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NLP Centre, Faculty of Informatics, Masaryk University 14

math_qa__5UghUbFAkExURWtQ

A,B,C can complete a piece of work in 18,6,12 days. Working together, they complete the same work in how many days? Choose the correct choice from the following answers: A) 2 B) 4 / 5 C) 7 / 9 D) 36 / 11 E) 24 / 7

<gadget id="calculator">1 / 18</gadget> <output>1/18 = around 0.055556</output> <gadget id="calculator">4 + 2</gadget> <output>6</output> <gadget id="calculator">1 / 6</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">(1/18) + (1/6)</gadget> <output>2/9 = around 0.222222</output> <gadget id="calculator">2 * 6</gadget> <output>12</output> <gadget id="calculator">1 / 12</gadget> <output>1/12 = around 0.083333</output> <gadget id="calculator">(2/9) + (1/12)</gadget> <output>11/36 = around 0.305556</output> <gadget id="calculator">1 / (11/36)</gadget> <output>36/11 = around 3.272727</output> <result>D</result>

D

A,B,C can complete a piece of work in 18,6,12 days. Working together, they complete the same work in how many days?

divide(const_1, add(add(divide(const_1, 18), divide(const_1, add(const_4, const_2))), divide(const_1, multiply(const_2, add(const_4, const_2)))))

add(const_2,const_4)|divide(const_1,n0)|divide(const_1,#0)|multiply(#0,const_2)|add(#1,#2)|divide(const_1,#3)|add(#4,#5)|divide(const_1,#6)|

"a + b + c 1 day work = 1 / 18 + 1 / 6 + 1 / 12 = 11 / 36 a , b , c together will complete the job in 36 / 11 days answer is d"

physics

math_qa__iZosXZVIM1o1KBU6

If the horse can run 10 miles/hour, how many days would it take for a horse to run from New York City to Washington. D.C.? (240 miles from NYC to D.C.) Select: A) 0.6 B) 0.8 C) 1 D) 1.2 E) 1.4

<gadget id="calculator">240 / 10</gadget> <output>24</output> <gadget id="calculator">24 / 24</gadget> <output>1</output> <result>C</result>

C

If the horse can run 10 miles/hour, how many days would it take for a horse to run from New York City to Washington. D.C.? (240 miles from NYC to D.C.)

divide(divide(240, 10), divide(240, 10))

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

the horse runs 10 miles / hour , thus it would take the horse 240 miles / 10 miles / hour to = 24 hours to run from nyc to d . c . there are 24 hours in a day , so days it take would be 24 hours / 24 hours / day = 1 day . correct option : 1

physics

math_qa__3OzwMvrgRSzmAohn

Solve below question 2x + 1 = -21 Choose one: A) - 11 B) - 9 C) 9 D) 8 E) - 7

<gadget id="calculator">21 + 1</gadget> <output>22</output> <gadget id="calculator">-22</gadget> <output>-22</output> <gadget id="calculator">(-22) / 2</gadget> <output>-11</output> <result>A</result>

A

Solve below question 2x + 1 = -21

divide(negate(add(21, 1)), 2)

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

"2 x + 1 = - 21 x = - 11 a"

general

math_qa__CnQqRhr2plYuJkPc

Solution for 2.12+.004+.345 Pick. A) 2.91 B) 2.911 C) 2.469 D) 2.586 E) 2.499

<gadget id="calculator">4 / 1_000</gadget> <output>1/250 = around 0.004</output> <gadget id="calculator">2.12 + (1/250)</gadget> <output>2.124</output> <gadget id="calculator">345 / 1_000</gadget> <output>69/200 = around 0.345</output> <gadget id="calculator">2.124 + (69/200)</gadget> <output>2.469</output> <result>C</result>

C

Solution for 2.12+.004+.345

add(add(2.12, divide(4, const_1000)), divide(345, const_1000))

divide(n1,const_1000)|divide(n2,const_1000)|add(n0,#0)|add(#2,#1)

2.12 + . 004 + . 345 0 = 0 - 2.12 - 0.004 - 0.345 0 = - 2.469 answer : c

general

math_qa__XDRrZsKPf4AREZIF

In a throw of dice what is the probability of geƫng number greater than 3 Answers. A) 1 / 2 B) 1 / 3 C) 1 / 5 D) 1 / 6 E) none of these

<gadget id="calculator">6 - 3</gadget> <output>3</output> <gadget id="calculator">3 / 6</gadget> <output>1/2 = around 0.5</output> <result>A</result>

A

In a throw of dice what is the probability of geƫng number greater than 3

divide(subtract(const_6, 3), const_6)

subtract(const_6,n0)|divide(#0,const_6)|

"explanation : number greater than 3 is 4 , 5 , 6 , so only 3 number total cases of dice = [ 1,2 , 3,4 , 5,6 ] so probability = 3 / 6 = 1 / 2 answer : a"

probability

math_qa__8IFPB4wfa8N3tUEH

A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.1300, what is the reduced price for kg? Choose the correct choice from the following options A) s . 40 B) s . 65 C) s . 49 D) s . 41 E) s . 42

<gadget id="calculator">1_300 * 25</gadget> <output>32_500</output> <gadget id="calculator">32_500 / 100</gadget> <output>325</output> <gadget id="calculator">325 / 5</gadget> <output>65</output> <result>B</result>

B

A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.1300, what is the reduced price for kg?

divide(divide(multiply(1300, 25), const_100), 5)

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

"1300 * ( 25 / 100 ) = 325 - - - - 5 ? - - - - 1 = > rs . 65 answer : b"

gain

math_qa__dVzBdR0ZJ3P3EWGK

How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1/2 m board? Choose the correct choice from the following: A) 90 B) 99 C) 97 D) 95 E) 65

<gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">16 + (1/2)</gadget> <output>33/2 = around 16.5</output> <gadget id="calculator">30 * (33/2)</gadget> <output>495</output> <gadget id="calculator">2 + (1/2)</gadget> <output>5/2 = around 2.5</output> <gadget id="calculator">(5/2) * 2</gadget> <output>5</output> <gadget id="calculator">495 / 5</gadget> <output>99</output> <result>B</result>

B

How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1/2 m board?

divide(multiply(30, add(16, divide(1, 2))), multiply(add(2, divide(1, 2)), 2))

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

"30 * 33 / 2 = 5 / 2 * 2 * x = > x = 99 answer b"

general

math_qa__WGxtgqISPFPCkJUP

20 liters of a mixture is created by mixing Liquid P and Liquid Q in the ratio 3:2. How many liters of Liquid Q must be added to make the ratio 4:3? Pick one: A) 1 B) 3 C) 5 D) 7 E) 9

<gadget id="calculator">4 + 3</gadget> <output>7</output> <gadget id="calculator">20 * 3</gadget> <output>60</output> <gadget id="calculator">3 + 2</gadget> <output>5</output> <gadget id="calculator">60 / 5</gadget> <output>12</output> <gadget id="calculator">7 * 12</gadget> <output>84</output> <gadget id="calculator">84 / 4</gadget> <output>21</output> <gadget id="calculator">21 * 3</gadget> <output>63</output> <gadget id="calculator">63 / 7</gadget> <output>9</output> <gadget id="calculator">20 * 2</gadget> <output>40</output> <gadget id="calculator">40 / 5</gadget> <output>8</output> <gadget id="calculator">9 - 8</gadget> <output>1</output> <result>A</result>

A

20 liters of a mixture is created by mixing Liquid P and Liquid Q in the ratio 3:2. How many liters of Liquid Q must be added to make the ratio 4:3?

subtract(divide(multiply(divide(multiply(add(4, 3), divide(multiply(20, 3), add(3, 2))), 4), 3), add(4, 3)), divide(multiply(20, 2), add(3, 2)))

add(n3,n4)|add(n1,n2)|multiply(n0,n1)|multiply(n0,n2)|divide(#2,#1)|divide(#3,#1)|multiply(#0,#4)|divide(#6,n3)|multiply(n4,#7)|divide(#8,#0)|subtract(#9,#5)|

"let x be the amount of liquid q to be added . ( 2 / 5 ) * 20 + x = ( 3 / 7 ) * ( 20 + x ) 280 + 35 x = 300 + 15 x 20 x = 20 x = 1 the answer is a ."

general

math_qa__mnW260sLtGm7ZF9y

A sum amounts to Rs.5292 in 2 years at the rate of 5% p.a. If interest was compounded yearly then what was the principal? Choose the correct choice from the following choices. A) s . 4000 B) s . 5000 C) s . 4500 D) s . 4800 E) s . 5800

<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">5_292 / (441/400)</gadget> <output>4_800</output> <result>D</result>

D

A sum amounts to Rs.5292 in 2 years at the rate of 5% p.a. If interest was compounded yearly then what was the principal?

divide(5292, power(add(divide(5, const_100), const_1), 2))

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

"ci = 5292 , r = 5 , n = 2 ci = p [ 1 + r / 100 ] ^ 2 = p [ 1 + 5 / 100 ] ^ 2 5292 = p [ 21 / 20 ] ^ 2 5292 [ 20 / 21 ] ^ 2 4800 answer : d"

gain

math_qa__YpwAc6LWd9Vte4Yu

Express a speed of 56 kmph in meters per second? Pick one: A) 10.56 mps B) 17.56 mps C) 97.56 mps D) 15.56 mps E) 18.56 mps

<gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">(5/18) * 56</gadget> <output>140/9 = around 15.555556</output> <result>D</result>

D

Express a speed of 56 kmph in meters per second?

multiply(const_0_2778, 56)

multiply(n0,const_0_2778)|

"56 * 5 / 18 = 15.56 mps answer : d"

physics

math_qa__juepMQHHUTlnnawU

A group of men decided to do a work in 12days, but 6 of them became absent. If the rest of the group did the work in 14days, Find the original number of men? Choose the correct choice from the following choices A) 15 B) 42 C) 44 D) 45 E) 18

