4 / 10

<gadget id="calculator">16 - 6</gadget> <output>10</output> <gadget id="calculator">1 + 1</gadget> <output>2</output> <gadget id="calculator">10 / 2</gadget> <output>5</output> <gadget id="calculator">5 + 6</gadget> <output>11</output> <gadget id="calculator">5 / 11</gadget> <output>5/11 = around 0.454545</output> <result>D</result>

D

There are 6 more women than there are men on a local co-ed softball team. If there are a total of 16 players on the team, what is the ratio of men to women?

divide(divide(subtract(16, 6), add(const_1, const_1)), add(divide(subtract(16, 6), add(const_1, const_1)), 6))

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

"w = m + 6 w + m = 16 m + 6 + m = 16 2 m = 10 m = 5 w = 11 ratio : 5 : 11 ans : d"

general

math_qa__Zrm9Nsjit9BlkbIe

A boat can travel with a speed of 16 km/hr in still water. If the rate of stream is 5 km/hr, then find the time taken by the boat to cover distance of 63 km downstream. Options: A) 3 hours B) 5 hours C) 6 hours D) 7 hours E) 8 hours

<gadget id="calculator">16 + 5</gadget> <output>21</output> <gadget id="calculator">63 / 21</gadget> <output>3</output> <result>A</result>

A

A boat can travel with a speed of 16 km/hr in still water. If the rate of stream is 5 km/hr, then find the time taken by the boat to cover distance of 63 km downstream.

divide(63, add(16, 5))

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

"explanation : it is very important to check , if the boat speed given is in still water or with water or against water . because if we neglect it we will not reach on right answer . i just mentioned here because mostly mistakes in this chapter are of this kind only . lets see the question now . speed downstream = ( 16 + 5 ) = 21 kmph time = distance / speed = 63 / 21 = 3 hours option a"

physics

math_qa__7MINnpo7fUzLatW1

A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 600 m long? Choices. A) 266 sec B) 180 sec C) 776 sec D) 166 sec E) 997 sec

<gadget id="calculator">1_200 + 600</gadget> <output>1_800</output> <gadget id="calculator">1_200 / 120</gadget> <output>10</output> <gadget id="calculator">1_800 / 10</gadget> <output>180</output> <result>B</result>

B

A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 600 m long?

divide(add(1200, 600), divide(1200, 120))

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

"l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 1800 m t = d / s t = 1800 / 10 t = 180 sec answer : b"

physics

math_qa__7gswTxX3SggXmSV6

Two MBA admissions committees are to be formed randomly from 6 second year MBAs with 3 members each. What is the probability V that Jane will be on the same committee as Albert? Pick one A) 12 % B) 20 % C) 33 % D) 40 % E) 50 %

<gadget id="calculator">binomial(4, 1)</gadget> <output>4</output> <gadget id="calculator">4 * 2</gadget> <output>8</output> <gadget id="calculator">binomial(6, 3)</gadget> <output>20</output> <gadget id="calculator">8 / 20</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">5 * 5</gadget> <output>25</output> <gadget id="calculator">25 * 4</gadget> <output>100</output> <gadget id="calculator">(2/5) * 100</gadget> <output>40</output> <result>D</result>

D

Two MBA admissions committees are to be formed randomly from 6 second year MBAs with 3 members each. What is the probability V that Jane will be on the same committee as Albert?

multiply(divide(multiply(choose(const_4, const_1), const_2), choose(6, 3)), multiply(multiply(const_5, const_5), const_4))

choose(const_4,const_1)|choose(n0,n1)|multiply(const_5,const_5)|multiply(#0,const_2)|multiply(#2,const_4)|divide(#3,#1)|multiply(#5,#4)|

"total number of ways to choose 3 member committee - 6 c 3 = ( 6 ! / 3 ! 3 ! ) = 20 no . of ways albert n jane are in same committee : - ( 4 c 1 * 2 ) = 8 probability v = ( 8 / 20 ) * 100 = 40 % . + 1 for me . . : d"

probability

math_qa__D3vkgyudhavAgxNL

A rectangular plot 15 m × 10 m, has a path of grass outside it. If the area of grassy pathway is 54 m2, find the width of the path. Choices: A) 4 m B) 3 m C) 2 m D) 1 m E) none of these

<gadget id="calculator">2 * (15 + 10)</gadget> <output>50</output> <gadget id="calculator">50 / 4</gadget> <output>25/2 = around 12.5</output> <gadget id="calculator">(25/2) ** 2</gadget> <output>625/4 = around 156.25</output> <gadget id="calculator">54 + (625/4)</gadget> <output>841/4 = around 210.25</output> <gadget id="calculator">(841/4) ** (1/2)</gadget> <output>29/2 = around 14.5</output> <gadget id="calculator">(29/2) - (25/2)</gadget> <output>2</output> <result>C</result>

C

A rectangular plot 15 m × 10 m, has a path of grass outside it. If the area of grassy pathway is 54 m2, find the width of the path.

subtract(sqrt(add(54, power(divide(rectangle_perimeter(15, 10), const_4), const_2))), divide(rectangle_perimeter(15, 10), const_4))

rectangle_perimeter(n0,n1)|divide(#0,const_4)|power(#1,const_2)|add(n2,#2)|sqrt(#3)|subtract(#4,#1)

let the width of the path = w m then , length of plot with path = ( 15 + 2 w ) m and breadth of plot with path = ( 10 + 2 w ) m therefore , area of rectangular plot ( without path ) = 15 × 10 = 150 m 2 and area of rectangular plot ( with path ) = 150 + 54 = 204 m 2 hence , ( 15 + 2 w ) × ( 10 + 2 w ) = 204 ⇒ 4 w 2 + 50 w – 54 = 0 ⇒ 2 w 2 + 25 w – 27 = 0 ⇒ ( w – 2 ) ( w + 27 ) = 0 thus w = 2 or – 27 ∴ with of the path = 2 m answer c

geometry

math_qa__d48qSGhZO0iGlVdd

If a car had traveled 40 kmh faster than it actually did, the trip would have lasted 30 minutes less. If the car went exactly 120 km, at what speed did it travel? Choose the correct choice from the following choices: A) 50 kmh B) 60 kmh C) 70 kmh D) 80 kmh E) 90 kmh

<gadget id="calculator">120 * 40</gadget> <output>4_800</output> <gadget id="calculator">2 * 4_800</gadget> <output>9_600</output> <gadget id="calculator">9_600 * 4</gadget> <output>38_400</output> <gadget id="calculator">40 ** 2</gadget> <output>1_600</output> <gadget id="calculator">38_400 + 1_600</gadget> <output>40_000</output> <gadget id="calculator">40_000 ** (1/2)</gadget> <output>200</output> <gadget id="calculator">200 - 40</gadget> <output>160</output> <gadget id="calculator">160 / 2</gadget> <output>80</output> <result>D</result>

D

If a car had traveled 40 kmh faster than it actually did, the trip would have lasted 30 minutes less. If the car went exactly 120 km, at what speed did it travel?

divide(subtract(sqrt(add(multiply(multiply(const_2, multiply(120, 40)), const_4), power(40, const_2))), 40), const_2)

multiply(n0,n2)|power(n0,const_2)|multiply(#0,const_2)|multiply(#2,const_4)|add(#3,#1)|sqrt(#4)|subtract(#5,n0)|divide(#6,const_2)|

"time = distance / speed difference in time = 1 / 2 hrs 120 / x - 120 / ( x + 40 ) = 1 / 2 substitute the value of x from the options . - - > x = 80 - - > 120 / 80 - 120 / 120 = 3 / 2 - 1 = 1 / 2 answer : d"

physics

math_qa__rczh9UNi46Kn5V3m

A grocer has a sale of Rs. 3435, Rs. 3927, Rs. 3855, Rs. 4230 and Rs. 3562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 3500? Choose the correct option. A) s . 1991 B) s . 2991 C) s . 3991 D) s . 4991 E) s . 5991

<gadget id="calculator">5 + 1</gadget> <output>6</output> <gadget id="calculator">6 * 3_500</gadget> <output>21_000</output> <gadget id="calculator">3_435 + 3_927</gadget> <output>7_362</output> <gadget id="calculator">7_362 + 3_855</gadget> <output>11_217</output> <gadget id="calculator">11_217 + 4_230</gadget> <output>15_447</output> <gadget id="calculator">15_447 + 3_562</gadget> <output>19_009</output> <gadget id="calculator">21_000 - 19_009</gadget> <output>1_991</output> <result>A</result>

A

A grocer has a sale of Rs. 3435, Rs. 3927, Rs. 3855, Rs. 4230 and Rs. 3562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 3500?

subtract(multiply(add(5, const_1), 3500), add(add(add(add(3435, 3927), 3855), 4230), 3562))

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

"explanation : total sale for 5 months = rs . ( 3435 + 3927 + 3855 + 4230 + 3562 ) = rs . 19009 . required sale = rs . [ ( 3500 x 6 ) â € “ 19009 ] = rs . ( 21000 â € “ 19009 ) = rs . 1991 . answer a"

general

math_qa__57eTnNXFv4EXYrAG

Two trains of equal length, running with the speeds of 60 and 40 kmph, take 40 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions? Choose the correct choice from the following: A) 10 sec B) 16 sec C) 13 sec D) 67 sec E) 8 sec

<gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">60 - 40</gadget> <output>20</output> <gadget id="calculator">(5/18) * 20</gadget> <output>50/9 = around 5.555556</output> <gadget id="calculator">(50/9) * 40</gadget> <output>2_000/9 = around 222.222222</output> <gadget id="calculator">60 + 40</gadget> <output>100</output> <gadget id="calculator">(5/18) * 100</gadget> <output>250/9 = around 27.777778</output> <gadget id="calculator">1 / (250/9)</gadget> <output>9/250 = around 0.036</output> <gadget id="calculator">(2_000/9) * (9/250)</gadget> <output>8</output> <result>E</result>

E

Two trains of equal length, running with the speeds of 60 and 40 kmph, take 40 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?

multiply(multiply(multiply(const_0_2778, subtract(60, 40)), 40), inverse(multiply(const_0_2778, add(60, 40))))

add(n0,n1)|subtract(n0,n1)|multiply(#0,const_0_2778)|multiply(#1,const_0_2778)|inverse(#2)|multiply(n2,#3)|multiply(#4,#5)|

"rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 40 d = 40 * 100 / 18 = 2000 / 9 rs = 60 + 40 = 100 * 5 / 18 t = 2000 / 9 * 18 / 500 = 8 sec answer : e"

physics

math_qa__s18fIaqrrjCCESFL

In a group of pigs and hens, the number of legs are 22 more than twice the number of heads. The number of pigs is Choose the correct choice from the following answers A) 5 B) 7 C) 10 D) 12 E) 11

<gadget id="calculator">22 / 2</gadget> <output>11</output> <result>E</result>

E

In a group of pigs and hens, the number of legs are 22 more than twice the number of heads. The number of pigs is

divide(22, const_2)

divide(n0,const_2)

explanation : let the number of pigs be x and the number of hens be y . then , 4 x + 2 y = 2 ( x + y ) + 22 4 x + 2 y = 2 x + 2 y + 22 2 x = 22 x = 11 answer : e

general

math_qa__VCYRDjLYte6GXtLV

x + y = 19 , and x + 3y = 1. Find the value of x + 2y Choose the correct choice from the following answers: A) 20 B) 18 C) 11 D) 10 E) 5

<gadget id="calculator">2 + 4</gadget> <output>6</output> <gadget id="calculator">6 * 2</gadget> <output>12</output> <gadget id="calculator">12 - 2</gadget> <output>10</output> <result>D</result>

D

x + y = 19 , and x + 3y = 1. Find the value of x + 2y

subtract(multiply(add(2, const_4), 2), 2)

add(n3,const_4)|multiply(n3,#0)|subtract(#1,n3)

add these two equations 2 x + 4 y = 20 divide by 2 ( to get x + 2 y ) answer will be d . 10

general

math_qa__ztlmDlZ1lC5pnb9B

In the fifth grade at Parkway elementary school there are 470 students. 300 students are boys and 250 students are playing soccer. 86% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer? Choose the correct option: A) 69 . B) 135 . C) 81 . D) 91 . E) 108 .