<gadget id="calculator">6 * 14</gadget> <output>84</output> <gadget id="calculator">14 - 12</gadget> <output>2</output> <gadget id="calculator">84 / 2</gadget> <output>42</output> <result>B</result>

B

A group of men decided to do a work in 12days, but 6 of them became absent. If the rest of the group did the work in 14days, Find the original number of men?

divide(multiply(6, 14), subtract(14, 12))

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

"original number of men = 6 * 14 / ( 14 - 12 ) = 42 answer is b"

physics

math_qa__trlw3XyykG0dLtXB

A sells a Cricket Bat to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays $234 for it, the cost price of the Cricket Bat for A is: Choose the correct choice from the following answers A) 156 B) 120 C) 130 D) 160 E) 210

<gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">1 + (1/5)</gadget> <output>6/5 = around 1.2</output> <gadget id="calculator">25 / 100</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">1 + (1/4)</gadget> <output>5/4 = around 1.25</output> <gadget id="calculator">(6/5) * (5/4)</gadget> <output>3/2 = around 1.5</output> <gadget id="calculator">234 / (3/2)</gadget> <output>156</output> <result>A</result>

A

A sells a Cricket Bat to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays $234 for it, the cost price of the Cricket Bat for A is:

divide(234, multiply(add(const_1, divide(20, const_100)), add(const_1, divide(25, const_100))))

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

"125 % of 120 % of a = 234 125 / 100 * 120 / 100 * a = 234 a = 234 * 2 / 3 = 156 . answer a"

gain

math_qa__UaeZx5Zin4KqZ3GX

A rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing. If the poles of the fence are kept 5 metres apart, how many poles will be needed? Choose the most appropriate option: A) 55 B) 56 C) 57 D) 58 E) none of these

<gadget id="calculator">2 * (90 + 50)</gadget> <output>280</output> <gadget id="calculator">280 / 5</gadget> <output>56</output> <result>B</result>

B

A rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing. If the poles of the fence are kept 5 metres apart, how many poles will be needed?

divide(rectangle_perimeter(90, 50), 5)

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

"solution perimeter of the plot = 2 ( 90 + 50 ) = 280 m . ∴ number of poles = [ 280 / 5 ] = 56 m answer b"

physics

math_qa__u36uZXOX228M1Th1

The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 90 metres? Answers A) 16 seconds B) 76 seconds C) 26 seconds D) 12 seconds E) 18 seconds

<gadget id="calculator">15 + 3</gadget> <output>18</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">18 * (5/18)</gadget> <output>5</output> <gadget id="calculator">90 / 5</gadget> <output>18</output> <result>E</result>

E

The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 90 metres?

divide(90, multiply(add(15, 3), const_0_2778))

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

"speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 90 m = 90 / 5 = 18 seconds . answer : e"

physics

math_qa__Z7giEW5oU9qdyll9

A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 9 seconds. Due to some problem, one boggies were detached. The train now crosses a telegraph post in Choose the correct option: A) 18 sec B) 12 sec C) 15 sec D) 8.25 sec E) none of these

<gadget id="calculator">12 * 15</gadget> <output>180</output> <gadget id="calculator">180 - 15</gadget> <output>165</output> <gadget id="calculator">180 / 9</gadget> <output>20</output> <gadget id="calculator">165 / 20</gadget> <output>33/4 = around 8.25</output> <result>D</result>

D

A train consists of 12 boggies, each boggy 15 metres long. The train crosses a telegraph post in 9 seconds. Due to some problem, one boggies were detached. The train now crosses a telegraph post in

divide(subtract(multiply(12, 15), 15), divide(multiply(12, 15), 9))

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

"length of train = 12 ã — 15 = 180 m . then , speed of train = 180 ⠁ „ 9 = 20 m / s now , length of train = 11 ã — 15 = 165 m â ˆ ´ required time = 165 ⠁ „ 20 = 8.25 sec . answer d"

physics

math_qa__o3OMM4aLoEEHWXFr

A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2640 in all from both of them as interest. The rate of interest per annum is? Choose the correct answer: A) 16 % B) 12 % C) 74 % D) 10 % E) 45 %

<gadget id="calculator">5_000 * 2</gadget> <output>10_000</output> <gadget id="calculator">3_000 * 4</gadget> <output>12_000</output> <gadget id="calculator">10_000 + 12_000</gadget> <output>22_000</output> <gadget id="calculator">2_640 / 22_000</gadget> <output>3/25 = around 0.12</output> <gadget id="calculator">(3/25) * 100</gadget> <output>12</output> <result>B</result>

B

A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2640 in all from both of them as interest. The rate of interest per annum is?

multiply(divide(2640, add(multiply(5000, 2), multiply(3000, 4))), const_100)

multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)|divide(n4,#2)|multiply(#3,const_100)|

"let the rate be r % p . a . then , ( 5000 * r * 2 ) / 100 + ( 3000 * r * 4 ) / 100 = 2640 100 r + 120 r = 2640 r = 12 % answer : b"

gain

math_qa__2S9UPnPysQ7C0Q2Q

In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 56 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp? Answers: A) 70 B) 400 C) 150 D) 35 E) 350

<gadget id="calculator">100 - 30</gadget> <output>70</output> <gadget id="calculator">70 / 100</gadget> <output>7/10 = around 0.7</output> <gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(7/10) * (1/5)</gadget> <output>7/50 = around 0.14</output> <gadget id="calculator">56 / (7/50)</gadget> <output>400</output> <result>B</result>

B

In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 56 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp?

divide(56, multiply(divide(subtract(const_100, 30), const_100), divide(20, const_100)))

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

"since 30 % of the boys from school a study science , then 70 % of the boys from school a do not study science and since 20 % of the total number of boys are from school a , then 0.2 * 0.7 = 0.14 , or 14 % of the boys in the camp are from school a and do not study science . we are told that this number equals to 56 , so 0.14 * { total } = 56 - - > { total } = 400 . answer : b ."

gain

math_qa__kxYj45J6f2SnG3Xc

The number 219 can be written as sum of the squares of 3 different positive integers. What is the sum of these 3 different integers? Choose one A) 20 B) 21 C) 19 D) 17 E) 15

<gadget id="calculator">219 / 2</gadget> <output>219/2 = around 109.5</output> <gadget id="calculator">(219/2) ** (1/2)</gadget> <output>sqrt(438)/2 = around 10.464225</output> <gadget id="calculator">2 * (sqrt(438)/2)</gadget> <output>sqrt(438) = around 20.92845</output> <result>B</result>

B

The number 219 can be written as sum of the squares of 3 different positive integers. What is the sum of these 3 different integers?

multiply(const_2, sqrt(divide(219, const_2)))

divide(n0,const_2)|sqrt(#0)|multiply(#1,const_2)|

"sum of the squares of 3 different positive integers = 219 13 ^ 2 + 7 ^ 2 + 1 ^ 2 = 219 now , sum of these 3 different integers = 13 + 7 + 1 = 21 ans - b"

geometry

math_qa__wVm32cC3NhrHQELX

In a boat there are 8 men whose average weight is increased by 1 kg when 1 man of 60 kg is replaced by a new man. What is weight of new comer? Choose the correct choice from the following answers. A) 70 B) 66 C) 68 D) 69 E) 72

<gadget id="calculator">60 + 8</gadget> <output>68</output> <result>C</result>

C

In a boat there are 8 men whose average weight is increased by 1 kg when 1 man of 60 kg is replaced by a new man. What is weight of new comer?

add(60, 8)

add(n0,n3)

solution : member in group * age increased = difference of replacement or , 8 * 1 = new comer - man going out or , new comer = 8 + 60 ; or , new comer = 68 years . answer : option c

general

math_qa__6W6J090ScuUt6F1w

The ratio of A and B is 5:3.After 2 years their ratio is 3:2.What is the age of B? Choose the correct choice from the following options. A) 5 B) 3 C) 6 D) 7 E) 8

<gadget id="calculator">5 * 2</gadget> <output>10</output> <gadget id="calculator">10 * 3</gadget> <output>30</output> <gadget id="calculator">30 / 2</gadget> <output>15</output> <gadget id="calculator">3 * 3</gadget> <output>9</output> <gadget id="calculator">15 - 9</gadget> <output>6</output> <result>C</result>

C

The ratio of A and B is 5:3.After 2 years their ratio is 3:2.What is the age of B?

subtract(divide(multiply(multiply(5, 2), 3), 2), multiply(3, 3))

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

the ratio of a and b is 5 x and 3 x years . after 2 years , their ratio will be 3 and 2 . ( i . e ) ( 5 x + 2 ) / ( 3 x + 2 ) = 3 / 2 10 x + 4 = 9 x + 6 x = 2 b ' s age = 3 x = 3 ( 2 ) = 6 years answer is option c

other

math_qa__FOqGaa6ZaX8Xg2OX

If the probability of rain on any given day in Chicago during the summer is 50%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 7, inclusive? Choose the correct choice from the following answers: A) 1 / 4 B) 1 / 8 C) 3 / 8 D) 3 / 16 E) 5 / 16

<gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">(1/2) ** 4</gadget> <output>1/16 = around 0.0625</output> <gadget id="calculator">4 * (1/16)</gadget> <output>1/4 = around 0.25</output> <result>A</result>

A

If the probability of rain on any given day in Chicago during the summer is 50%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 7, inclusive?

multiply(4, power(divide(const_1, const_2), 4))

divide(const_1,const_2)|power(#0,n2)|multiply(n2,#1)

one case is rainy - rainy - rainy - not rainy . the probability of this case is ( 1 / 2 ) ^ 4 = 1 / 16 the number of possible cases is 4 c 3 = 4 . p ( exactly 3 rainy days ) = 4 * 1 / 16 = 1 / 4 the answer is a .

general

math_qa__ysT8O8oDMiEMJsXO

Eight cubes, each with a volume of 512 cm^3, are joined to form one large cube. What is the surface area of the large cube? Choose the correct choice from the following: A) 4096 sq cm B) 1536 sq cm C) 1024 sq cm D) 2048 sq cm E) 512 sq cm

<gadget id="calculator">2 * 4</gadget> <output>8</output> <gadget id="calculator">8 * 512</gadget> <output>4_096</output> <gadget id="calculator">4_096 ** (1/3)</gadget> <output>16</output> <gadget id="calculator">6 * (16 ** 2)</gadget> <output>1_536</output> <result>B</result>

B

Eight cubes, each with a volume of 512 cm^3, are joined to form one large cube. What is the surface area of the large cube?

surface_cube(cube_edge_by_volume(multiply(multiply(const_2, const_4), 512)))

multiply(const_2,const_4)|multiply(n0,#0)|cube_edge_by_volume(#1)|surface_cube(#2)

volume = a x a x a = a ^ 3 volume of cube = 8 x 512 = 4096 cm ^ 3 4096 = a ^ 3 a = 16 surface area of cube = 6 a ^ 2 = 6 x 16 ^ 2 = 1536 answer is b

geometry

math_qa__WSfsbasouDAHukZE

The length of a rectangle is twice its breadth. If its lengthis decreased by 5cm & breadth is increased by 5cm, the area of the rectangle is increased by 75sq.cm. What is the length of the rectangle? Answers A) 25 cm B) 30 cm C) 40 cm D) 45 cm E) 60 cm

<gadget id="calculator">5 * 5</gadget> <output>25</output> <gadget id="calculator">75 + 25</gadget> <output>100</output> <gadget id="calculator">2 * 5</gadget> <output>10</output> <gadget id="calculator">10 - 5</gadget> <output>5</output> <gadget id="calculator">100 / 5</gadget> <output>20</output> <gadget id="calculator">2 * 20</gadget> <output>40</output> <result>C</result>

C

The length of a rectangle is twice its breadth. If its lengthis decreased by 5cm & breadth is increased by 5cm, the area of the rectangle is increased by 75sq.cm. What is the length of the rectangle?

multiply(const_2, divide(add(75, multiply(5, 5)), subtract(multiply(const_2, 5), 5)))

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

let breadth = x cm then , length = 2 x cm area = x × 2 x = 2 x 2 sq . cm . new length = ( 2 x − 5 ) cm new breadth = ( x + 5 ) cm new area = ( 2 x − 5 ) ( x + 5 ) sq . cm . given that , new area = initial area + 75 sq . cm . ⇒ ( 2 x − 5 ) ( x + 5 ) = 2 x 2 + 75 ⇒ 2 x 2 + 10 x − 5 x − 25 = 2 x 2 + 75 ⇒ 5 x − 25 = 75 ⇒ 5 x = 75 + 25 = 100 ⇒ x = 1005 = 20 cm length = 2 x = 2 × 20 = 40 cm c

geometry

math_qa__hLGVihs9Pi1bXQPa

Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.51200? Options: A) 81000 B) 81028 C) 27772 D) 29889 E) 64800

<gadget id="calculator">1 / 8</gadget> <output>1/8 = around 0.125</output> <gadget id="calculator">(1/8) * 51_200</gadget> <output>6_400</output> <gadget id="calculator">51_200 + 6_400</gadget> <output>57_600</output> <gadget id="calculator">(1/8) * 57_600</gadget> <output>7_200</output> <gadget id="calculator">57_600 + 7_200</gadget> <output>64_800</output> <result>E</result>

E

Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.51200?

add(add(51200, multiply(divide(1, 8), 51200)), multiply(divide(1, 8), add(51200, multiply(divide(1, 8), 51200))))

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

51200 * 9 / 8 * 9 / 8 = 64800 . answer : e

general

math_qa__8YyehqbUVDvzhjf6

Set S contains exactly 10 numbers and has an average (arithmetic mean) of 6.2. If one of the numbers in Set S is increased by 4, while all other numbers remain the same, what is the new average of Set S? Select: A) 6.6 B) 6.7 C) 6.8 D) 6.85 E) 6.9

<gadget id="calculator">10 * 6.2</gadget> <output>62</output> <gadget id="calculator">62 + 4</gadget> <output>66</output> <gadget id="calculator">66 / 10</gadget> <output>33/5 = around 6.6</output> <result>A</result>

A

Set S contains exactly 10 numbers and has an average (arithmetic mean) of 6.2. If one of the numbers in Set S is increased by 4, while all other numbers remain the same, what is the new average of Set S?

divide(add(multiply(10, 6.2), 4), 10)

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

"old set s - total is avg * no of elements = 6.2 * 10 = 62 if one number is increased by 4 then total increased to 62 + 4 = 66 new avg - 66 / 10 = 6.6 . hence answer is a ."

general

math_qa__7PM2UBOmssOoqnZk

How many numbers are divisible by 4 between 1 and 100. Choose the correct choice from the following. A) 24 B) 23 C) 22 D) 21 E) 25

<gadget id="calculator">4 * 1</gadget> <output>4</output> <gadget id="calculator">100 / 4</gadget> <output>25</output> <result>A</result>

A

How many numbers are divisible by 4 between 1 and 100.

divide(100, multiply(4, 1))

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

"numbers divisible by 4 till 100 = ( 100 / 4 ) = 25 but we should not consider 100 as we are asked to find the number between 1 to 100 which are divisible by 4 . so answer is 24 numbers . option : a"

general

math_qa__XEh6yEHDj748nfB3

If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. What is the actual distance travelled by him? Select the correct option: A) 33 B) 11 C) 38 D) 50 E) 12

<gadget id="calculator">14 - 10</gadget> <output>4</output> <gadget id="calculator">20 / 4</gadget> <output>5</output> <gadget id="calculator">10 * 5</gadget> <output>50</output> <result>D</result>

D

If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. What is the actual distance travelled by him?

multiply(10, divide(20, subtract(14, 10)))

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

"assume that the person would have covered x km if travelled at 10 km / hr ⇒ speed = distancetime = x 10 . . . . . ( equation 1 ) give that the person would have covered ( x + 20 ) km if travelled at 14 km / hr ⇒ speed = distancetime = ( x + 20 ) 14 . . . . . ( equation 2 ) from equations 1 and 2 , x 10 = ( x + 20 ) 1414 x = 10 x + 2004 x = 200 x = 2004 = 50 answer : d"

general

math_qa__dgtLfZfy99facFzz

If 5 < x < 11 and y = x + 6, what is the greatest possible integer value of x + y? Choose the most appropriate option: A) 25 B) 26 C) 27 D) 28 E) 29

<gadget id="calculator">6 + 10</gadget> <output>16</output> <gadget id="calculator">16 + 10</gadget> <output>26</output> <result>C</result>

C

If 5 < x < 11 and y = x + 6, what is the greatest possible integer value of x + y?

add(add(6, const_10), const_10)

add(n2,const_10)|add(#0,const_10)|

"x + y = x + x + 6 = 2 x + 6 we need to maximize this value and it needs to be an integer . 2 x is an integer when the decimal of x is . 0 or . 5 the largest such value is 10.5 then x + y = 10.5 + 16.5 = 27 . the answer is c ."

general

math_qa__aXI27w6DEfx0TeBx

Pipe P can fill a tank in 8 hours, pipe Q in 12 hours and pipe R in 20 hours. If all the pipes are open, in how many hours will the tank be filled? Choose the correct choice from the following answers: A) 2 hours B) 2.4 hours C) 3.8 hours D) 3.5 hours E) 4.5 hours

<gadget id="calculator">1 / 20</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">1 / 8</gadget> <output>1/8 = around 0.125</output> <gadget id="calculator">1 / 12</gadget> <output>1/12 = around 0.083333</output> <gadget id="calculator">(1/8) + (1/12)</gadget> <output>5/24 = around 0.208333</output> <gadget id="calculator">(1/20) + (5/24)</gadget> <output>31/120 = around 0.258333</output> <gadget id="calculator">1 / (31/120)</gadget> <output>120/31 = around 3.870968</output> <result>C</result>

C

Pipe P can fill a tank in 8 hours, pipe Q in 12 hours and pipe R in 20 hours. If all the pipes are open, in how many hours will the tank be filled?

inverse(add(divide(const_1, 20), add(divide(const_1, 8), divide(const_1, 12))))

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

explanation : part filled by ( p + q + r ) in 1 hour = ( 1 / 8 + 1 / 12 + 1 / 20 ) = 31 / 120 all the three pipes together will fill the tank = 120 / 31 = 3.8 hours answer c

physics

math_qa__Kh15ayr3SuOZR7HR

A worker's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 5 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month? Choose the most appropriate option: A) 2 / 11 B) 3 / 14 C) 5 / 17 D) 7 / 20 E) 11 / 30

<gadget id="calculator">12 / 5</gadget> <output>12/5 = around 2.4</output> <gadget id="calculator">(12/5) + 1</gadget> <output>17/5 = around 3.4</output> <gadget id="calculator">1 / (17/5)</gadget> <output>5/17 = around 0.294118</output> <result>C</result>

C

A worker's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of the year was 5 times the amount of that portion of her monthly take-home pay that she did NOT save. If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?

inverse(add(divide(const_12, 5), const_1))

divide(const_12,n0)|add(#0,const_1)|inverse(#1)|

"let x be the fraction of her take - home pay that the worker saved . let p be the monthly pay . 12 xp = 5 ( 1 - x ) p 12 xp = 5 p - 5 xp 17 xp = 5 p x = 5 / 17 the answer is c ."

general

math_qa__7yredTuELNClDFdM

A trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg. In order to earn a profit of 35%, what should be the sale price of the mixed tea? Choose the correct choice from the following answers. A) 23.75 B) 21.6 C) 20 D) 19.2 E) none of these