<gadget id="calculator">470 - 300</gadget> <output>170</output> <gadget id="calculator">250 * 86</gadget> <output>21_500</output> <gadget id="calculator">21_500 / 100</gadget> <output>215</output> <gadget id="calculator">250 - 215</gadget> <output>35</output> <gadget id="calculator">170 - 35</gadget> <output>135</output> <result>B</result>

B

In the fifth grade at Parkway elementary school there are 470 students. 300 students are boys and 250 students are playing soccer. 86% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer?

subtract(subtract(470, 300), subtract(250, divide(multiply(250, 86), const_100)))

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

"total students = 470 boys = 300 , girls = 170 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 170 - 35 = 135 . correct option : b"

gain

math_qa__67DoqavkjAMZEa3k

How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 390 m in length? Pick. A) 18.9 sec B) 88.9 sec C) 22.9 sec D) 30.00 sec E) 72.0 sec

<gadget id="calculator">110 + 390</gadget> <output>500</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">500 / (50/3)</gadget> <output>30</output> <result>D</result>

D

How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 390 m in length?

divide(add(110, 390), multiply(60, const_0_2778))

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

"d = 110 + 390 = 500 m s = 60 * 5 / 18 = 50 / 3 t = 500 * 3 / 50 = 30 sec answer : d"

physics

math_qa__TVgMwdzZw5T53sfu

In a recent election, James received 1.5 percent of the 2,000 votes cast. To win the election, a candidate needed to receive more than 50 percent of the vote. How many additional votes would James have needed to win the election? Choose the correct choice from the following answers A) 901 B) 989 C) 990 D) 971 E) 1,001

<gadget id="calculator">1_000 + 1_000</gadget> <output>2_000</output> <gadget id="calculator">2_000 * 0.5</gadget> <output>1_000</output> <gadget id="calculator">2_000 - 1_000</gadget> <output>1_000</output> <result>D</result>

D

In a recent election, James received 1.5 percent of the 2,000 votes cast. To win the election, a candidate needed to receive more than 50 percent of the vote. How many additional votes would James have needed to win the election?

subtract(add(const_1000, const_1000), multiply(add(const_1000, const_1000), const_0.5))

add(const_1000,const_1000)|multiply(const_0.5,#0)|subtract(#0,#1)|

"james = ( 1.5 / 100 ) * 2000 = 30 votes to win = ( 50 / 100 ) * total votes + 1 = ( 50 / 100 ) * 2000 + 1 = 1001 remaining voted needed to win election = 1001 - 30 = 971 answer : option d"

general

math_qa__yXGqDAFp8r66cGbz

Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 10 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract? Choose the correct choice from the following answers: A) $ 506.00 B) $ 726.24 C) $ 900.00 D) $ 920.24 E) $ 926.24

<gadget id="calculator">3 / 100</gadget> <output>3/100 = around 0.03</output> <gadget id="calculator">2 / 100</gadget> <output>1/50 = around 0.02</output> <gadget id="calculator">100 ** 2</gadget> <output>10_000</output> <gadget id="calculator">(1/50) * 10_000</gadget> <output>200</output> <gadget id="calculator">200 + 10_000</gadget> <output>10_200</output> <gadget id="calculator">(3/100) * 10_200</gadget> <output>306</output> <gadget id="calculator">306 + 10_200</gadget> <output>10_506</output> <gadget id="calculator">4 / 100</gadget> <output>1/25 = around 0.04</output> <gadget id="calculator">10_506 * (1/25)</gadget> <output>10_506/25 = around 420.24</output> <gadget id="calculator">(10_506/25) + 306</gadget> <output>18_156/25 = around 726.24</output> <result>B</result>

B

Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 10 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract?

add(multiply(add(multiply(divide(3, const_100), add(multiply(divide(2, const_100), power(const_100, const_2)), power(const_100, const_2))), add(multiply(divide(2, const_100), power(const_100, const_2)), power(const_100, const_2))), divide(4, const_100)), multiply(divide(3, const_100), add(multiply(divide(2, const_100), power(const_100, const_2)), power(const_100, const_2))))

divide(n1,const_100)|divide(n3,const_100)|divide(n5,const_100)|power(const_100,const_2)|multiply(#0,#3)|add(#4,#3)|multiply(#5,#1)|add(#5,#6)|multiply(#7,#2)|add(#8,#6)

if interest were not compounded in every six months ( so if interest were not earned on interest ) then we would have ( 2 + 3 + 4 ) = 9 % simple interest earned on $ 10,000 , which is $ 900 . so , you can rule out a , b and c right away . interest earned after the first time interval : $ 10,000 * 2 % = $ 200 ; interest earned after the second time interval : ( $ 10,000 + $ 200 ) * 3 % = $ 300 + $ 6 = $ 306 ; interest earned after the third time interval : ( $ 10,000 + $ 200 + $ 306 ) * 4 % = $ 400 + $ 8 + ( ~ $ 12 ) = ~ $ 420 ; total : 200 + 306 + ( ~ 420 ) = ~ $ 726.24 . answer : b .

gain

math_qa__1rbWLpiJTrH5pxlG

Walking 4/3 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school? Choose the correct choice from the following: A) 22 B) 16 C) 27 D) 28 E) 20

<gadget id="calculator">4 * 4</gadget> <output>16</output> <result>B</result>

B

Walking 4/3 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?

multiply(4, 4)

multiply(n0,n2)|

"speed ratio = 1 : 4 / 3 = 3 : 4 time ratio = 4 : 3 1 - - - - - - - - 4 4 - - - - - - - - - ? 16 m . answer : b"

gain

math_qa__i7aJNjUslTBa94pz

The average of 1st 3 of 4 numbers is 6 and of the last 3 are 5. If the sum of the first and the last number is 11. What is the last numbers? Choose one: A) 4 B) 5 C) 6 D) 7 E) 8

<gadget id="calculator">3 * 6</gadget> <output>18</output> <gadget id="calculator">11 - 6</gadget> <output>5</output> <gadget id="calculator">5 + 3</gadget> <output>8</output> <gadget id="calculator">18 - 8</gadget> <output>10</output> <gadget id="calculator">10 - 6</gadget> <output>4</output> <result>A</result>

A

The average of 1st 3 of 4 numbers is 6 and of the last 3 are 5. If the sum of the first and the last number is 11. What is the last numbers?

subtract(subtract(multiply(3, 6), add(subtract(11, 6), 3)), 6)

multiply(n1,n3)|subtract(n6,n3)|add(n1,#1)|subtract(#0,#2)|subtract(#3,n3)|

"a + b + c = 18 b + c + d = 15 a + d = 11 a – d = 3 a + d = 11 2 d = 8 d = 4 answer : a"

general

math_qa__r9RyC5AIqH4PjgBQ

If the cost price of 50 articles is equal to the selling price of 35 articles, then the gain or loss percent is? Select. A) 16 B) 127 C) 12 D) 18 E) 43

<gadget id="calculator">100 * 35</gadget> <output>3_500</output> <gadget id="calculator">3_500 / 50</gadget> <output>70</output> <gadget id="calculator">100 - 70</gadget> <output>30</output> <gadget id="calculator">30 / 70</gadget> <output>3/7 = around 0.428571</output> <gadget id="calculator">100 * (3/7)</gadget> <output>300/7 = around 42.857143</output> <result>E</result>

E

If the cost price of 50 articles is equal to the selling price of 35 articles, then the gain or loss percent is?

multiply(const_100, divide(subtract(const_100, divide(multiply(const_100, 35), 50)), divide(multiply(const_100, 35), 50)))

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

"percentage of profit = 15 / 35 * 100 = 43 % answer : e"

gain

math_qa__prASanz8m7QYLw2H

10 different biology books and 8 different chemistry books lie on a shelf. In how many ways can a student pick 2 books of each type? Select the correct option. A) 80 B) 160 C) 720 D) 1100 E) 1260

<gadget id="calculator">factorial(10)</gadget> <output>3_628_800</output> <gadget id="calculator">10 - 2</gadget> <output>8</output> <gadget id="calculator">factorial(8)</gadget> <output>40_320</output> <gadget id="calculator">3_628_800 / 40_320</gadget> <output>90</output> <gadget id="calculator">90 / 2</gadget> <output>45</output> <gadget id="calculator">8 - 2</gadget> <output>6</output> <gadget id="calculator">factorial(6)</gadget> <output>720</output> <gadget id="calculator">40_320 / 720</gadget> <output>56</output> <gadget id="calculator">56 / 2</gadget> <output>28</output> <gadget id="calculator">45 * 28</gadget> <output>1_260</output> <result>E</result>

E

10 different biology books and 8 different chemistry books lie on a shelf. In how many ways can a student pick 2 books of each type?

multiply(divide(divide(factorial(10), factorial(subtract(10, 2))), 2), divide(divide(factorial(8), factorial(subtract(8, 2))), 2))

factorial(n0)|factorial(n1)|subtract(n0,n2)|subtract(n1,n2)|factorial(#2)|factorial(#3)|divide(#0,#4)|divide(#1,#5)|divide(#6,n2)|divide(#7,n2)|multiply(#8,#9)|

"no . of ways of picking 2 biology books ( from 10 books ) = 10 c 2 = ( 10 * 9 ) / 2 = 45 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 45 * 28 = 1260 ( option e )"

other

math_qa__ESuJZNuefcYbRahu

A grocer has a sale of Rs. 6400, Rs. 7000, Rs. 6800, Rs. 7200 and Rs. 6500 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500? Select A) rs . 4500 B) rs . 4700 C) rs . 4800 D) rs . 5000 E) rs . 5100

<gadget id="calculator">5 + 1</gadget> <output>6</output> <gadget id="calculator">6 * 6_500</gadget> <output>39_000</output> <gadget id="calculator">6_400 + 7_000</gadget> <output>13_400</output> <gadget id="calculator">13_400 + 6_800</gadget> <output>20_200</output> <gadget id="calculator">20_200 + 7_200</gadget> <output>27_400</output> <gadget id="calculator">27_400 + 6_500</gadget> <output>33_900</output> <gadget id="calculator">39_000 - 33_900</gadget> <output>5_100</output> <result>E</result>

E

A grocer has a sale of Rs. 6400, Rs. 7000, Rs. 6800, Rs. 7200 and Rs. 6500 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?

subtract(multiply(add(5, const_1), 6500), add(add(add(add(6400, 7000), 6800), 7200), 6500))

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

"total sale for 5 months = rs . ( 6400 + 7000 + 6800 + 7200 + 6500 ) = rs . 33900 required sale = rs . [ ( 6500 x 6 ) - 34009 ] = rs . ( 39000 - 33900 ) = rs . 5100 answer : e"

general

math_qa__O7w0svrbLSgY3JZ5

given that a is the average ( arithmetic mean ) of the first 5 positive multiples of 6 and b is the median of the first 12 positive multiples of 6 , what is the ratio of a to b ? Select A) 3 : 4 B) 6 : 13 C) 5 : 6 D) 13 : 10 E) 4 : 3

<gadget id="calculator">5 + 1</gadget> <output>6</output> <gadget id="calculator">6 / 2</gadget> <output>3</output> <gadget id="calculator">3 * 6</gadget> <output>18</output> <gadget id="calculator">12 + 1</gadget> <output>13</output> <gadget id="calculator">13 / 2</gadget> <output>13/2 = around 6.5</output> <gadget id="calculator">(13/2) * 6</gadget> <output>39</output> <gadget id="calculator">18 / 39</gadget> <output>6/13 = around 0.461538</output> <result>B</result>

B

given that a is the average ( arithmetic mean ) of the first 5 positive multiples of 6 and b is the median of the first 12 positive multiples of 6 , what is the ratio of a to b ?

divide(multiply(divide(add(5, const_1), const_2), 6), multiply(divide(add(12, const_1), const_2), 6))

add(n0,const_1)|add(n2,const_1)|divide(#0,const_2)|divide(#1,const_2)|multiply(n1,#2)|multiply(n1,#3)|divide(#4,#5)

the first nine positive multiples of six are { 6 , 12 , 18 , 24,30 } the first twelve positive multiples of six are { 6 , 12 , 18 , 24 , 30 , 36,42 , 48 , 54 , 60 , 66 , 72 } both sets are evenly spaced , thus their median = mean : a = 18 and b = ( 36 + 42 ) / 2 = 39 - - > a / b = 18 / 39 = 6 / 13 . answer : b .