<gadget id="calculator">80 * 15</gadget> <output>1_200</output> <gadget id="calculator">20 * 20</gadget> <output>400</output> <gadget id="calculator">1_200 + 400</gadget> <output>1_600</output> <gadget id="calculator">80 + 20</gadget> <output>100</output> <gadget id="calculator">1_600 / 100</gadget> <output>16</output> <gadget id="calculator">16 * 35</gadget> <output>560</output> <gadget id="calculator">560 / 100</gadget> <output>28/5 = around 5.6</output> <gadget id="calculator">(28/5) + 16</gadget> <output>108/5 = around 21.6</output> <result>B</result>

B

A trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg. In order to earn a profit of 35%, what should be the sale price of the mixed tea?

add(divide(multiply(divide(add(multiply(80, 15), multiply(20, 20)), add(80, 20)), 35), const_100), divide(add(multiply(80, 15), multiply(20, 20)), add(80, 20)))

add(n0,n2)|multiply(n0,n1)|multiply(n2,n2)|add(#1,#2)|divide(#3,#0)|multiply(n4,#4)|divide(#5,const_100)|add(#6,#4)|

"c . p . of mixture = 80 × 15 + 20 × 20 / 80 + 20 = 16 ∴ s . p . = ( 100 + 35 ) / 100 × 16 = 21.6 answer b"

gain

math_qa__qxZtOxZesOs66H0Q

A cube of edge 12cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 20cm * 15cm , find the rise in water level? Answers. A) 5.76 cm B) 8.25 cm C) 11.25 cm D) 15.12 cm E) 20.62 cm

<gadget id="calculator">12 ** 3</gadget> <output>1_728</output> <gadget id="calculator">20 * 15</gadget> <output>300</output> <gadget id="calculator">1_728 / 300</gadget> <output>144/25 = around 5.76</output> <result>A</result>

A

A cube of edge 12cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 20cm * 15cm , find the rise in water level?

divide(volume_cube(12), multiply(20, 15))

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

"increase in volume = volume of the cube = 12 * 12 * 12 cm ^ 3 rise in water level = volume / area = 12 * 12 * 12 / 20 * 15 = 5.76 cm answer is a"

geometry

math_qa__kX3Bbpt11nI98SXX

A train 140 m long running at 84 kmph crosses a platform in 16 sec. What is the length of the platform? Answers. A) 287 B) 298 C) 233 D) 726 E) 267

<gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">84 * (5/18)</gadget> <output>70/3 = around 23.333333</output> <gadget id="calculator">16 * (70/3)</gadget> <output>1_120/3 = around 373.333333</output> <gadget id="calculator">(1_120/3) - 140</gadget> <output>700/3 = around 233.333333</output> <result>C</result>

C

A train 140 m long running at 84 kmph crosses a platform in 16 sec. What is the length of the platform?

subtract(multiply(16, multiply(84, const_0_2778)), 140)

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

"d = 84 * 5 / 18 = 16 = 373 â € “ 140 = 233 answer : c"

physics

math_qa__0JUL5VVFxAcvK1v9

By travelling at 70 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time? Answers A) 25 kmph B) 20 kmph C) 28 kmph D) 35 kmph E) 32 kmph

<gadget id="calculator">70 * 3</gadget> <output>210</output> <gadget id="calculator">210 * 2</gadget> <output>420</output> <gadget id="calculator">420 / 3</gadget> <output>140</output> <gadget id="calculator">210 - 140</gadget> <output>70</output> <gadget id="calculator">3 - 1</gadget> <output>2</output> <gadget id="calculator">70 / 2</gadget> <output>35</output> <result>D</result>

D

By travelling at 70 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?

divide(subtract(multiply(70, const_3), divide(multiply(multiply(70, const_3), const_2), const_3)), subtract(const_3, const_1))

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

let the time taken to reach the destination be 3 x hours . total distance = 70 * 3 x = 210 x km he covered 2 / 3 * 210 x = 140 x km in 1 / 3 * 3 x = x hours so , the remaining 70 x km , he has to cover in 2 x hours . required speed = 70 x / 2 x = 35 kmph . answer : d

physics

math_qa__3qMQvjp0Hi4FhEtD

How many times will the digit 8 be written when listing the integers from 1 to 1000? Pick: A) 164 B) 297 C) 300 D) 345 E) 482

<gadget id="calculator">1 * 10</gadget> <output>10</output> <gadget id="calculator">10 * 10</gadget> <output>100</output> <gadget id="calculator">100 * 3</gadget> <output>300</output> <result>C</result>

C

How many times will the digit 8 be written when listing the integers from 1 to 1000?

multiply(multiply(multiply(1, const_10), const_10), const_3)

multiply(n1,const_10)|multiply(#0,const_10)|multiply(#1,const_3)|

"many approaches are possible . for example : consider numbers from 0 to 999 written as follows : 1 . 000 2 . 001 3 . 002 4 . 003 . . . . . . . . . 1000 . 999 we have 1000 numbers . we used 3 digits per number , hence used total of 3 * 1000 = 3000 digits . now , why should any digit have preferences over another ? we used each of 10 digits equal # of times , thus we used each digit ( including 8 ) 3000 / 10 = 300 times . answer : c ."

general

math_qa__ggvIBhYPc5Jvo4pp

Machine A and machine B are each used to manufacture 330 sprockets. It takes machine A 10 hours longer to produce 330 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces? Select: A) 5 B) 4 C) 6 D) 8 E) 3

<gadget id="calculator">10 * 330</gadget> <output>3_300</output> <gadget id="calculator">100 + 10</gadget> <output>110</output> <gadget id="calculator">110 / 100</gadget> <output>11/10 = around 1.1</output> <gadget id="calculator">3_300 * (11/10)</gadget> <output>3_630</output> <gadget id="calculator">330 * (11/10)</gadget> <output>363</output> <gadget id="calculator">363 - 330</gadget> <output>33</output> <gadget id="calculator">3_630 / 33</gadget> <output>110</output> <gadget id="calculator">330 / 110</gadget> <output>3</output> <result>E</result>

E

Machine A and machine B are each used to manufacture 330 sprockets. It takes machine A 10 hours longer to produce 330 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?

divide(330, divide(multiply(multiply(10, 330), divide(add(const_100, 10), const_100)), subtract(multiply(330, divide(add(const_100, 10), const_100)), 330)))

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

"machine b : takes x hours to produce 330 sprockets machine a : takes ( x + 10 ) hours to produce 330 sprockets machine b : in 1 hour , b makes 330 / x sprockets machine a : in 1 hour , a makes 330 / ( x + 10 ) sprockets equating : 1.1 ( 330 / ( x + 10 ) ) = 330 / x 484 / ( x + 10 ) = 330 / x 363 x = 330 x + 3300 33 x = 3300 x = 100 a makes 330 / ( 110 ) = 3 sprockets per hour answer : e"

gain

math_qa__IdW60MKFncpNiRFl

If the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 217, what is the common ratio of the G.P? Pick one: A) 3 B) 1 / 3 C) 2 D) 6 E) 1 / 6

<gadget id="calculator">217 - 1</gadget> <output>216</output> <gadget id="calculator">1 / 3</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">216 ** (1/3)</gadget> <output>6</output> <result>D</result>

D

If the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 217, what is the common ratio of the G.P?

power(subtract(217, const_1), divide(const_1, 3))

divide(const_1,n1)|subtract(n2,const_1)|power(#1,#0)|

"217 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 217 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2 . . . . . . . . . 217 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 216 = ( r ^ 3 ( 1 + r ^ 1 + r ^ 2 ) ) / ( ( 1 + r ^ 1 + r ^ 2 ) ) 216 = r ^ 3 r = 6 d"

other

math_qa__r5CEpvJ7XByQzglV

On dividing 136 by a number, the quotient is 9 and the remainder is 1. Find the divisor? Choose the correct choice from the following. A) 12 B) 15 C) 16 D) 17 E) 18

<gadget id="calculator">136 / 9</gadget> <output>136/9 = around 15.111111</output> <gadget id="calculator">floor(136/9)</gadget> <output>15</output> <result>B</result>

B

On dividing 136 by a number, the quotient is 9 and the remainder is 1. Find the divisor?

floor(divide(136, 9))

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

"d = ( d - r ) / q = ( 136 - 1 ) / 9 = 135 / 9 = 15 b )"

general

math_qa__yj8MHNwzLq5eHDdP

A 72 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume? Pick one. A) 8 B) 12 C) 18 D) 14 E) 16

<gadget id="calculator">10 - 8</gadget> <output>2</output> <gadget id="calculator">72 * 2</gadget> <output>144</output> <gadget id="calculator">144 / 8</gadget> <output>18</output> <result>C</result>

C

A 72 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume?

divide(multiply(72, subtract(10, 8)), 8)

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

"amount of salt = 7.2 assume x gallons of water are added . 7.2 / 72 + x = 8 / 100 720 = 8 x + 576 8 x = 144 x = 18 correct option : c"

general

math_qa__ASksfluSabKyG8en

The radius of a cylindrical vessel is 9cm and height is 3cm. Find the whole surface of the cylinder? Choose the correct choice: A) 308 sq cm B) 220 sq cm C) 440 sq cm D) 132 sq cm E) 678.8 sq cm

<gadget id="calculator">2 * pi * 9 * (9 + 3)</gadget> <output>216*pi = around 678.584013</output> <result>E</result>

E

The radius of a cylindrical vessel is 9cm and height is 3cm. Find the whole surface of the cylinder?

surface_cylinder(9, 3)

surface_cylinder(n0,n1)|

"r = 9 h = 3 2 π r ( h + r ) = 2 * 22 / 7 * 9 ( 12 ) = 678.8 answer : e"

geometry

math_qa__XowqFTuYVFdHoUji

The simple interest on a sum of money will be Rs.600 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year? Choose the correct choice from the following choices. A) 8981 B) 3799 C) 1200 D) 2693 E) 1732