general

math_qa__YGGp4oYvnqqTxD6N

How much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 13 inches than that of a rectangular sheet of paper measuring 6.5 inches by 11 inches? Choose the most appropriate option. A) 50 % B) 87 % C) 100 % D) 187 % E) 200 %

<gadget id="calculator">11 * 13</gadget> <output>143</output> <gadget id="calculator">143 * 2</gadget> <output>286</output> <gadget id="calculator">6.5 * 11</gadget> <output>71.5</output> <gadget id="calculator">71.5 * 2</gadget> <output>143</output> <gadget id="calculator">286 - 143</gadget> <output>143</output> <gadget id="calculator">143 / 143</gadget> <output>1</output> <gadget id="calculator">1 * 100</gadget> <output>100</output> <result>C</result>

C

How much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 13 inches than that of a rectangular sheet of paper measuring 6.5 inches by 11 inches?

multiply(divide(subtract(multiply(rectangle_area(11, 13), const_2), multiply(rectangle_area(6.5, 11), const_2)), rectangle_area(11, 13)), const_100)

rectangle_area(n0,n1)|rectangle_area(n0,n2)|multiply(#0,const_2)|multiply(#1,const_2)|subtract(#2,#3)|divide(#4,#0)|multiply(#5,const_100)

let ' s just look at the dimensions ( no calculation needed ) . with dimension 11 the same , the other dimension 13 is twice 6.5 then the area will be double which means 100 % greater . the answer is c .

geometry

math_qa__1tpblwdeCpkjjGcV

If a sum of money doubles itself in 5 years at simple interest, the ratepercent per annum is Choose one: A) 12 B) 12.5 C) 20 D) 13.5 E) 14

<gadget id="calculator">5 / 100</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">2 / (1/20)</gadget> <output>40</output> <gadget id="calculator">40 / 2</gadget> <output>20</output> <result>C</result>

C

If a sum of money doubles itself in 5 years at simple interest, the ratepercent per annum is

divide(divide(const_2, divide(5, const_100)), const_2)

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

"explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 5 ) = 20 option c"

gain

math_qa__KlseoolHTHD2axPg

Elvin's monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for Internet service. Elvin's total telephone bill for January was $52 and Elvin's total telephone bill for February was 76$. If Elvin's charge for the calls he made in February was twice the charge for the calls he made in January, what is Elvin's fixed monthly charge for Internet service? Choose the most appropriate option. A) $ 5 B) $ 10 C) $ 14 D) $ 28 E) $ 29

<gadget id="calculator">52 * 2</gadget> <output>104</output> <gadget id="calculator">104 - 76</gadget> <output>28</output> <result>D</result>

D

Elvin's monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for Internet service. Elvin's total telephone bill for January was $52 and Elvin's total telephone bill for February was 76$. If Elvin's charge for the calls he made in February was twice the charge for the calls he made in January, what is Elvin's fixed monthly charge for Internet service?

subtract(multiply(52, const_2), 76)

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

"bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 52 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 76 i . e . x + y = 52 and 2 x + y = 76 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 76 - 52 i . e . x = 24 i . e . fixed monthly charge , y = 28 answer : option d"

general

math_qa__kuGOL6R8SCp62mlr

A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3000, A will get: Answers. A) rs . 1200 B) rs . 1500 C) rs . 1800 D) rs . 2000 E) none of these

<gadget id="calculator">15 * 2</gadget> <output>30</output> <gadget id="calculator">30 / 10</gadget> <output>3</output> <gadget id="calculator">30 / 15</gadget> <output>2</output> <gadget id="calculator">3 + 2</gadget> <output>5</output> <gadget id="calculator">3 / 5</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">(3/5) * 3_000</gadget> <output>1_800</output> <result>C</result>

C

A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3000, A will get:

multiply(divide(divide(multiply(15, const_2), 10), add(divide(multiply(15, const_2), 10), divide(multiply(15, const_2), 15))), 3000)

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

"explanation : ratio of working days of a : b = 10 : 15 therefore , their wages ratio = reverse ratio = 15 : 10 therefore , a will get 15 units of ratio total ratio = 25 1 unit of ratio = 3000 / 25 = 120 so , a ’ s amount = 120 × 15 = rs . 1800 . answer : option c"

physics

math_qa__XE220aCsY0tEI9JX

If an object travels 90 feet in 3 seconds, what is the object’s approximate speed in miles per hour? (Note: 1 mile = 5280 feet) Choose the correct choice from the following answers. A) 17.36 B) 20.45 C) 23.87 D) 26.92 E) 29.56

<gadget id="calculator">90 / 5_280</gadget> <output>3/176 = around 0.017045</output> <gadget id="calculator">1 / 3_600</gadget> <output>1/3_600 = around 0.000278</output> <gadget id="calculator">3 * (1/3_600)</gadget> <output>1/1_200 = around 0.000833</output> <gadget id="calculator">(3/176) / (1/1_200)</gadget> <output>225/11 = around 20.454545</output> <result>B</result>

B

If an object travels 90 feet in 3 seconds, what is the object’s approximate speed in miles per hour? (Note: 1 mile = 5280 feet)

divide(divide(90, 5280), multiply(3, divide(1, const_3600)))

divide(n0,n3)|divide(n2,const_3600)|multiply(n1,#1)|divide(#0,#2)|

"90 feet / 3 seconds = 30 feet / second ( 30 feet / second ) * ( 3600 seconds / hour ) * ( 1 mile / 5280 feet ) = 20.45 miles / hour ( approximately ) the answer is b ."

physics

math_qa__VMtsBwnyOt7oIjxX

Of 800 surveyed students, 20% of those who read book A also read book B and 25% of those who read book B also read book A. If each student read at least one of the books, what is the difference between the number of students who read only book A and the number of students who read only book B? Pick A) 20 B) 25 C) 30 D) 55 E) 100

<gadget id="calculator">25 / 100</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(1/4) / (1/5)</gadget> <output>5/4 = around 1.25</output> <gadget id="calculator">(5/4) + 1</gadget> <output>9/4 = around 2.25</output> <gadget id="calculator">(9/4) - (1/4)</gadget> <output>2</output> <gadget id="calculator">800 / 2</gadget> <output>400</output> <gadget id="calculator">400 * (5/4)</gadget> <output>500</output> <gadget id="calculator">1 - (1/5)</gadget> <output>4/5 = around 0.8</output> <gadget id="calculator">500 * (4/5)</gadget> <output>400</output> <gadget id="calculator">1 - (1/4)</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">400 * (3/4)</gadget> <output>300</output> <gadget id="calculator">400 - 300</gadget> <output>100</output> <result>E</result>

E

Of 800 surveyed students, 20% of those who read book A also read book B and 25% of those who read book B also read book A. If each student read at least one of the books, what is the difference between the number of students who read only book A and the number of students who read only book B?

subtract(multiply(multiply(divide(800, subtract(add(divide(divide(25, const_100), divide(20, const_100)), const_1), divide(25, const_100))), divide(divide(25, const_100), divide(20, const_100))), subtract(const_1, divide(20, const_100))), multiply(divide(800, subtract(add(divide(divide(25, const_100), divide(20, const_100)), const_1), divide(25, const_100))), subtract(const_1, divide(25, const_100))))

divide(n2,const_100)|divide(n1,const_100)|divide(#0,#1)|subtract(const_1,#1)|subtract(const_1,#0)|add(#2,const_1)|subtract(#5,#0)|divide(n0,#6)|multiply(#7,#2)|multiply(#7,#4)|multiply(#8,#3)|subtract(#10,#9)|

"say the number of students who read book a is a and the number of students who read book b is b . given that 20 % of those who read book a also read book b and 25 % of those who read book b also read book a , so the number of students who read both books is 0.2 a = 0.25 b - - > a = 1.25 b . since each student read at least one of the books then { total } = { a } + { b } - { both } - - > 800 = 1.25 b + b - 0.25 b - - > b = 400 , a = 1.25 b = 500 and { both } = 0.25 b = 100 . the number of students who read only book a is { a } - { both } = 500 - 100 = 400 ; the number of students who read only book b is { b } - { both } = 400 - 100 = 300 ; the difference is 400 - 300 = 100 . answer : e ."

gain

math_qa__hryhWZ9smHiWqyti

What annual payment will discharge a debt of Rs. 1090 due in 2 years at the rate of 5% compound interest? Choose one: A) 993.2 B) 586.21 C) 534.33 D) 543.33 E) 646.33

<gadget id="calculator">5 / 100</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">(1/20) + 1</gadget> <output>21/20 = around 1.05</output> <gadget id="calculator">(21/20) ** 2</gadget> <output>441/400 = around 1.1025</output> <gadget id="calculator">(441/400) * 1_090</gadget> <output>48_069/40 = around 1_201.725</output> <gadget id="calculator">(48_069/40) / 2</gadget> <output>48_069/80 = around 600.8625</output> <result>B</result>

B

What annual payment will discharge a debt of Rs. 1090 due in 2 years at the rate of 5% compound interest?

divide(multiply(power(add(divide(5, const_100), const_1), 2), 1090), 2)

divide(n2,const_100)|add(#0,const_1)|power(#1,n1)|multiply(n0,#2)|divide(#3,n1)

explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1090 820 x + 1090 * 441 x = 586.21 so , value of each installment = rs . 586.21 answer : option b

gain

math_qa__6Qy4DaFnHaQ6Qk7N

A man sells a car to his friend at 15% loss. If the friend sells it for Rs.54000 and gains 20%, the original C.P.of the car was : Choose the correct option: A) rs . 22941.18 B) rs . 32941.18 C) rs . 52941.18 D) rs . 62941.18 E) none of these

<gadget id="calculator">54_000 * 100</gadget> <output>5_400_000</output> <gadget id="calculator">100 + 20</gadget> <output>120</output> <gadget id="calculator">5_400_000 / 120</gadget> <output>45_000</output> <gadget id="calculator">45_000 * 100</gadget> <output>4_500_000</output> <gadget id="calculator">100 - 15</gadget> <output>85</output> <gadget id="calculator">4_500_000 / 85</gadget> <output>900_000/17 = around 52_941.176471</output> <result>C</result>

C

A man sells a car to his friend at 15% loss. If the friend sells it for Rs.54000 and gains 20%, the original C.P.of the car was :

divide(multiply(divide(multiply(54000, const_100), add(const_100, 20)), const_100), subtract(const_100, 15))

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

"explanation : s . p = rs . 54,000 . gain earned = 20 % c . p = rs . [ 100 / 120 ã — 54000 ] = rs . 45000 this is the price the first person sold to the second at at loss of 15 % . now s . p = rs . 45000 and loss = 15 % c . p . rs . [ 100 / 85 ã — 45000 ] = rs . 52941.18 correct option : c"

gain

math_qa__YnArQUXMwYGZfAwO

The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost? Choices: A) 399 B) 272 C) 666 D) 277 E) 311

<gadget id="calculator">3_136 ** (1/2)</gadget> <output>56</output> <gadget id="calculator">56 * 4</gadget> <output>224</output> <gadget id="calculator">2 * 1</gadget> <output>2</output> <gadget id="calculator">224 - 2</gadget> <output>222</output> <gadget id="calculator">222 * 1</gadget> <output>222</output> <gadget id="calculator">222 * 3</gadget> <output>666</output> <result>C</result>

C

The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?

multiply(multiply(subtract(multiply(sqrt(3136), const_4), multiply(const_2, 1)), 1), 3)

multiply(n3,const_2)|sqrt(n0)|multiply(#1,const_4)|subtract(#2,#0)|multiply(n2,#3)|multiply(#4,n1)|

"answer : option c explanation : a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 â € “ 6 = 666 * 1 = 666 answer : c"

physics

math_qa__ubIzmwWM0hwq0IWP

How many 0's are there in the binary form of 6*1024 + 4*64 + 2 Choose the correct choice from the following answers A) 6 B) 7 C) 8 D) 10 E) 9

<gadget id="calculator">6 + 4</gadget> <output>10</output> <gadget id="calculator">10 - 1</gadget> <output>9</output> <result>E</result>

E

How many 0's are there in the binary form of 6*1024 + 4*64 + 2

subtract(add(6, 4), const_1)

add(n1,n3)|subtract(#0,const_1)

6 * 1024 + 4 * 64 + 2 = 6144 + 256 + 2 = 6402 in binary code 6402 base 10 = 11001 000000 10 in base 2 . so 9 zeros are there . answer : e

general

math_qa__p0EkRAex1QVPXCAh

The mean daily profit made by a shopkeeper in a month of 30 days was Rs. 350. If the mean profit for the first fifteen days was Rs. 225, then the mean profit for the last 15 days would be Pick: A) rs . 200 B) rs . 350 C) rs . 475 D) rs . 425 E) none of these

<gadget id="calculator">30 * 350</gadget> <output>10_500</output> <gadget id="calculator">15 * 225</gadget> <output>3_375</output> <gadget id="calculator">10_500 - 3_375</gadget> <output>7_125</output> <gadget id="calculator">7_125 / 15</gadget> <output>475</output> <result>C</result>

C

The mean daily profit made by a shopkeeper in a month of 30 days was Rs. 350. If the mean profit for the first fifteen days was Rs. 225, then the mean profit for the last 15 days would be

divide(subtract(multiply(30, 350), multiply(15, 225)), 15)

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

"average would be : 350 = ( 225 + x ) / 2 on solving , x = 475 . answer : c"

gain

math_qa__B8kSmBnCNsHXd8ok

Find out the C.I on Rs.8000 at 4% p.a. compound half-yearly for 1 1/2 years Pick one. A) 489.66 B) 406.07 C) 406.04 D) 306.03 E) 306.01

<gadget id="calculator">4 / 100</gadget> <output>1/25 = around 0.04</output> <gadget id="calculator">1 + (1/25)</gadget> <output>26/25 = around 1.04</output> <gadget id="calculator">3 / 2</gadget> <output>3/2 = around 1.5</output> <gadget id="calculator">(26/25) ** (3/2)</gadget> <output>26*sqrt(26)/125 = around 1.060596</output> <gadget id="calculator">8_000 * (26*sqrt(26)/125)</gadget> <output>1664*sqrt(26) = around 8_484.768471</output> <gadget id="calculator">(1664*sqrt(26)) - 8_000</gadget> <output>-8000 + 1664*sqrt(26) = around 484.768471</output> <result>A</result>

A

Find out the C.I on Rs.8000 at 4% p.a. compound half-yearly for 1 1/2 years

subtract(multiply(8000, power(add(1, divide(4, const_100)), divide(const_3, 2))), 8000)

divide(n1,const_100)|divide(const_3,n4)|add(#0,n2)|power(#2,#1)|multiply(n0,#3)|subtract(#4,n0)|

"a = 8000 ( 51 / 50 ) 3 = 8489.66 8000 - - - - - - - - - - - 489.66 answer : a"

general

math_qa__bqlFzseTTJvUNJap

Jayes can eat 25 marshmallows is 20 minutes. Dylan can eat 25 in one hour. In how much time will the two eat 150 marshmallows? Options: A) 40 minutes . B) 1 hour and 30 minutes . C) 1 hour . D) 1 hour and 40 minutes . E) 2 hours and 15 minutes .

<gadget id="calculator">20 / 20</gadget> <output>1</output> <result>C</result>

C

Jayes can eat 25 marshmallows is 20 minutes. Dylan can eat 25 in one hour. In how much time will the two eat 150 marshmallows?

divide(20, 20)

divide(n1,n1)

rate = output / time jayes rate = 25 / 20 = 5 / 4 dylan rate = 25 / 60 = 5 / 12 combined rate = 5 / 4 + 5 / 12 = 20 / 12 combinedrate * combinedtime = combinedoutput 20 / 12 * t = 150 t = 90 mins = > 1 hr 30 min

physics

math_qa__xH4EfUzRXrXhgnU9

How many even number in the range between 10 to 120 inclusive are not divisible by 3 Pick: A) 15 B) 30 C) 31 D) 37 E) 46

<gadget id="calculator">120 - 10</gadget> <output>110</output> <gadget id="calculator">110 - 2</gadget> <output>108</output> <gadget id="calculator">108 / 2</gadget> <output>54</output> <gadget id="calculator">120 - 2</gadget> <output>118</output> <gadget id="calculator">3 * 4</gadget> <output>12</output> <gadget id="calculator">118 - 12</gadget> <output>106</output> <gadget id="calculator">106 - 3</gadget> <output>103</output> <gadget id="calculator">103 - 3</gadget> <output>100</output> <gadget id="calculator">100 / 3</gadget> <output>100/3 = around 33.333333</output> <gadget id="calculator">(100/3) / 2</gadget> <output>50/3 = around 16.666667</output> <gadget id="calculator">54 - (50/3)</gadget> <output>112/3 = around 37.333333</output> <result>D</result>

D

How many even number in the range between 10 to 120 inclusive are not divisible by 3

subtract(divide(subtract(subtract(120, 10), const_2), const_2), divide(divide(subtract(subtract(subtract(subtract(120, const_2), multiply(3, const_4)), 3), 3), 3), const_2))

multiply(n2,const_4)|subtract(n1,n0)|subtract(n1,const_2)|subtract(#1,const_2)|subtract(#2,#0)|divide(#3,const_2)|subtract(#4,n2)|subtract(#6,n2)|divide(#7,n2)|divide(#8,const_2)|subtract(#5,#9)|

"we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 10 , 12,14 . . . 120 using ap formula , we can say 120 = 10 + ( n - 1 ) * 2 or n = 56 . for 6 , 12,18 , . . . 120 using ap formula , we can say 120 = 12 + ( n - 1 ) * 6 or n = 19 . hence , only divisible by 2 but not 3 = 56 - 19 = 37 . hence , answer d"

general

math_qa__oy6rNcQTrdogWXFg

In the biology lab of "Jefferson" High School there are 0.037*10^5 germs, equally divided among 74000*10^(-3) Petri dishes. How many germs live happily in a single dish? Choose the correct choice from the following choices: A) 10 B) 20 C) 30 D) 40 E) 50

<gadget id="calculator">1_000 * 100</gadget> <output>100_000</output> <gadget id="calculator">100_000 * 0.037</gadget> <output>3_700</output> <gadget id="calculator">74_000 / 1_000</gadget> <output>74</output> <gadget id="calculator">3_700 / 74</gadget> <output>50</output> <result>E</result>

E

In the biology lab of "Jefferson" High School there are 0.037*10^5 germs, equally divided among 74000*10^(-3) Petri dishes. How many germs live happily in a single dish?

divide(multiply(multiply(const_1000, const_100), 0.037), divide(74000, const_1000))

divide(n3,const_1000)|multiply(const_100,const_1000)|multiply(n0,#1)|divide(#2,#0)

0.037 * 10 ^ 5 can be written as 3700 74000 * 10 ^ ( - 3 ) can be written as 74 required = 3700 / 74 = 50 answer : e

general

math_qa__darbneVkTr4SKZiO

If a certain number is divided by 2, the quotient, dividend, and divisor, added together, will amount to 62. What is the number? Answers: A) 18 B) 28 C) 40 D) 38 E) 59

<gadget id="calculator">62 - 2</gadget> <output>60</output> <gadget id="calculator">60 * 2</gadget> <output>120</output> <gadget id="calculator">2 + 1</gadget> <output>3</output> <gadget id="calculator">120 / 3</gadget> <output>40</output> <result>C</result>

C

If a certain number is divided by 2, the quotient, dividend, and divisor, added together, will amount to 62. What is the number?

divide(multiply(subtract(62, 2), 2), add(2, const_1))

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

"let x = the number sought . then x / 2 + x + 2 = 62 . x = 40 . c"

general

math_qa__2yF0nwfqzYpxC2xB

For the symbol, m”n=n^2−m for all values of m and n. What is the value of 4”2? Choose the correct answer: A) 5 B) 3 C) 2 D) 1 E) 0

<gadget id="calculator">2 ** 2</gadget> <output>4</output> <gadget id="calculator">4 - 4</gadget> <output>0</output> <result>E</result>

E

For the symbol, m”n=n^2−m for all values of m and n. What is the value of 4”2?

subtract(power(2, 2), 4)

power(n2,n0)|subtract(#0,n1)|

"4 ” 2 = 4 - 4 = 0 answer : e"

general

math_qa__xcXUzaFmEjqB1vac

In an office in Singapore there are 60% female employees. 50 % of all the male employees are computer literate. If there are total 62% employees computer literate out of total 1100 employees, then the no. of female employees who are computer literate ? Choose the correct choice from the following options A) 462 B) 674 C) 672 D) 960 E) none

<gadget id="calculator">62 / 100</gadget> <output>31/50 = around 0.62</output> <gadget id="calculator">60 / 100</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">50 / 100</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">(2/5) * (1/2)</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(31/50) - (1/5)</gadget> <output>21/50 = around 0.42</output> <gadget id="calculator">(21/50) * 1_100</gadget> <output>462</output> <result>A</result>

A

In an office in Singapore there are 60% female employees. 50 % of all the male employees are computer literate. If there are total 62% employees computer literate out of total 1100 employees, then the no. of female employees who are computer literate ?

multiply(subtract(divide(62, const_100), multiply(subtract(const_1, divide(60, const_100)), divide(50, const_100))), 1100)

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

"solution : total employees , = 1100 female employees , 60 % of 1100 . = ( 60 * 1100 ) / 100 = 660 . then male employees , = 440 50 % of male are computer literate , = 220 male computer literate . 62 % of total employees are computer literate , = ( 62 * 1100 ) / 100 = 682 computer literate . thus , female computer literate = 682 - 220 = 462 . answer : option a"

gain

math_qa__SjivbYA692eQkpAg

total 48 matches are conducted in Knockout match type. How many players will be participated in that tournament? Pick A) 48 B) 47 C) 40 D) 42 E) 47

<gadget id="calculator">48 + 1</gadget> <output>49</output> <result>E</result>

E

total 48 matches are conducted in Knockout match type. How many players will be participated in that tournament?

add(48, const_1)

add(n0,const_1)|

"47 players answer : e"

general

math_qa__Y2N6OvZdrF0KilQh

In 130 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by: Choose the correct answer: A) 20 m B) 25 m C) 22.5 m D) 26 m E) 12 m

<gadget id="calculator">130 / 45</gadget> <output>26/9 = around 2.888889</output> <gadget id="calculator">45 - 36</gadget> <output>9</output> <gadget id="calculator">(26/9) * 9</gadget> <output>26</output> <result>D</result>

D

In 130 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:

multiply(divide(130, 45), subtract(45, 36))

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

"distance covered by b in 9 sec . = 130 / 45 x 9 m = 26 m . a beats b by 26 metres . answer : option d"

physics

math_qa__F5GdAfHGd0rS8nAY

At a certain university, 69% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women, tenured, or both, then what percent of the men are tenured? Choices A) 25 B) 37.5 C) 50 D) 52.5 E) 75

<gadget id="calculator">100 - 69</gadget> <output>31</output> <gadget id="calculator">90 - 69</gadget> <output>21</output> <gadget id="calculator">31 + 21</gadget> <output>52</output> <result>D</result>

D

At a certain university, 69% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women, tenured, or both, then what percent of the men are tenured?

add(subtract(const_100, 69), subtract(90, 69))

subtract(const_100,n0)|subtract(n2,n0)|add(#0,#1)|

"answer is 75 % total women = 69 % total men = 40 % total tenured = 70 % ( both men and women ) therefore , women tenured + women professors + men tenured = 90 % men tenured = 21 % but question wants to know the percent of men that are tenured 21 % / 40 % = 52.5 % d"

gain

math_qa__lJ9nIP8ZDn7WEycS

In a dairy farm, 26 cows eat 26 bags of husk in 26 days. In how many days one cow will eat one bag of husk? Choose the correct choice from the following. A) 1 B) 40 C) 20 D) 26 E) 30

<gadget id="calculator">26 / 26</gadget> <output>1</output> <gadget id="calculator">1 * 26</gadget> <output>26</output> <result>D</result>

D

In a dairy farm, 26 cows eat 26 bags of husk in 26 days. In how many days one cow will eat one bag of husk?

multiply(divide(26, 26), 26)

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

"explanation : one bag of husk = 26 cows per day ⇒ 26 × 1 × 26 = 1 × 26 × x for one cow = 26 days answer : d"

physics

math_qa__Pgw2QAXdKxHE0L5R

The average age of a group of n people is 14 years old. One more person aged 34 joins the group and the new average is 16 years old. What is the value of n? Choose the correct choice from the following choices: A) 7 B) 8 C) 9 D) 10 E) 11