<gadget id="calculator">600 / 10</gadget> <output>60</output> <gadget id="calculator">60 * 5</gadget> <output>300</output> <gadget id="calculator">300 * 3</gadget> <output>900</output> <gadget id="calculator">900 + 300</gadget> <output>1_200</output> <result>C</result>

C

The simple interest on a sum of money will be Rs.600 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?

add(multiply(multiply(divide(600, 10), 5), const_3), multiply(divide(600, 10), 5))

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

"p - - - 10 - - - - 600 p - - - 5 - - - - - 300 3 p - - - 5 - - - - - 900 - - - - - - = > 1200 answer : c"

general

math_qa__O13djsQJupmNDFoB

A rectangular floor that measures 24 meters by 64 meters is to be covered with carpet squares that each measure 8 meters by 8 meters. If the carpet squares cost $24 apiece, what is the total cost for the number of carpet squares needed to cover the floor? Choose the correct choice from the following answers A) $ 200 B) $ 576 C) $ 480 D) $ 960 E) $ 1,920

<gadget id="calculator">24 * 24</gadget> <output>576</output> <result>B</result>

B

A rectangular floor that measures 24 meters by 64 meters is to be covered with carpet squares that each measure 8 meters by 8 meters. If the carpet squares cost $24 apiece, what is the total cost for the number of carpet squares needed to cover the floor?

multiply(24, 24)

multiply(n0,n0)

the width of the rectangular floor ( 24 m ) is a multiple of one side of the square ( 8 m ) , and the length of the floor ( 64 m ) is also a multiple of the side of the square . so the number of carpets to cover the floor is ( 24 / 8 ) * ( 64 / 8 ) = 24 . the total cost is 24 * 24 = $ 576 . the answer is , therefore , b .

geometry

math_qa__t1619jagcc1SCEmk

What least number must be subtracted from 427751 so that remaining no.is divisible by 10 Choose the correct choice from the following answers A) 3 B) 1 C) 6 D) 8 E) 9

<gadget id="calculator">427_751 / 10</gadget> <output>427_751/10 = around 42_775.1</output> <gadget id="calculator">floor(427_751/10)</gadget> <output>42_775</output> <gadget id="calculator">42_775 * 10</gadget> <output>427_750</output> <gadget id="calculator">427_751 - 427_750</gadget> <output>1</output> <result>B</result>

B

What least number must be subtracted from 427751 so that remaining no.is divisible by 10

subtract(427751, multiply(floor(divide(427751, 10)), 10))

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

"explanation : on dividing 427751 by 10 we get the remainder 1 , so 1 should be subtracted option b"

general

math_qa__4SIQsU5u6wOus8MH

Jim is able to sell a hand-carved statue for $660 which was a 20% profit over his cost. How much did the statue originally cost him? Choose the correct choice from the following choices A) $ 496.30 B) $ 512.40 C) $ 550 D) $ 574.90 E) $ 588.20

<gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(1/5) + 1</gadget> <output>6/5 = around 1.2</output> <gadget id="calculator">660 / (6/5)</gadget> <output>550</output> <result>C</result>

C

Jim is able to sell a hand-carved statue for $660 which was a 20% profit over his cost. How much did the statue originally cost him?

divide(660, add(divide(20, const_100), const_1))

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

"cost price = 660 / 120 * 100 = 550 answer : c"

gain

math_qa__2GkpGfBnam0UYyXq

The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of correct time. How much does the clock gain or lose in 12 hours? Choose the correct choice from the following options: A) 27.273 seconds B) 29.273 seconds C) 37.273 seconds D) 47.273 seconds E) 17.273 seconds

<gadget id="calculator">2 * 3</gadget> <output>6</output> <gadget id="calculator">6 * 60</gadget> <output>360</output> <gadget id="calculator">3 * 4</gadget> <output>12</output> <gadget id="calculator">360 / 12</gadget> <output>30</output> <gadget id="calculator">360 - 30</gadget> <output>330</output> <gadget id="calculator">330 / 60</gadget> <output>11/2 = around 5.5</output> <gadget id="calculator">360 / (11/2)</gadget> <output>720/11 = around 65.454545</output> <gadget id="calculator">(720/11) - 65</gadget> <output>5/11 = around 0.454545</output> <gadget id="calculator">(5/11) * 60</gadget> <output>300/11 = around 27.272727</output> <result>A</result>

A

The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of correct time. How much does the clock gain or lose in 12 hours?

multiply(subtract(divide(multiply(multiply(const_2, const_3), const_60), divide(subtract(multiply(multiply(const_2, const_3), const_60), divide(multiply(multiply(const_2, const_3), const_60), multiply(const_3, const_4))), const_60)), 65), const_60)

multiply(const_2,const_3)|multiply(const_3,const_4)|multiply(#0,const_60)|divide(#2,#1)|subtract(#2,#3)|divide(#4,const_60)|divide(#2,#5)|subtract(#6,n0)|multiply(#7,const_60)

after 60 minute rotation the minute hand will make an angle of 30 degree with hour hand . after that let the time required to make an overtake is t minute in this time angle covered by minute hand = ( 360 / 60 ) t = 6 t similarly angle covered by hour hand = ( 30 / 60 ) t = t / 2 so for overtake 6 t = 30 + t / 2 or t = 60 / 11 min = 5 min and 5 / 11 min = 5 min and 300 / 11 sec = 5 min and 27.273 sec so clock loses 27.273 seconds answer : a

physics

math_qa__PcT6PVRBVflLGK0W

Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 184 cms. What was the ratio F of men to women? Choose one A) 5 : 2 B) 5 : 1 C) 4 : 3 D) 4 : 1 E) 3 : 1

<gadget id="calculator">180 - 170</gadget> <output>10</output> <gadget id="calculator">184 - 180</gadget> <output>4</output> <gadget id="calculator">10 / 4</gadget> <output>5/2 = around 2.5</output> <result>A</result>

A

Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 184 cms. What was the ratio F of men to women?

divide(subtract(180, 170), subtract(184, 180))

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

( a ) f = 184 x 5 + 170 x 2 = 1260 . a

general

math_qa__NutAbwPQliuu6gFD

Average monthly income of a family of 3 earning members was Rs. 735. One of the earning members died and therefore, the average income came down to Rs 650. The income of the deceased was? Choose the correct choice from the following answers: A) rs . 692.80 B) rs . 905 C) rs . 990 D) rs . 1385 E) none

<gadget id="calculator">735 * 3</gadget> <output>2_205</output> <gadget id="calculator">3 - 1</gadget> <output>2</output> <gadget id="calculator">650 * 2</gadget> <output>1_300</output> <gadget id="calculator">2_205 - 1_300</gadget> <output>905</output> <result>B</result>

B

Average monthly income of a family of 3 earning members was Rs. 735. One of the earning members died and therefore, the average income came down to Rs 650. The income of the deceased was?

subtract(multiply(735, 3), multiply(650, subtract(3, const_1)))

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

"answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 735 x 3 - 650 x 2 rs . = 905 rs . correct option : b"

general

math_qa__Fn9jmGy45jJr6WAZ

A tank can supply water to a village for 20 days. If a leak at the bottom of the tank drains out 10 liters per day, the supply lasts for 15 days only. For how many days will the supply last if the leak drains out 20 liters per day? Choose the correct choice from the following answers: A) 9 B) 10 C) 11 D) 12 E) 14

<gadget id="calculator">10 * 15</gadget> <output>150</output> <gadget id="calculator">20 - 15</gadget> <output>5</output> <gadget id="calculator">150 / 5</gadget> <output>30</output> <gadget id="calculator">30 * 20</gadget> <output>600</output> <gadget id="calculator">20 + 30</gadget> <output>50</output> <gadget id="calculator">600 / 50</gadget> <output>12</output> <result>D</result>

D

A tank can supply water to a village for 20 days. If a leak at the bottom of the tank drains out 10 liters per day, the supply lasts for 15 days only. For how many days will the supply last if the leak drains out 20 liters per day?

divide(multiply(divide(multiply(10, 15), subtract(20, 15)), 20), add(20, divide(multiply(10, 15), subtract(20, 15))))

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

"losing 10 liters per day results in a loss of 150 liters in 15 days . so , those 150 liters were for 5 days , making daily consumption of the village 30 liters per day . thus the capacity of the tank is 30 * 20 = 600 liters . losing 20 liters plus 30 liters gives 50 liters per day . at this rate the supply will last 600 / 50 = 12 days . the answer is d ."

physics

math_qa__TsEgOLlDnrD9DtVS

31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 14 of these 31 were also Nobel Prize laureates. Of the scientists that attended that workshop and had not received the Wolf prize, the number of scientists that had received the Nobel Prize was 3 greater than the number of scientists that had not received the Nobel Prize. If 50 of the scientists attended that workshop, how many of them were Nobel Prize laureates? Pick: A) 11 B) 18 C) 25 D) 29 E) d ) 36

<gadget id="calculator">50 - 31</gadget> <output>19</output> <gadget id="calculator">19 - 3</gadget> <output>16</output> <gadget id="calculator">16 / 2</gadget> <output>8</output> <gadget id="calculator">3 + 8</gadget> <output>11</output> <gadget id="calculator">11 + 14</gadget> <output>25</output> <result>C</result>

C

31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 14 of these 31 were also Nobel Prize laureates. Of the scientists that attended that workshop and had not received the Wolf prize, the number of scientists that had received the Nobel Prize was 3 greater than the number of scientists that had not received the Nobel Prize. If 50 of the scientists attended that workshop, how many of them were Nobel Prize laureates?

add(add(3, divide(subtract(subtract(50, 31), 3), const_2)), 14)