<gadget id="calculator">34 - 16</gadget> <output>18</output> <gadget id="calculator">16 - 14</gadget> <output>2</output> <gadget id="calculator">18 / 2</gadget> <output>9</output> <result>C</result>

C

The average age of a group of n people is 14 years old. One more person aged 34 joins the group and the new average is 16 years old. What is the value of n?

divide(subtract(34, 16), subtract(16, 14))

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

"14 n + 34 = 16 ( n + 1 ) 2 n = 18 n = 9 the answer is c ."

general

math_qa__8qbs3XvsKxqCLfa9

The number 0.650 is how much greater than 1/8 ? Choose the most appropriate option A) ½ B) 21 / 40 C) 1 / 50 D) 1 / 500 E) 2 / 500

<gadget id="calculator">1 / 8</gadget> <output>1/8 = around 0.125</output> <gadget id="calculator">0.65 - (1/8)</gadget> <output>0.525</output> <result>B</result>

B

The number 0.650 is how much greater than 1/8 ?

subtract(0.650, divide(1, 8))

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

"let x be the difference then . 65 - 1 / 8 = x 65 / 100 - 1 / 8 = x x = 21 / 40 ans b"

general

math_qa__DMtu5mzEcmkbMkfT

1000 men have provisions for 17 days. If 500 more men join them, for how many days will the provisions last now? Choose the correct choice from the following answers: A) 12.9 B) 12.5 C) 11.3 D) 12.2 E) 12.1

<gadget id="calculator">17 * 1_000</gadget> <output>17_000</output> <gadget id="calculator">1_000 + 500</gadget> <output>1_500</output> <gadget id="calculator">17_000 / 1_500</gadget> <output>34/3 = around 11.333333</output> <result>C</result>

C

1000 men have provisions for 17 days. If 500 more men join them, for how many days will the provisions last now?

divide(multiply(17, 1000), add(1000, 500))

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

"1000 * 17 = 1500 * x x = 11.3 answer : c"

physics

math_qa__gRF4Gv1gaaxbAxVq

If x is an integer such that 0 < x < 7, 0 < x < 15, 5 > x > –1, 3 > x > 0, and x + 2 < 4, then x is Choose the correct answer: A) 1 B) 2 C) 3 D) 4 E) 5

<gadget id="calculator">5 - 2</gadget> <output>3</output> <gadget id="calculator">3 - 2</gadget> <output>1</output> <result>A</result>

A

If x is an integer such that 0 < x < 7, 0 < x < 15, 5 > x > –1, 3 > x > 0, and x + 2 < 4, then x is

subtract(subtract(5, 2), 2)

subtract(n4,n8)|subtract(#0,n8)|

"0 < x < 7 , 0 < x < 15 , 5 > x > – 1 3 > x > 0 x < 2 from above : 0 < x < 2 - - > x = 1 . answer : a ."

general

math_qa__0F7jXogePve1bEZn

An error 5% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is: Choices: A) 10.01 B) 9.25 C) 10.25 D) 8.25 E) 6.25

<gadget id="calculator">100 + 5</gadget> <output>105</output> <gadget id="calculator">105 ** 2</gadget> <output>11_025</output> <gadget id="calculator">100 ** 2</gadget> <output>10_000</output> <gadget id="calculator">11_025 - 10_000</gadget> <output>1_025</output> <gadget id="calculator">1_025 * 100</gadget> <output>102_500</output> <gadget id="calculator">102_500 / 10_000</gadget> <output>41/4 = around 10.25</output> <result>C</result>

C

An error 5% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:

divide(multiply(subtract(square_area(add(const_100, 5)), 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)|

"explanation : 100 cm is read as 105 cm . a 1 = ( 100 × 100 ) cm 2 = 10000 and a 2 = ( 105 × 105 ) cm 2 = 10816 ( a 2 - a 1 ) = 11025 - 10000 = 1025 = > 1025 / 10000 * 100 = 10.25 answer : c"

gain

math_qa__cVY49wrls8C6sej1

Rahul can do a work in 3 days while Rajesh can do the same work in 2days. Both of them finish the work together and get $150. What is the share of Rahul? Select the correct option: A) $ 50 B) $ 40 C) $ 60 D) $ 100 E) $ 90

<gadget id="calculator">3 + 2</gadget> <output>5</output> <gadget id="calculator">2 / 5</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">(2/5) * 150</gadget> <output>60</output> <result>C</result>

C

Rahul can do a work in 3 days while Rajesh can do the same work in 2days. Both of them finish the work together and get $150. What is the share of Rahul?

multiply(divide(2, add(3, 2)), 150)

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

"rahul ' s wages : rajesh ' s wages = 1 / 3 : 1 / 2 = 2 : 3 rahul ' s share = 150 * 2 / 5 = $ 60 answer is c"

physics

math_qa__hPwxcyf4rdFaJrnH

A boat M leaves shore A and at the same time boat B leaves shore B. They move across the river. They met at 500 yards away from A and after that they met 300 yards away from shore B without halting at shores. Find the distance between the shore A & B Choose the correct choice from the following choices: A) 1000 yards B) 1200 yards C) 1400 yards D) 1600 yards E) 1800 yards

<gadget id="calculator">300 * 4</gadget> <output>1_200</output> <result>B</result>

B

A boat M leaves shore A and at the same time boat B leaves shore B. They move across the river. They met at 500 yards away from A and after that they met 300 yards away from shore B without halting at shores. Find the distance between the shore A & B

multiply(300, const_4)

multiply(n1,const_4)

if x is the distance , a is speed of a and b is speed of b , then ; 500 / a = ( x - 500 ) / b and ( x + 300 ) / a = ( 2 x - 300 ) / b , solving it , we get x = 1200 yards answer : b

physics

math_qa__z282Ddo47MjLQchn

A pineapple costs Rs 7 each and a watermelon costs Rs. 5 each. If I spend Rs 38 on total what is the number of pineapple I purchased? Options: A) 7 B) 6 C) 5 D) 2 E) 3

<gadget id="calculator">4 * 7</gadget> <output>28</output> <gadget id="calculator">38 - 28</gadget> <output>10</output> <gadget id="calculator">10 / 5</gadget> <output>2</output> <result>D</result>

D

A pineapple costs Rs 7 each and a watermelon costs Rs. 5 each. If I spend Rs 38 on total what is the number of pineapple I purchased?

divide(subtract(38, multiply(const_4, 7)), 5)

multiply(n0,const_4)|subtract(n2,#0)|divide(#1,n1)

explanation : the equation for this problem can be made as : 5 x + 7 y = 38 where x is the number of watermelons and y is the number of pineapples . now test for 2 , 3 and 4 : for y = 2 5 x + 14 = 38 x is not an integer for y = 3 5 x = 17 x not an integer for y = 4 x = 2 so 4 pineapples and 2 watermelons can be bought by 38 rs . answer : d

general

math_qa__tcH2neHDHY2R41vd

The sub-duplicate ratio of 25:16 is Choose the correct choice: A) 4 : 3 B) 1 : 2 C) 1 : 3 D) 5 : 4 E) 2 : 3

<gadget id="calculator">25 ** (1/2)</gadget> <output>5</output> <gadget id="calculator">16 ** (1/2)</gadget> <output>4</output> <gadget id="calculator">5 / 4</gadget> <output>5/4 = around 1.25</output> <result>D</result>

D

The sub-duplicate ratio of 25:16 is

divide(sqrt(25), sqrt(16))

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

"root ( 25 ) : root ( 16 ) = 5 : 4 answer : d"

other

math_qa__fqQH0eP3DIeR9x98

Ajay can ride 50km in 1 hour. In how many hours he can ride 1250km? Choose the correct option. A) 10 hrs B) 15 hrs C) 20 hrs D) 25 hrs E) 18 hrs

<gadget id="calculator">1_250 / 50</gadget> <output>25</output> <result>D</result>

D

Ajay can ride 50km in 1 hour. In how many hours he can ride 1250km?

divide(1250, 50)

divide(n2,n0)|

"1 hour he ride 50 km he ride 1250 km in = 1250 / 50 * 1 = 25 hours answer is d"

physics

math_qa__SDKzS0qxXtEQtuNO

In a division, a student took 87 as divisor instead of 36. his answer was 24 . The correct answer is- Choose the most appropriate option A) 42 B) 32 C) 48 D) 28 E) 58

<gadget id="calculator">87 * 24</gadget> <output>2_088</output> <gadget id="calculator">2_088 / 36</gadget> <output>58</output> <result>E</result>

E

In a division, a student took 87 as divisor instead of 36. his answer was 24 . The correct answer is-

divide(multiply(87, 24), 36)

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

x / 87 = 24 . x = 24 * 87 . so correct answer would be , ( 24 * 87 ) / 36 = 58 . answer : e

general

math_qa__TkN1cma7sDLGceu9

What is the measure of the angle W made by the diagonals of the any adjacent sides of a cube. Choose the correct choice from the following answers A) 30 B) 45 C) 60 D) 75 E) 90

<gadget id="calculator">180 / 3</gadget> <output>60</output> <result>C</result>

C

What is the measure of the angle W made by the diagonals of the any adjacent sides of a cube.

divide(const_180, const_3)

divide(const_180,const_3)|

"c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be 60 . c"

geometry

math_qa__3iBmnKmFgAMz1SSk

What is the compound interest paid on a sum of Rs.6000 for the period of 2 years at 10% per annum. Choose the correct choice from the following options: A) 1260 B) 1320 C) 1200 D) 1250 E) none of these

<gadget id="calculator">10 / 100</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">1 + (1/10)</gadget> <output>11/10 = around 1.1</output> <gadget id="calculator">(11/10) ** 2</gadget> <output>121/100 = around 1.21</output> <gadget id="calculator">6_000 * (121/100)</gadget> <output>7_260</output> <gadget id="calculator">7_260 - 6_000</gadget> <output>1_260</output> <result>A</result>

A

What is the compound interest paid on a sum of Rs.6000 for the period of 2 years at 10% per annum.

subtract(multiply(6000, power(add(const_1, divide(10, const_100)), const_2)), 6000)

divide(n2,const_100)|add(#0,const_1)|power(#1,const_2)|multiply(n0,#2)|subtract(#3,n0)

solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 6000 = 6000 * ( 21 / 100 ) = 1260 answer a

gain

math_qa__jparbxYfgYhOkkmA

Find the compound ratio of (1:2), (2:3) and (3:4) is Choose the correct choice: A) 1 : 2 B) 3 : 5 C) 5 : 7 D) 1 : 4 E) 2 : 1

<gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">2 / 2</gadget> <output>1</output> <gadget id="calculator">(1/2) * 1</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">(1/2) * (1/2)</gadget> <output>1/4 = around 0.25</output> <result>D</result>

D

Find the compound ratio of (1:2), (2:3) and (3:4) is

multiply(divide(1, 2), multiply(divide(1, 2), divide(2, 2)))

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

"required ratio = 1 / 2 * 2 / 3 * 3 / 4 = 1 / 4 = 1 : 4 answer is d"

other

math_qa__k04ADv7gVEQXJj3V

If 1 is added to the denominator of fraction, the fraction becomes 1/2. If 1 is added to the numerator, the fraction becomes 1. The fraction is Options: A) 4 / 7 B) 5 / 9 C) 2 / 3 D) 10 / 11 E) none of these

<gadget id="calculator">1 + 1</gadget> <output>2</output> <gadget id="calculator">2 + 1</gadget> <output>3</output> <gadget id="calculator">2 / 3</gadget> <output>2/3 = around 0.666667</output> <result>C</result>

C

If 1 is added to the denominator of fraction, the fraction becomes 1/2. If 1 is added to the numerator, the fraction becomes 1. The fraction is

divide(add(1, 1), add(2, 1))

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

explanation : let the required fraction be a / b . then ⇒ a / b + 1 = 1 / 2 ⇒ 2 a – b = 1 - - - - ( 1 ) ⇒ a + 1 / b = 1 ⇒ a – b = – 1 ⇒ a – b = – 1 - - - - - - - ( 2 ) solving ( 1 ) & ( 2 ) we get a = 2 , b = 3 fraction = a / b = 2 / 3 correct option : c

general

math_qa__FWxolP4IU8a2FKAe

if the ratio of two number is 2:3 and LCM of the number is 120 then what is the number. Choose the correct option: A) 15 B) 20 C) 25 D) 30 E) 35

<gadget id="calculator">2 * 3</gadget> <output>6</output> <gadget id="calculator">120 / 6</gadget> <output>20</output> <result>B</result>

B

if the ratio of two number is 2:3 and LCM of the number is 120 then what is the number.

divide(120, multiply(2, 3))

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

"product of two no = lcm * hcf 2 x * 3 x = 120 * x x = 20 answer : b"

other

math_qa__zUJiYJtnSyKjmui0

Find out the C.I on Rs.4000 at 4% p.a. compound half-yearly for 1 1/2 years Choose the most appropriate option: A) 244.83 B) 306.07 C) 306.04 D) 306.03 E) 306.01

<gadget id="calculator">4 / 100</gadget> <output>1/25 = around 0.04</output> <gadget id="calculator">1 + (1/25)</gadget> <output>26/25 = around 1.04</output> <gadget id="calculator">3 / 2</gadget> <output>3/2 = around 1.5</output> <gadget id="calculator">(26/25) ** (3/2)</gadget> <output>26*sqrt(26)/125 = around 1.060596</output> <gadget id="calculator">4_000 * (26*sqrt(26)/125)</gadget> <output>832*sqrt(26) = around 4_242.384235</output> <gadget id="calculator">(832*sqrt(26)) - 4_000</gadget> <output>-4000 + 832*sqrt(26) = around 242.384235</output> <result>A</result>

A

Find out the C.I on Rs.4000 at 4% p.a. compound half-yearly for 1 1/2 years

subtract(multiply(4000, power(add(1, divide(4, const_100)), divide(const_3, 2))), 4000)

divide(n1,const_100)|divide(const_3,n4)|add(#0,n2)|power(#2,#1)|multiply(n0,#3)|subtract(#4,n0)|

"a = 4000 ( 51 / 50 ) 3 = 4244.832 4000 - - - - - - - - - - - 244.83 answer : a"

general

math_qa__ZSpof40fQGagoraz

Bert and Rebecca were looking at the price of a condominium. The price of the condominium was 40% more than Bert had in savings, and separately, the same price was also 75% more than Rebecca had in savings. What is the ratio of what Bert has in savings to what Rebecca has in savings. Choices: A) 1 : 4 B) 4 : 1 C) 2 : 3 D) 3 : 2 E) 5 : 4

<gadget id="calculator">100 + 40</gadget> <output>140</output> <gadget id="calculator">100 / 140</gadget> <output>5/7 = around 0.714286</output> <gadget id="calculator">100 + 75</gadget> <output>175</output> <gadget id="calculator">100 / 175</gadget> <output>4/7 = around 0.571429</output> <gadget id="calculator">(5/7) / (4/7)</gadget> <output>5/4 = around 1.25</output> <result>E</result>

E

Bert and Rebecca were looking at the price of a condominium. The price of the condominium was 40% more than Bert had in savings, and separately, the same price was also 75% more than Rebecca had in savings. What is the ratio of what Bert has in savings to what Rebecca has in savings.

divide(divide(const_100, add(const_100, 40)), divide(const_100, add(const_100, 75)))

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

suppose bert had 100 so price becomes 140 , this 140 = 1.75 times r ' s saving . . so r ' s saving becomes 80 so required ratio is 100 : 80 = 5 : 4 answer : e

gain

math_qa__tOrcs8d3CZ5iLUIQ

Walking at 5/6 of her normal speed, a worker is 12 minutes later than usual in reaching her office. The usual time (in minutes) taken by her to cover the distance between her home and her office is Choose the correct choice: A) 36 B) 42 C) 48 D) 54 E) 60

<gadget id="calculator">5 * 12</gadget> <output>60</output> <result>E</result>

E

Walking at 5/6 of her normal speed, a worker is 12 minutes later than usual in reaching her office. The usual time (in minutes) taken by her to cover the distance between her home and her office is

multiply(5, 12)

multiply(n0,n2)|

"let v be her normal speed and let t be her normal time . d = ( 5 / 6 ) v * ( t + 12 ) since the distance is the same we can equate this to a regular day which is d = v * t v * t = ( 5 / 6 ) v * ( t + 12 ) t / 6 = 10 t = 60 the answer is e ."

physics

math_qa__TPGg21GEarsPGlqA

If 12 lions can kill 12 deers in 12 minutes how long will it take 100 lions to kill 100 deers? Choose the correct choice: A) 1 minutes B) 12 minute C) 120 minutes D) 10000 minutes E) 1000 minutes

<gadget id="calculator">12 / 12</gadget> <output>1</output> <gadget id="calculator">1 * 12</gadget> <output>12</output> <result>B</result>

B

If 12 lions can kill 12 deers in 12 minutes how long will it take 100 lions to kill 100 deers?

multiply(divide(12, 12), 12)

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

"we can try the logic of time and work , our work is to kill the deers so 12 ( lions ) * 12 ( min ) / 12 ( deers ) = 100 ( lions ) * x ( min ) / 100 ( deers ) hence answer is x = 12 answer : b"

physics

math_qa__rzBmw5Q8xgHGyGTs

A man cycling along the road noticed that every 18 minutes a bus overtakes him and every 6 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses? Select: A) 5 minutes B) 6 minutes C) 8 minutes D) 9 minutes E) 10 minutes

<gadget id="calculator">6 + 18</gadget> <output>24</output> <gadget id="calculator">18 - 6</gadget> <output>12</output> <gadget id="calculator">24 / 12</gadget> <output>2</output> <gadget id="calculator">18 / 2</gadget> <output>9</output> <gadget id="calculator">18 - 9</gadget> <output>9</output> <gadget id="calculator">9 / 1</gadget> <output>9</output> <result>D</result>

D

A man cycling along the road noticed that every 18 minutes a bus overtakes him and every 6 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?

divide(subtract(18, divide(18, divide(add(6, 18), subtract(18, 6)))), const_1)

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

let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 18 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 18 , d = 18 b - 18 c ; every 6 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 6 , d = 6 b + 6 c ; d = 18 b - 18 c = 6 b + 6 c , - - > b = 2 c , - - > d = 18 b - 9 b = 9 b . interval = \ frac { d } { b } = \ frac { 9 b } { b } = 9 answer : d ( 9 minutes ) .

physics

math_qa__Od89B7h7D9VzSK1C

the hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 15 miles per hour. the cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate, how many minutes must the cyclist wait until the hiker catches up? Choose the correct option: A) 20 B) 55 / 4 C) 25 D) 14 E) 13

<gadget id="calculator">15 - 4</gadget> <output>11</output> <gadget id="calculator">5 / 60</gadget> <output>1/12 = around 0.083333</output> <gadget id="calculator">11 * (1/12)</gadget> <output>11/12 = around 0.916667</output> <gadget id="calculator">(11/12) / 4</gadget> <output>11/48 = around 0.229167</output> <gadget id="calculator">(11/48) * 60</gadget> <output>55/4 = around 13.75</output> <result>B</result>

B

the hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 15 miles per hour. the cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate, how many minutes must the cyclist wait until the hiker catches up?

multiply(divide(multiply(subtract(15, 4), divide(5, const_60)), 4), const_60)

divide(n2,const_60)|subtract(n1,n0)|multiply(#0,#1)|divide(#2,n0)|multiply(#3,const_60)|

"after passing the hiker the cyclist travels for 5 minutes at a rate of 15 miles / hour . in those 5 mins the cyclist travels a distance of 5 / 4 miles . in those 5 mins the hiker travels a distance of 1 / 3 miles . so the hiker still has to cover 11 / 12 miles to meet the waiting cyclist . the hiker will need 55 / 4 mins to cover the remaining 11 / 12 miles . so the answer is b ."

physics

math_qa__rbDJ4jJ0MrKn7lDo

If x+y=10, x-y=18, for integers of x and y, x=? Select: A) 14 B) 15 C) 25 D) 13 E) 42

<gadget id="calculator">10 + 18</gadget> <output>28</output> <gadget id="calculator">28 / 2</gadget> <output>14</output> <result>A</result>

A

If x+y=10, x-y=18, for integers of x and y, x=?

divide(add(10, 18), const_2)

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

x + y = 10 x - y = 18 2 x = 28 x = 14 answer is a

general

math_qa__E9G35VW73rC4NFgP

Find the least number must be subtracted from 964807 so that remaining no.is divisible by 8? Choose the correct choice from the following answers A) 7 B) 6 C) 5 D) 4 E) 3

<gadget id="calculator">964_807 / 8</gadget> <output>964_807/8 = around 120_600.875</output> <gadget id="calculator">floor(964_807/8)</gadget> <output>120_600</output> <gadget id="calculator">120_600 * 8</gadget> <output>964_800</output> <gadget id="calculator">964_807 - 964_800</gadget> <output>7</output> <result>A</result>

A

Find the least number must be subtracted from 964807 so that remaining no.is divisible by 8?

subtract(964807, multiply(floor(divide(964807, 8)), 8))

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

"on dividing 964807 by 15 we get the remainder 7 , so 7 should be subtracted a"

general

math_qa__OofC8e71KpRnyYNn

if 8 people take an hour to complete a piece of work, then how long should 16 people will take to complete the same piece of work? Choose the correct choice from the following answers. A) 15 min B) 30 min C) 26 min D) 28 min E) 18 min

<gadget id="calculator">8 / 16</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">(1/2) * 60</gadget> <output>30</output> <result>B</result>

B

if 8 people take an hour to complete a piece of work, then how long should 16 people will take to complete the same piece of work?

multiply(divide(8, 16), const_60)

divide(n0,n1)|multiply(#0,const_60)

if 8 people take an hour to complete a piece of work , then 16 people will take 8 * 60 / 16 = 30 mins to complete the same piece of work . answer : b

physics

math_qa__gAHsWRY1iEBOoIIo

Find the area of a parallelogram with base 25 cm and height 15 cm? Choose the correct option. A) 295 cm 2 B) 385 cm 2 C) 275 cm 2 D) 375 cm 2 E) 285 cm 2

<gadget id="calculator">25 * 15</gadget> <output>375</output> <result>D</result>

D

Find the area of a parallelogram with base 25 cm and height 15 cm?

multiply(25, 15)

multiply(n0,n1)|

"area of a parallelogram = base * height = 25 * 15 = 375 cm 2 answer : d"

geometry

math_qa__nWiEtUYXuwMGFUh1

In a certain company, a third of the workers do not have a retirement plan.60% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women? Pick one: A) 80 B) 95 C) 180 D) 120 E) 210

<gadget id="calculator">1 / 3</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">60 / 100</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">(1/3) * (3/5)</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(1/3) - (1/5)</gadget> <output>2/15 = around 0.133333</output> <gadget id="calculator">1 - (1/3)</gadget> <output>2/3 = around 0.666667</output> <gadget id="calculator">40 / 100</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">(2/3) * (2/5)</gadget> <output>4/15 = around 0.266667</output> <gadget id="calculator">(2/15) + (4/15)</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">120 / (2/5)</gadget> <output>300</output> <gadget id="calculator">(2/3) - (4/15)</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">(1/5) + (2/5)</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">300 * (3/5)</gadget> <output>180</output> <result>C</result>

C

In a certain company, a third of the workers do not have a retirement plan.60% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?

multiply(divide(120, add(subtract(divide(const_1, const_3), multiply(divide(const_1, const_3), divide(60, const_100))), multiply(subtract(const_1, divide(const_1, const_3)), divide(40, const_100)))), add(multiply(divide(const_1, const_3), divide(60, const_100)), subtract(subtract(const_1, divide(const_1, const_3)), multiply(subtract(const_1, divide(const_1, const_3)), divide(40, const_100)))))

divide(const_1,const_3)|divide(n0,const_100)|divide(n1,const_100)|multiply(#0,#1)|subtract(const_1,#0)|multiply(#2,#4)|subtract(#0,#3)|add(#5,#6)|subtract(#4,#5)|add(#3,#8)|divide(n2,#7)|multiply(#9,#10)|