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

"lets solve by creating equation . . w = 31 . . total = 50 . . not w = 50 - 31 = 19 . . now let people who were neither be x , so out of 19 who won nobel = x + 3 . . so x + x + 3 = 19 or x = 8 . . so who won nobel but not wolf = x + 3 = 11 . . but people who won both w and n = 13 . . so total who won n = 11 + 14 = 25 . . c"

physics

math_qa__0nrpre05KarrQulU

A committee is reviewing a total of 20x black-and-white films and 6y color films for a festival. If the committee selects y/x% of the black-and-white films and all of the color films, what fraction X of the selected films are in color? Choose the most appropriate option. A) 1 / 130 B) 1 / 5 C) 3 / 13 D) 10 / 13 E) 30 / 31

<gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(1/5) + 6</gadget> <output>31/5 = around 6.2</output> <gadget id="calculator">6 / (31/5)</gadget> <output>30/31 = around 0.967742</output> <result>E</result>

E

A committee is reviewing a total of 20x black-and-white films and 6y color films for a festival. If the committee selects y/x% of the black-and-white films and all of the color films, what fraction X of the selected films are in color?

divide(6, add(divide(20, const_100), 6))

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

"it ' s y / xpercentnot y / x . if x = 20 and y = 10 . then : 20 x = 400 black - and - white films ; 6 y = 60 color films . y / x % = 10 / 20 % = 0.5 % of the black - and - white films , so 2 black - and - white films and all 60 color films , thus total of 62 films were selected . color films thus compose x = 60 / 62 = 30 / 31 of the selected films . answer : e ."

general

math_qa__OGzVWc9ZWbiPAFqt

For how many integers pair (x,y) satisfies the result (1/x)+((1/y)=1/16 Choose one A) 12 B) 6 C) 10 D) 16 E) 19

<gadget id="calculator">16 + 1</gadget> <output>17</output> <gadget id="calculator">17 + 1</gadget> <output>18</output> <gadget id="calculator">18 + 1</gadget> <output>19</output> <result>E</result>

E

For how many integers pair (x,y) satisfies the result (1/x)+((1/y)=1/16

add(add(add(16, 1), 1), 1)

add(n0,n3)|add(n0,#0)|add(n0,#1)

it seems that the accepted answer is wrong , according to wolframalpha . the answer should be 31 , which is n ' t even listed as a selectable answer . e

general

math_qa__vrlFcVavOV9c9vcf

ABCD is a square. E and F are the midpoints of sides CD and BC, respectively. What is the ratio of the shaded region area to the unshaded region? Answers A) 1 : 1 B) 2 : 1 C) 3 : 1 D) 5 : 3 E) 8 : 3

<gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">1 + (1/2)</gadget> <output>3/2 = around 1.5</output> <gadget id="calculator">(3/2) + (1/2)</gadget> <output>2</output> <gadget id="calculator">2 + (1/2)</gadget> <output>5/2 = around 2.5</output> <gadget id="calculator">(1/2) + (1/2)</gadget> <output>1</output> <gadget id="calculator">(5/2) / (3/2)</gadget> <output>5/3 = around 1.666667</output> <result>D</result>

D

ABCD is a square. E and F are the midpoints of sides CD and BC, respectively. What is the ratio of the shaded region area to the unshaded region?

divide(add(add(add(const_1, divide(const_1, const_2)), divide(const_1, const_2)), divide(const_1, const_2)), add(add(divide(const_1, const_2), divide(const_1, const_2)), divide(const_1, const_2)))

divide(const_1,const_2)|add(#0,const_1)|add(#0,#0)|add(#1,#0)|add(#2,#0)|add(#3,#0)|divide(#5,#4)

let ' s join the midpoints as shown in the figure then we ' ll get four small squares . . . aodx be 1 and similarly all squares . . and we can split the unit 1 into half and half as per the mid points . . . then shaded will be 1 + 1 / 2 + 1 / 2 + 1 / 2 = 5 / 2 and unshaded is 1 / 2 + 1 / 2 + 1 / 2 = 3 / 2 . . shaded : unshaded is 5 : 3 . . ans option d .

geometry

math_qa__raVPy7VBJq6GgD3U

A certain clock marks every hour by striking a number of times equal to the hour, and the time require for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds. At 7:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke? Options: A) 26 B) 29 C) 19 D) 30 E) 40

<gadget id="calculator">7 - 1</gadget> <output>6</output> <gadget id="calculator">6 + 7</gadget> <output>13</output> <gadget id="calculator">6 - 1</gadget> <output>5</output> <gadget id="calculator">5 + 6</gadget> <output>11</output> <gadget id="calculator">22 / 11</gadget> <output>2</output> <gadget id="calculator">13 * 2</gadget> <output>26</output> <result>A</result>

A

A certain clock marks every hour by striking a number of times equal to the hour, and the time require for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds. At 7:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?

multiply(add(subtract(7, const_1), 7), divide(22, add(subtract(6, const_1), 6)))

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

"at 6 ' o clock , there would be 6 strikes . first strike , then a short interval , the second strike , then a short interval and so on till the 6 th strike . so there would be in all 5 intervals between 6 strikes . similarly , between 7 strikes , there would be 6 intervals . according to the question , the time spent in the strike and the interval is same . at 6 ' o clock , the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs . at 7 ' o clock , the 7 strikes and 6 intervals will take 2 * ( 7 + 6 ) = 26 secs a"

general

math_qa__ZkvjPOPt15jCgRYH

A dishonest dealer professes to sell goods at the cost price but uses a weight of 600 grams per kg, what is his percent? Choose the correct choice from the following: A) 28 % B) 66.7 % C) 55 % D) 28 % E) 55 %

<gadget id="calculator">100 / 600</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">3 + 2</gadget> <output>5</output> <gadget id="calculator">5 * 2</gadget> <output>10</output> <gadget id="calculator">100 * 10</gadget> <output>1_000</output> <gadget id="calculator">(1/6) * 1_000</gadget> <output>500/3 = around 166.666667</output> <gadget id="calculator">(500/3) - 100</gadget> <output>200/3 = around 66.666667</output> <result>B</result>

B

A dishonest dealer professes to sell goods at the cost price but uses a weight of 600 grams per kg, what is his percent?

subtract(multiply(divide(const_100, 600), multiply(const_100, multiply(add(const_3, const_2), const_2))), const_100)

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

"600 - - - 400 100 - - - ? = > 66.7 % answer : b"

gain

math_qa__qV3xkFAetveUyVHb

15 men can complete a piece of work in 25 days. In how many days can 20 men complete that piece of work? Choose the correct choice from the following answers A) 55 days B) 18.75 days C) 20 days D) 88 days E) 44 days

<gadget id="calculator">25 * 15</gadget> <output>375</output> <gadget id="calculator">375 / 20</gadget> <output>75/4 = around 18.75</output> <result>B</result>

B

15 men can complete a piece of work in 25 days. In how many days can 20 men complete that piece of work?

divide(multiply(25, 15), 20)

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

"15 * 25 = 20 * x = > x = 18.75 days answer : b"

physics

math_qa__p2lSSoKOauWKtuXY

80 is what percent of 160? Choose the correct choice: A) 35 % B) 40 % C) 45 % D) 50 % E) 55 %

<gadget id="calculator">80 / 160</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">(1/2) * 100</gadget> <output>50</output> <result>D</result>

D

80 is what percent of 160?

multiply(divide(80, 160), const_100)

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

80 / 160 × 100 = 50 % answer : d

gain

math_qa__d2QZZ48UL6i0iNJQ

The price of commodity X increases by 30 cents every year, while the price of commodity Y increases by 20 cents every year. If in 2001, the price of commodity X was $4.20 and the price of commodity Y was $4.40, in which year will commodity X cost 40 cents more than the commodity Y? Choose the most appropriate option. A) 2007 B) 2008 C) 2009 D) 2010 E) 2011

<gadget id="calculator">40 / 100</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">4.4 - 4.2</gadget> <output>0.2</output> <gadget id="calculator">(2/5) + 0.2</gadget> <output>0.6</output> <gadget id="calculator">30 / 100</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">(3/10) - 0.2</gadget> <output>0.1</output> <gadget id="calculator">0.6 / 0.1</gadget> <output>6</output> <gadget id="calculator">2_001 + 6</gadget> <output>2_007</output> <result>A</result>

A

The price of commodity X increases by 30 cents every year, while the price of commodity Y increases by 20 cents every year. If in 2001, the price of commodity X was $4.20 and the price of commodity Y was $4.40, in which year will commodity X cost 40 cents more than the commodity Y?

add(2001, divide(add(divide(40, const_100), subtract(4.40, 4.20)), subtract(divide(30, const_100), subtract(4.40, 4.20))))

divide(n5,const_100)|divide(n0,const_100)|subtract(n4,n3)|add(#0,#2)|subtract(#1,#2)|divide(#3,#4)|add(n2,#5)|

"the cost of commodity x increases by 10 cents per year relative to commodity y . the price of x must gain 20 + 40 = 60 cents on commodity y , which will take 6 years . the answer is a ."

general

math_qa__Iw436RSkiq7SFulo

A 300 metre long train crosses a platform in 39 seconds while it crosses a post in 18 seconds. What is the length of the platform? Choose the correct answer: A) 150 m B) 350 m C) 420 m D) 600 m E) 700 m

<gadget id="calculator">18 / 3</gadget> <output>6</output> <gadget id="calculator">300 / 6</gadget> <output>50</output> <gadget id="calculator">50 * 39</gadget> <output>1_950</output> <gadget id="calculator">3 * 300</gadget> <output>900</output> <gadget id="calculator">1_950 - 900</gadget> <output>1_050</output> <gadget id="calculator">1_050 / 3</gadget> <output>350</output> <result>B</result>

B

A 300 metre long train crosses a platform in 39 seconds while it crosses a post in 18 seconds. What is the length of the platform?

divide(subtract(multiply(divide(300, divide(18, const_3)), 39), multiply(const_3, 300)), const_3)