"set up equation : x = total number of workers 120 = 0,4 * 2 / 3 * x + 0,4 * 1 / 3 * x 120 = 12 / 30 x x = 300 300 - 120 = 180 answer c"

gain

math_qa__nYEzu7Y8qNw4HMSZ

A bus started its journey from Mumbai and reached Pune in 65 min with its average speed of 60km/hr. If the average speed of the bus is increased by 5 km/hr, how much time will it take to cover the same distance? Choices: A) 2 hrs B) 3 hrs C) 1 hrs D) 1 1 / 2 hrs E) 2 1 / 2 hrs

<gadget id="calculator">65 / 60</gadget> <output>13/12 = around 1.083333</output> <gadget id="calculator">60 * (13/12)</gadget> <output>65</output> <gadget id="calculator">60 + 5</gadget> <output>65</output> <gadget id="calculator">65 / 65</gadget> <output>1</output> <result>C</result>

C

A bus started its journey from Mumbai and reached Pune in 65 min with its average speed of 60km/hr. If the average speed of the bus is increased by 5 km/hr, how much time will it take to cover the same distance?

divide(multiply(60, divide(65, 60)), add(60, 5))

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

sol . distance between ramgarh and devgarh = ( 60 * 65 ) / 60 = 60 average speed of the bus is increased by 5 km / hr then the speed of the bus = 60 km / hr required time = 60 / 60 = 1 hr c

general

math_qa__SyZK2WykQ5lRLV3d

The mean of 50 observations is 200. But later he found that there is decrements of 47 from each observations. what is the the updated mean is ? Answers: A) 165 B) 185 C) 153 D) 198 E) 199

<gadget id="calculator">200 - 47</gadget> <output>153</output> <result>C</result>

C

The mean of 50 observations is 200. But later he found that there is decrements of 47 from each observations. what is the the updated mean is ?

subtract(200, 47)

subtract(n1,n2)|

"153 answer is c"

general

math_qa__qwSaFd0Tv65jewvT

How many 1/2s are there in 37 1/2? Choose the correct choice from the following answers: A) 75 B) 150 C) 300 D) 600 E) 700

<gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">37 + (1/2)</gadget> <output>75/2 = around 37.5</output> <gadget id="calculator">(75/2) / (1/2)</gadget> <output>75</output> <result>A</result>

A

How many 1/2s are there in 37 1/2?

divide(add(37, divide(1, 2)), divide(1, 2))

divide(n0,n4)|divide(n0,n1)|add(n2,#0)|divide(#2,#1)|

"required number = ( 75 / 2 ) / ( 1 / 2 ) = ( 75 / 2 x 2 / 1 ) = 75 answer : a"

general

math_qa__Ku4Zf5vyuQ0NAXX4

A, B, C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 175, then how much amount should C pay as his share of rent? Choose one. A) 23 B) 45 C) 15 D) 28 E) 18

<gadget id="calculator">3 * 15</gadget> <output>45</output> <result>B</result>

B

A, B, C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 175, then how much amount should C pay as his share of rent?

multiply(3, 15)

multiply(n4,n5)

a : b : c = 10 * 7 : 12 * 5 : 15 * 3 = 2 * 7 : 12 * 1 : 3 * 3 = 14 : 12 : 9 amount that c should pay = 175 * ( 9 / 35 ) = 5 * 9 = 45 answer is b

general

math_qa__XYUwGmGvHHlFwzqn

In a box of 12 pens, a total of 6 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective? Choose the correct choice from the following A) 1 / 6 B) 5 / 22 C) 6 / 11 D) 9 / 16 E) 3 / 4

<gadget id="calculator">12 - 6</gadget> <output>6</output> <gadget id="calculator">6 / 12</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">6 - 1</gadget> <output>5</output> <gadget id="calculator">12 - 1</gadget> <output>11</output> <gadget id="calculator">5 / 11</gadget> <output>5/11 = around 0.454545</output> <gadget id="calculator">(1/2) * (5/11)</gadget> <output>5/22 = around 0.227273</output> <result>B</result>

B

In a box of 12 pens, a total of 6 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?

multiply(divide(subtract(12, 6), 12), divide(subtract(subtract(12, 6), const_1), subtract(12, const_1)))

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

"method - 1 there are 9 fine pieces of pen and 6 defective in a lot of 12 pens i . e . probability of first pen not being defective = ( 6 / 12 ) i . e . probability of second pen not being defective = ( 5 / 11 ) [ 11 pen remaining with 5 defective remaining considering that first was defective ] probability of both pen being non - defective = ( 6 / 12 ) * ( 5 / 11 ) = 5 / 22 answer : option b"

general

math_qa__42fGD3yjmhh1ZK1a

If a randomly selected non-negative single digit integer is added to {2, 3, 5, 8}. What is the probability that the median of the set will increase but the range still remains the same? Choose the correct choice from the following answers: A) 0.2 B) 0.3 C) 0.4 D) 0.5 E) 0.6

<gadget id="calculator">4 / 10</gadget> <output>2/5 = around 0.4</output> <result>C</result>

C

If a randomly selected non-negative single digit integer is added to {2, 3, 5, 8}. What is the probability that the median of the set will increase but the range still remains the same?

divide(const_4, const_10)

divide(const_4,const_10)

we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the same . the median of the set is ( 3 + 5 ) / 2 = 4 , thus the number selected must be 5 or greater . for the range to remain the same , the number must be between 2 and 8 inclusive . to satisfy both conditions , the number selected must be 5 , 6 , 7 , or 8 . the probability is 4 / 10 = 0.4 the answer is c .

general

math_qa__RNt7IfnIYlP34e2x

On a sum of money, the S.I. for 2 years is $600, while the C.I. is $630, the rate of interest being the same in both the cases. The rate of interest is? Choose the correct choice from the following choices A) 8 % B) 10 % C) 12 % D) 14 % E) 16 %

<gadget id="calculator">630 - 600</gadget> <output>30</output> <gadget id="calculator">100 * 30</gadget> <output>3_000</output> <gadget id="calculator">600 / 2</gadget> <output>300</output> <gadget id="calculator">3_000 / 300</gadget> <output>10</output> <result>B</result>

B

On a sum of money, the S.I. for 2 years is $600, while the C.I. is $630, the rate of interest being the same in both the cases. The rate of interest is?

divide(multiply(const_100, subtract(630, 600)), divide(600, 2))

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

"difference in c . i . and s . i for 2 years = $ 630 - $ 600 = $ 30 s . i for one year = $ 300 s . i . on $ 300 for 1 year = $ 30 rate = ( 100 * 30 ) / ( 300 ) = 10 % the answer is b ."

gain

math_qa__GipJFVA07wqksUBn

Y and Z walk around a circular track. They start at 5 a.m from the same point in the opposite directions. Y and Z walk at a speed of 3 rounds per hour and 4 rounds per hour respectively. How many times shall they cross each other before 7 a.m Choose the correct answer: A) 14 B) 15 C) 16 D) 17 E) 18

<gadget id="calculator">60 / 4</gadget> <output>15</output> <gadget id="calculator">15 / 10</gadget> <output>3/2 = around 1.5</output> <gadget id="calculator">60 / 3</gadget> <output>20</output> <gadget id="calculator">20 / 10</gadget> <output>2</output> <gadget id="calculator">(3/2) + 2</gadget> <output>7/2 = around 3.5</output> <gadget id="calculator">60 / (7/2)</gadget> <output>120/7 = around 17.142857</output> <result>E</result>

E

Y and Z walk around a circular track. They start at 5 a.m from the same point in the opposite directions. Y and Z walk at a speed of 3 rounds per hour and 4 rounds per hour respectively. How many times shall they cross each other before 7 a.m

divide(const_60, add(divide(divide(const_60, 4), const_10), divide(divide(const_60, 3), const_10)))

divide(const_60,n2)|divide(const_60,n1)|divide(#0,const_10)|divide(#1,const_10)|add(#2,#3)|divide(const_60,#4)

explanation : relative speed = ( 3 + 4 ) = 9 rounds per hour so , they cross each other 9 times in an hour hence , they cross 18 times before 7 a . m answer : option e

physics

math_qa__AYg0SIMs504o0scH

A towel, when bleached, lost 20% of its length and 10% of its breadth. What is the percentage decrease in area? Answers: A) 26 B) 28 C) 24 D) 20 E) 22

<gadget id="calculator">100 * 100</gadget> <output>10_000</output> <gadget id="calculator">100 - 20</gadget> <output>80</output> <gadget id="calculator">100 - 10</gadget> <output>90</output> <gadget id="calculator">80 * 90</gadget> <output>7_200</output> <gadget id="calculator">10_000 - 7_200</gadget> <output>2_800</output> <gadget id="calculator">2_800 / 100</gadget> <output>28</output> <result>B</result>

B

A towel, when bleached, lost 20% of its length and 10% of its breadth. What is the percentage decrease in area?

divide(subtract(multiply(const_100, const_100), multiply(subtract(const_100, 20), subtract(const_100, 10))), const_100)

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

"formula for percentage change in area is : = ( − x − y + ( xy ) / 100 ) % = ( − 20 − 10 + ( 20 × 10 ) / 100 ) % = − 28 % i . e . , area is decreased by 28 % answer is b ."

gain

math_qa__C0rAerHRYLmnumvK

A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.272 less than the sum lent. What was the sum lent? Select. A) 400 B) 278 C) 289 D) 500 E) 821

<gadget id="calculator">4 * 8</gadget> <output>32</output> <gadget id="calculator">32 / 100</gadget> <output>8/25 = around 0.32</output> <gadget id="calculator">1 - (8/25)</gadget> <output>17/25 = around 0.68</output> <gadget id="calculator">272 / (17/25)</gadget> <output>400</output> <result>A</result>

A

A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.272 less than the sum lent. What was the sum lent?

divide(272, subtract(const_1, divide(multiply(4, 8), const_100)))

multiply(n0,n1)|divide(#0,const_100)|subtract(const_1,#1)|divide(n2,#2)|

"p - 272 = ( p * 4 * 8 ) / 100 p = 400 answer : a"

gain

math_qa__7x8qRrzEbsrQkwVJ

A marketing firm determined that, of 200 households surveyed, 80 used neither Brand R nor Brand B soap, 60 used only Brand R soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap? Select: A) 15 B) 20 C) 30 D) 40 E) 45

<gadget id="calculator">80 + 60</gadget> <output>140</output> <gadget id="calculator">200 - 140</gadget> <output>60</output> <gadget id="calculator">3 + 1</gadget> <output>4</output> <gadget id="calculator">60 / 4</gadget> <output>15</output> <gadget id="calculator">15 + 15</gadget> <output>30</output> <gadget id="calculator">30 + 10</gadget> <output>40</output> <result>D</result>

D

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

add(add(divide(subtract(200, add(80, 60)), add(3, const_1)), divide(subtract(200, add(80, 60)), add(3, const_1))), const_10)

add(n1,n2)|add(n3,const_1)|subtract(n0,#0)|divide(#2,#1)|add(#3,#3)|add(#4,const_10)

solution for soap r and soap b ( d ) 40

other

math_qa__sMZ7bQcIKICmIVcH

The length of the bridge, which a train 150 meters long and travelling at 45 km/hr can cross in 30 seconds, is? Select the correct option: A) 388 B) 267 C) 225 D) 288 E) 261

<gadget id="calculator">1_000 / 1</gadget> <output>1_000</output> <gadget id="calculator">45 * 1_000</gadget> <output>45_000</output> <gadget id="calculator">3_600 / 1</gadget> <output>3_600</output> <gadget id="calculator">45_000 / 3_600</gadget> <output>25/2 = around 12.5</output> <gadget id="calculator">(25/2) * 30</gadget> <output>375</output> <gadget id="calculator">375 - 150</gadget> <output>225</output> <result>C</result>

C

The length of the bridge, which a train 150 meters long and travelling at 45 km/hr can cross in 30 seconds, is?

subtract(multiply(divide(multiply(45, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 150)

speed(const_1000,const_1)|speed(const_3600,const_1)|multiply(n1,#0)|divide(#2,#1)|multiply(n2,#3)|subtract(#4,n0)|

"speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 150 + x ) / 30 = 25 / 2 = = > 2 ( 150 + x ) = 750 = = > x = 225 m . answer : c"

physics

math_qa__hrC1HImnXmmTIMuG

If x and y are numbers such that (x+4)(y-4)=0, what is the smallest possible value of x^2 + y^2 Select A) 0 B) 9 C) 12 D) 16 E) 18

<gadget id="calculator">4 ** 2</gadget> <output>16</output> <result>D</result>

D

If x and y are numbers such that (x+4)(y-4)=0, what is the smallest possible value of x^2 + y^2

power(4, 2)

power(n0,n3)|

"from ( x + 4 ) ( y - 4 ) = 0 it follows that either x = - 4 or y = 4 . thus either x ^ 2 = 16 or y ^ 2 = 16 . now , if x ^ 2 = 16 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 16 + 0 = 16 . similarly if y ^ 2 = 16 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 0 + 16 = 16 . answer : d ."

general

math_qa__ABRM1fa6hOnYdfl9

1000 men have provisions for 18 days. If 400 more men join them, for how many days will the provisions last now? Answers: A) 12.9 B) 12.8 C) 12.6 D) 12.2 E) 12.1

<gadget id="calculator">18 * 1_000</gadget> <output>18_000</output> <gadget id="calculator">1_000 + 400</gadget> <output>1_400</output> <gadget id="calculator">18_000 / 1_400</gadget> <output>90/7 = around 12.857143</output> <result>B</result>

B

1000 men have provisions for 18 days. If 400 more men join them, for how many days will the provisions last now?

divide(multiply(18, 1000), add(1000, 400))

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

1000 * 18 = 1400 * x x = 12.8 answer : b

physics

math_qa__l27fj72AnD6jnUuT

If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2014) = ? Choose one: A) 2015 B) 2088 C) 270 D) 1881 E) 1781

<gadget id="calculator">1 + 2_014</gadget> <output>2_015</output> <result>A</result>

A

If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2014) = ?

add(1, 2014)

add(n3,n4)|

"f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 ⇒ ⇒ f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 ⇒ ⇒ f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 ⇒ ⇒ f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2014 ) = 2015 ans : a"

general

math_qa__sfKHy8U1bYdksnsk

A, B and C can do a piece of work in 30 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed? Answers. A) 12 days B) 16 days C) 18 days D) 11 days E) 38 days

<gadget id="calculator">1 / 30</gadget> <output>1/30 = around 0.033333</output> <gadget id="calculator">(1/30) + (1/30)</gadget> <output>1/15 = around 0.066667</output> <gadget id="calculator">(1/15) * 4</gadget> <output>4/15 = around 0.266667</output> <gadget id="calculator">1 - (4/15)</gadget> <output>11/15 = around 0.733333</output> <gadget id="calculator">2 + 3</gadget> <output>5</output> <gadget id="calculator">2 * 4</gadget> <output>8</output> <gadget id="calculator">5 * 8</gadget> <output>40</output> <gadget id="calculator">1 / 40</gadget> <output>1/40 = around 0.025</output> <gadget id="calculator">(1/40) + (1/15)</gadget> <output>11/120 = around 0.091667</output> <gadget id="calculator">(11/15) / (11/120)</gadget> <output>8</output> <gadget id="calculator">8 + 4</gadget> <output>12</output> <result>A</result>

A

A, B and C can do a piece of work in 30 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?

add(divide(subtract(const_1, multiply(add(divide(const_1, 30), divide(const_1, 30)), 4)), add(divide(const_1, multiply(add(const_2, const_3), multiply(const_2, 4))), add(divide(const_1, 30), divide(const_1, 30)))), 4)

add(const_2,const_3)|divide(const_1,n0)|divide(const_1,n1)|multiply(const_2,n3)|add(#1,#2)|multiply(#0,#3)|divide(const_1,#5)|multiply(n3,#4)|add(#4,#6)|subtract(const_1,#7)|divide(#9,#8)|add(n3,#10)|

"one day work of a , b and c = 1 / 30 + 1 / 30 + 1 / 40 = 1 / 11 work done by a and b together in the last 4 days = 4 * ( 1 / 30 + 1 / 30 ) = 4 / 15 remaining work = 11 / 15 the number of days required for this initial work = 8 days . the total number of days required = 4 + 8 = 12 days . answer : a"

physics

math_qa__fY8qT0TV6ScCE38S

A man buys an article for $100. and sells it for $110. Find the gain percent? Choose the correct choice from the following: A) 10 % B) 15 % C) 25 % D) 20 % E) 30 %

<gadget id="calculator">100 / 100</gadget> <output>1</output> <gadget id="calculator">110 / 1</gadget> <output>110</output> <gadget id="calculator">110 - 100</gadget> <output>10</output> <result>A</result>

A

A man buys an article for $100. and sells it for $110. Find the gain percent?

subtract(divide(110, divide(100, const_100)), const_100)

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

"c . p . = $ 100 s . p . = $ 110 gain = $ 10 gain % = 10 / 100 * 100 = 10 % answer is a"

gain

math_qa__FnNTGcyVioRdD6Er

John makes $60 a week from his job. He earns a raise andnow makes $72 a week. What is the % increase? Choose the most appropriate option A) 20 % B) 16.66 % C) 16.56 % D) 17.66 % E) 18.1 %

<gadget id="calculator">72 - 60</gadget> <output>12</output> <gadget id="calculator">12 / 60</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(1/5) * 100</gadget> <output>20</output> <result>A</result>

A

John makes $60 a week from his job. He earns a raise andnow makes $72 a week. What is the % increase?

multiply(divide(subtract(72, 60), 60), const_100)

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

"increase = ( 12 / 60 ) * 100 = ( 1 / 5 ) * 100 = 20 % . a"

gain

math_qa__Jy0bM8BsfxEwBFcb

50 + 5 * 12 / (180/3) = ? Select: A) 23 B) 78 C) 27 D) 51 E) 81

<gadget id="calculator">5 * 12</gadget> <output>60</output> <gadget id="calculator">180 / 3</gadget> <output>60</output> <gadget id="calculator">60 / 60</gadget> <output>1</output> <gadget id="calculator">50 + 1</gadget> <output>51</output> <result>D</result>

D

50 + 5 * 12 / (180/3) = ?

add(50, divide(multiply(5, 12), divide(180, 3)))

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

"explanation : 50 + 5 * 12 / ( 180 / 3 ) = 50 + 5 * 12 / ( 60 ) = 50 + ( 5 * 12 ) / 60 = 50 + 1 = 51 . answer : d"

general

math_qa__WJbX7QHSVTKmq0rL

Find number which is 50% less than 60. Choose the correct answer: A) 18 B) 30 C) 32 D) 26 E) 98

<gadget id="calculator">60 * 50</gadget> <output>3_000</output> <gadget id="calculator">3_000 / 100</gadget> <output>30</output> <result>B</result>

B

Find number which is 50% less than 60.

divide(multiply(60, 50), const_100)

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

explanation : 50 % less is 50 % of the given number therefore , 50 % of 60 is 30 . answer : b

gain

math_qa__EbTmxYf0CYOShQRE

Mark bought a set of 6 flower pots of different sizes at a total cost of $7.80. Each pot cost 0.25 more than the next one below it in size. What was the cost, in dollars, of the largest pot? Answers: A) $ 1.75 B) $ 1.93 C) $ 2.00 D) $ 2.15 E) $ 2.30

<gadget id="calculator">6 - 1</gadget> <output>5</output> <gadget id="calculator">5 * 6</gadget> <output>30</output> <gadget id="calculator">30 / 2</gadget> <output>15</output> <gadget id="calculator">15 * 0.25</gadget> <output>3.75</output> <gadget id="calculator">7.8 - 3.75</gadget> <output>4.05</output> <gadget id="calculator">4.05 / 6</gadget> <output>0.675</output> <gadget id="calculator">5 * 0.25</gadget> <output>1.25</output> <gadget id="calculator">0.675 + 1.25</gadget> <output>1.925</output> <result>B</result>

B

Mark bought a set of 6 flower pots of different sizes at a total cost of $7.80. Each pot cost 0.25 more than the next one below it in size. What was the cost, in dollars, of the largest pot?

add(divide(subtract(7.8, multiply(divide(multiply(subtract(6, const_1), 6), const_2), 0.25)), 6), multiply(subtract(6, const_1), 0.25))

subtract(n0,const_1)|multiply(n0,#0)|multiply(n2,#0)|divide(#1,const_2)|multiply(n2,#3)|subtract(n1,#4)|divide(#5,n0)|add(#6,#2)

this question can be solved with a handful of different algebra approaches ( as has been shown in the various posts ) . since the question asks for the price of the largest pot , and the answers are prices , we can test the answers . we ' re told that there are 6 pots and that each pot costs 25 cents more than the next . the total price of the pots is $ 8.25 . we ' re asked for the price of the largest ( most expensive ) pot . since the total price is $ 7.80 ( a 25 - cent increment ) and the the difference in sequential prices of the pots is 25 cents , the largest pot probably has a price that is a 25 - cent increment . from the answer choices , i would then test answer c first ( since answers b and d are not in 25 - cent increments ) . if . . . . the largest pot = $ 1.75 the other 5 pots are . . . . 1.75 1.50 1.25 1.00 0.75 total = $ 7.80 so this must be the answer . b

general

math_qa__a6lv1hshHe4jdvO9

A circular well with a diameter of 2 metres , is dug to a depth of 10 metres. What is the volume of the earth dug out? Choose the correct answer: A) 32 m 3 B) 31.4 m 3 C) 40 m 3 D) 44 m 3 E) none

<gadget id="calculator">2 / 2</gadget> <output>1</output> <gadget id="calculator">pi * (1 ** 2) * 10</gadget> <output>10*pi = around 31.415927</output> <result>B</result>

B

A circular well with a diameter of 2 metres , is dug to a depth of 10 metres. What is the volume of the earth dug out?

volume_cylinder(divide(2, 2), 10)

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

"solution volume = π r 2 h ‹ = › ( 22 / 7 × 1 × 1 × 10 ) m 3 ‹ = › 31.4 m 3 . answer b"

geometry

math_qa__8AdF1805isn6E57T

in a survey of political preferences , 78 % of those asked were in favour of at least one of the proposals : i , ii and iii . 50 % of those asked favoured proposal i , 30 % favoured proposal ii , and 20 % favoured proposal iii . if 5 % of those asked favoured all 3 of the proposals , what x percentage of those asked favoured more than one of the 3 proposals . Choose the most appropriate option: A) 10 B) 12 C) 17 D) 22 E) 30

<gadget id="calculator">50 + 30</gadget> <output>80</output> <gadget id="calculator">80 - 5</gadget> <output>75</output> <gadget id="calculator">75 + 20</gadget> <output>95</output> <gadget id="calculator">95 - 5</gadget> <output>90</output> <gadget id="calculator">90 - 78</gadget> <output>12</output> <gadget id="calculator">12 + 5</gadget> <output>17</output> <result>C</result>

C

in a survey of political preferences , 78 % of those asked were in favour of at least one of the proposals : i , ii and iii . 50 % of those asked favoured proposal i , 30 % favoured proposal ii , and 20 % favoured proposal iii . if 5 % of those asked favoured all 3 of the proposals , what x percentage of those asked favoured more than one of the 3 proposals .

add(subtract(subtract(add(subtract(add(50, 30), 5), 20), 5), 78), 5)

add(n1,n2)|subtract(#0,n4)|add(n3,#1)|subtract(#2,n4)|subtract(#3,n0)|add(n4,#4)

bunuel , my answer for exactly 2 people was 17 and this was my approach : 100 % = ( a + b + c ) - ( anb + anc + bnc ) - 5 % + 22 % which leads me to x = 100 % = ( 50 + 30 + 20 ) - ( at least 2 people ) - 5 % + 22 % . c

general

math_qa__OLeEU6xDP4WaA74f

A certain bag contains 60 balls — 22 white, 18 green, 2 yellow, 15 red, and 3 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple? Options: A) 0.7 B) 0.15 C) 0.54 D) 0.85 E) 0.91

<gadget id="calculator">22 + 18</gadget> <output>40</output> <gadget id="calculator">40 + 2</gadget> <output>42</output> <gadget id="calculator">42 / 60</gadget> <output>7/10 = around 0.7</output> <result>A</result>

A

A certain bag contains 60 balls — 22 white, 18 green, 2 yellow, 15 red, and 3 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple?

divide(add(add(22, 18), 2), 60)

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

"according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 22 + 18 + 2 ) / 60 = 42 / 60 = 0.7 . answer : a ."

other