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

explanation : length of the train = distance covered in crossing the post = speed × time = speed × 18 speed of the train = 300 / 18 m / s = 50 / 3 m / s time taken to cross the platform = 39 s ( 300 + x ) / ( 50 / 3 ) = 39 s where x is the length of the platform 300 + x = ( 39 × 50 ) / 3 = 650 meter x = 650 - 300 = 350 meter answer : option b

physics

math_qa__NZxW7Ngwuw1Acbqi

39 persons can repair a road in 24 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work? Pick: A) 10 B) 13 C) 14 D) 15 E) 26

<gadget id="calculator">39 * 24</gadget> <output>936</output> <gadget id="calculator">936 * 5</gadget> <output>4_680</output> <gadget id="calculator">30 * 6</gadget> <output>180</output> <gadget id="calculator">4_680 / 180</gadget> <output>26</output> <result>E</result>

E

39 persons can repair a road in 24 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?

divide(multiply(multiply(39, 24), 5), multiply(30, 6))

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

"let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 39 : : 12 : x working hours / day 6 : 5 30 x 6 x x = 39 x 5 x 24 x = ( 39 x 5 x 24 ) / ( 30 x 6 ) x = 26 . answer : e"

physics

math_qa__1HTvEvB3P1ew3KDg

Two boats are heading towards each other at constant speeds of 4 miles/hr and 20 miles/hr respectively. They begin at a distance 20 miles from each other. How far are they (in miles) one minute before they collide ? Pick one: A) 1 / 12 B) 6 / 15 C) 1 / 6 D) 1 / 3 E) 1 / 5

<gadget id="calculator">20 + 4</gadget> <output>24</output> <gadget id="calculator">24 / 60</gadget> <output>2/5 = around 0.4</output> <result>B</result>

B

Two boats are heading towards each other at constant speeds of 4 miles/hr and 20 miles/hr respectively. They begin at a distance 20 miles from each other. How far are they (in miles) one minute before they collide ?

divide(add(20, 4), const_60)

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

"the question asks : how far apart will they be 1 minute = 1 / 60 hours before they collide ? since the combined rate of the boats is 4 + 20 = 25 mph then 1 / 60 hours before they collide they ' ll be rate * time = distance - - > 24 * 1 / 60 = 6 / 15 miles apart . answer : b ."

physics

math_qa__3L0wCeFnbDPDw4vR

1/0.04 is equal to Choose the correct choice: A) 25.5 B) 2.5 C) 25 D) . 25 E) none of these

<gadget id="calculator">1 / 0.04</gadget> <output>25</output> <result>C</result>

C

1/0.04 is equal to

divide(1, 0.04)

divide(n0,n1)|

"explanation : 1 / 0.04 = ( 1 * 100 ) / 4 = 100 / 4 = 25 option c"

general

math_qa__fpE3nX1MCA31wxAc

A retail appliance store priced a video recorder at 20 percent above the wholesale cost of $200. If a store employee applied the 30 percent employee discount to the retail price to buy the recorder, how much did the employee pay for the recorder? Select the correct option. A) $ 198 B) $ 216 C) $ 220 D) $ 230 E) $ 168

<gadget id="calculator">200 / 100</gadget> <output>2</output> <gadget id="calculator">2 * 20</gadget> <output>40</output> <gadget id="calculator">200 + 40</gadget> <output>240</output> <gadget id="calculator">240 / 100</gadget> <output>12/5 = around 2.4</output> <gadget id="calculator">(12/5) * 30</gadget> <output>72</output> <gadget id="calculator">240 - 72</gadget> <output>168</output> <result>E</result>

E

A retail appliance store priced a video recorder at 20 percent above the wholesale cost of $200. If a store employee applied the 30 percent employee discount to the retail price to buy the recorder, how much did the employee pay for the recorder?

subtract(add(200, multiply(divide(200, const_100), 20)), multiply(divide(add(200, multiply(divide(200, const_100), 20)), const_100), 30))

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

"wholesale cost of video recorder = 200 $ video recorder was priced at 20 percent above 200 = 240 $ % discount given by store employee = 30 emlpoyee paid = . 7 * 240 = 168 $ answer e"

gain

math_qa__hZNsJxrFBmNH2d4l

If an integer n is to be chosen at random from the integers 1 to 92, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8? Choose the correct option A) 1 / 4 B) 3 / 8 C) 1 / 2 D) 29 / 46 E) 3 / 4

<gadget id="calculator">92 / 2</gadget> <output>46</output> <gadget id="calculator">92 / 8</gadget> <output>23/2 = around 11.5</output> <gadget id="calculator">46 + (23/2)</gadget> <output>115/2 = around 57.5</output> <gadget id="calculator">(115/2) / 92</gadget> <output>5/8 = around 0.625</output> <result>D</result>

D

If an integer n is to be chosen at random from the integers 1 to 92, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?

divide(add(divide(92, 2), divide(92, 8)), 92)

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

"n ( n + 1 ) ( n + 2 ) will be divisible by 8 when n is a multiple of 2 or when ( n + 1 ) is a multiple of 8 . thus when n is even , this whole expression will be divisible by 8 . from 1 to 96 , there are 46 even integers . now when ( n + 1 ) is multiple by 8 , we have 12 such values for ( n + 1 ) probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 = ( 46 + 12 ) / 92 = 58 / 96 = 29 / 46 ans is d"

general

math_qa__FQUGy66a9NxmnCiM

What sum of money will produce Rs.90 as simple interest in 4 years at 3 1/2 percent? Options A) 263 B) 500 C) 367 D) 642.9 E) 339

<gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">3 + (1/2)</gadget> <output>7/2 = around 3.5</output> <gadget id="calculator">4 * (7/2)</gadget> <output>14</output> <gadget id="calculator">14 / 100</gadget> <output>7/50 = around 0.14</output> <gadget id="calculator">90 / (7/50)</gadget> <output>4_500/7 = around 642.857143</output> <result>D</result>

D

What sum of money will produce Rs.90 as simple interest in 4 years at 3 1/2 percent?

divide(90, divide(multiply(4, add(3, divide(1, 2))), const_100))

divide(n3,n4)|add(n2,#0)|multiply(n1,#1)|divide(#2,const_100)|divide(n0,#3)|

"90 = ( p * 4 * 7 / 2 ) / 100 p = 642.9 answer : d"

gain

math_qa__dAdVTxhMIx1wbrv1

A and B enter into a partnership. A contributed Rs.5000 for 8 months and B Rs.6000 for 5 months. Find A's share in a total profit of rs.8400. Choose the correct choice from the following answers: A) rs . 4800 B) rs . 2400 C) rs . 3600 D) rs . 5600 E) none of these

<gadget id="calculator">5_000 * 8</gadget> <output>40_000</output> <gadget id="calculator">6_000 * 5</gadget> <output>30_000</output> <gadget id="calculator">40_000 + 30_000</gadget> <output>70_000</output> <gadget id="calculator">40_000 / 70_000</gadget> <output>4/7 = around 0.571429</output> <gadget id="calculator">8_400 * (4/7)</gadget> <output>4_800</output> <result>A</result>

A

A and B enter into a partnership. A contributed Rs.5000 for 8 months and B Rs.6000 for 5 months. Find A's share in a total profit of rs.8400.

multiply(8400, divide(multiply(5000, 8), add(multiply(5000, 8), multiply(6000, 5))))

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

explanation : ratio of capitals of a and b = ratio of their investments = 5000 × 8 : 6000 × 5 = 40000 : 30000 = 4 : 3 . : a ' s share = rs . [ ( 4 / 7 ) × 8400 ] = rs . 4800 answer : option a

gain

math_qa__Rcr8iHwUTfNunk3q

Two vessels A and B contain spirit and water in the ratio 5 : 2 and 7 : 6 respectively. Find the ratio in which these mixtures be mixed to obtain a new mixture in vessel C containing spirit and water in the ratio 8 : 5 ? Choose the most appropriate option. A) 3 : 4 B) 4 : 3 C) 9 : 7 D) 7 : 9 E) 8 : 1

<gadget id="calculator">2 + 7</gadget> <output>9</output> <gadget id="calculator">7 / 9</gadget> <output>7/9 = around 0.777778</output> <result>D</result>

D

Two vessels A and B contain spirit and water in the ratio 5 : 2 and 7 : 6 respectively. Find the ratio in which these mixtures be mixed to obtain a new mixture in vessel C containing spirit and water in the ratio 8 : 5 ?

divide(7, add(2, 7))

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

"explanation : let cost price ( cp ) of 1 litre spirit be rs . 1 quantity of spirit in 1 litre mixture from vessel a = 5 / 7 cost price ( cp ) of 1 litre mixture from vessel a = rs . = 5 / 7 quantity of spirit in 1 litre mixture from vessel b = 7 / 13 cost price ( cp ) of 1 litre mixture from vessel b = rs . = 7 / 13 quantity of spirit to be obtained in 1 litre mixture from vessel c = 8 / 13 cost price ( cp ) of 1 litre mixture from vessel c ( mean price ) = rs . = 8 / 13 = > mixture from vessel a : mixture from vessel b = 1 / 13 : 9 / 91 = 7 : 9 answer is d"

other

math_qa__vIJujwKU12xfJOtU

A rectangular lawn of dimensions 80 m * 40 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m? Choose the correct choice from the following. A) 2288 B) 2779 C) 3300 D) 3900 E) 2781

<gadget id="calculator">80 + 40</gadget> <output>120</output> <gadget id="calculator">120 - 10</gadget> <output>110</output> <gadget id="calculator">110 * 10</gadget> <output>1_100</output> <gadget id="calculator">1_100 * 3</gadget> <output>3_300</output> <result>C</result>

C

A rectangular lawn of dimensions 80 m * 40 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?

multiply(multiply(subtract(add(80, 40), 10), 10), 3)

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

"area = ( l + b â € “ d ) d ( 80 + 40 â € “ 10 ) 10 = > 1100 m 2 1100 * 3 = rs . 3300 answer : c"

geometry

math_qa__qNH5Poov1Lid3IoX

A 50 kg metal bar made of alloy of tin and silver lost 5 kg of its weight in the water. 10 kg of tin loses 1.375 kg in the water; 5 kg of silver loses 0.375 kg. What is the ratio of tin to silver in the bar? Select the correct option: A) 1 / 4 B) 2 / 5 C) 1 / 2 D) 3 / 5 E) 2 / 3

<gadget id="calculator">0.375 / 5</gadget> <output>0.075</output> <gadget id="calculator">0.075 * 50</gadget> <output>3.75</output> <gadget id="calculator">5 - 3.75</gadget> <output>1.25</output> <gadget id="calculator">1.375 / 10</gadget> <output>0.1375</output> <gadget id="calculator">0.1375 - 0.075</gadget> <output>0.0625</output> <gadget id="calculator">1.25 / 0.0625</gadget> <output>20</output> <gadget id="calculator">50 - 20</gadget> <output>30</output> <gadget id="calculator">20 / 30</gadget> <output>2/3 = around 0.666667</output> <result>E</result>

E

A 50 kg metal bar made of alloy of tin and silver lost 5 kg of its weight in the water. 10 kg of tin loses 1.375 kg in the water; 5 kg of silver loses 0.375 kg. What is the ratio of tin to silver in the bar?

divide(divide(subtract(5, multiply(divide(0.375, 5), 50)), subtract(divide(1.375, 10), divide(0.375, 5))), subtract(50, divide(subtract(5, multiply(divide(0.375, 5), 50)), subtract(divide(1.375, 10), divide(0.375, 5)))))

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

"you can simply use this formula to avoid confusion : w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2 . we have an overall loss ( average loss ) . the average loss is 5 kg when 50 kg alloy is immersed . this is a loss of ( 5 / 50 ) * 100 = 10 % . this is aavg the loss of tin is 1.375 kg for every 10 kg . this means it loses ( 1.375 / 10 ) * 100 = 13.75 % of its weight in water . this is a 1 . the loss of silver is . 375 kg for every 5 kg . this means it loses ( . 375 / 5 ) * 100 = 7.5 % of its weight in water . this is a 2 . weight of tin / weight of silver = ( silver ' s loss - avg loss ) / ( avg loss - tin ' s loss ) x / y = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2 / 3 e"

other

math_qa__13ib1RcNHLNiHEWt

A, B and C have Rs.300 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have? Answers A) 250 B) 249 C) 248 D) 247 E) 246

<gadget id="calculator">200 + 350</gadget> <output>550</output> <gadget id="calculator">550 - 300</gadget> <output>250</output> <result>A</result>

A

A, B and C have Rs.300 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?

subtract(add(200, 350), 300)

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

"a + b + c = 300 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 300 - - - - - - - - - - - - - - - - c = 250 answer : a"

general

math_qa__gj9eKoi8ABbUu8WW

United Telephone charges a base rate of $7.00 for service, plus an additional charge of $0.25 per minute. Atlantic Call charges a base rate of $12.00 for service, plus an additional charge of $0.20 per minute. For what number of minutes would the bills for each telephone company be the same? Choose the correct choice from the following choices A) 200 minutes B) 100 minutes C) 120 minutes D) 140 minutes E) 160 minutes

<gadget id="calculator">12 - 7</gadget> <output>5</output> <gadget id="calculator">0.25 - 0.2</gadget> <output>0.05</output> <gadget id="calculator">5 / 0.05</gadget> <output>100</output> <result>B</result>

B

United Telephone charges a base rate of $7.00 for service, plus an additional charge of $0.25 per minute. Atlantic Call charges a base rate of $12.00 for service, plus an additional charge of $0.20 per minute. For what number of minutes would the bills for each telephone company be the same?

divide(subtract(12.00, 7.00), subtract(0.25, 0.20))

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

"lets take number of minutesx . given that , 7 + 0.25 x = 12 + 0.2 x - > 0.05 x = 2 - > x = 100 minutes ans b"

general

math_qa__jAqFLWQA4EblA1G7

There are 50 students in a class. If 12% are absent on a particular day, find the number of students present in the class. Choose the correct option: A) 43 B) 36 C) 28 D) 129 E) 44

<gadget id="calculator">12 / 100</gadget> <output>3/25 = around 0.12</output> <gadget id="calculator">1 - (3/25)</gadget> <output>22/25 = around 0.88</output> <gadget id="calculator">(22/25) * 50</gadget> <output>44</output> <result>E</result>

E

There are 50 students in a class. If 12% are absent on a particular day, find the number of students present in the class.

multiply(subtract(const_1, divide(12, const_100.0)), 50)

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

"number of students absent on a particular day = 12 % of 50 i . e . , 12 / 100 × 50 = 6 therefore , the number of students present = 50 - 6 = 44 students . answer : e"

gain

math_qa__O42z07yIvcVoAyV2

How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 50 percent butterfat to obtain milk that is 20 percent butterfat? Pick one: A) 6 B) 12 C) 14 D) 24 E) 28

<gadget id="calculator">50 - 20</gadget> <output>30</output> <gadget id="calculator">30 * 8</gadget> <output>240</output> <gadget id="calculator">240 / 10</gadget> <output>24</output> <result>D</result>

D

How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 50 percent butterfat to obtain milk that is 20 percent butterfat?

divide(multiply(subtract(50, 20), 8), 10)

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

"equate the fat : 0.1 x + 0.5 * 8 = 0.2 ( x + 8 ) - - > x = 24 . answer : d ."

general

math_qa__gurZ6o2DX9IHdesv

Can C and can В are both right circular cylinders. The radius of can C is twice the radius of can B, while the height of can C is half the height of can B. If it costs $4.00 to fill half of can B with a certain brand of gasoline, how much would it cost to completely fill can C with the same brand of gasoline? Choose one: A) $ 1 B) $ 2 C) $ 4 D) $ 8 E) $ 16

<gadget id="calculator">2 * 4</gadget> <output>8</output> <gadget id="calculator">8 * 2</gadget> <output>16</output> <result>E</result>

E

Can C and can В are both right circular cylinders. The radius of can C is twice the radius of can B, while the height of can C is half the height of can B. If it costs $4.00 to fill half of can B with a certain brand of gasoline, how much would it cost to completely fill can C with the same brand of gasoline?

multiply(multiply(const_2, 4), const_2)

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

let x be the radius of b and 2 h be the height of b . therefore , radius of c = 2 x and height = h vol of b = 3.14 * x ^ 2 * 2 h vol of a = 3.14 * 4 x ^ 2 * h cost to fill half of b = $ 4 - - > cost to fill full b = $ 8 - - > 3.14 * x ^ 2 * 2 h = 8 - - > 3.14 * x ^ 2 * h = 4 - - > 4 * ( 3.14 * x ^ 2 * h ) = $ 16 ans e

geometry

math_qa__ZsjiY75r6uAFSZe1

A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 3 years ago? Choose one. A) 11 B) 10 C) 12 D) 14 E) 16

<gadget id="calculator">6 + 8</gadget> <output>14</output> <gadget id="calculator">14 - 3</gadget> <output>11</output> <result>A</result>

A

A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 3 years ago?

subtract(add(6, 8), 3)

add(n1,n2)|subtract(#0,n4)|

"let ' s say age of richard is ` ` r ' ' age of david is ` ` d ' ' age of scott is ` ` s ' ' now richard is 6 years older than david , i . e . r = d + 6 david is 8 years older than scott i . e . d = s + 8 if in 8 years , richard will be twice as old as scott i . e . r + 8 = 2 x ( s + 8 ) i . e . r + 8 = 2 s + 16 i . e . r = 2 s + 8 but r = d + 6 = ( s + 8 ) + 6 = s + 14 therefore , 2 s + 8 = s + 14 i . e . s = 6 i . e . r = 20 i . e . d = 14 now , how old was david 3 years ago ? i . e . d - 4 = 14 - 3 = 11 years answer : a"

general

math_qa__F2DhRPUlk4bbZzzA

6 years ago , the ratio of the ages of vimal and saroj was 6 : 5 . 4 years hence , the ratio of their ages will be 11 : 10 . what is saroj ' s age at present ? Choose the correct choice from the following answers: A) 12 B) 14 C) 16 D) 18 E) 15

<gadget id="calculator">11 * 10</gadget> <output>110</output> <gadget id="calculator">10 * 10</gadget> <output>100</output> <gadget id="calculator">110 - 100</gadget> <output>10</output> <gadget id="calculator">10 * 6</gadget> <output>60</output> <gadget id="calculator">11 * 5</gadget> <output>55</output> <gadget id="calculator">60 - 55</gadget> <output>5</output> <gadget id="calculator">10 / 5</gadget> <output>2</output> <gadget id="calculator">5 * 2</gadget> <output>10</output> <gadget id="calculator">10 + 6</gadget> <output>16</output> <result>C</result>

C

6 years ago , the ratio of the ages of vimal and saroj was 6 : 5 . 4 years hence , the ratio of their ages will be 11 : 10 . what is saroj ' s age at present ?

add(multiply(5, divide(subtract(multiply(11, 10), multiply(const_10, 10)), subtract(multiply(10, 6), multiply(11, 5)))), 6)

multiply(n4,n5)|multiply(n5,const_10)|multiply(n0,n5)|multiply(n2,n4)|subtract(#0,#1)|subtract(#2,#3)|divide(#4,#5)|multiply(n2,#6)|add(n0,#7)

given that , six years ago , the ratio of the ages of vimal and saroj = 6 : 5 hence we can assume that age of vimal six years ago = 6 x age of saroj six years ago = 5 x after 4 years , the ratio of their ages = 11 : 10 ⇒ ( 6 x + 10 ) : ( 5 x + 10 ) = 11 : 10 ⇒ 10 ( 6 x + 10 ) = 11 ( 5 x + 10 ) ⇒ 5 x = 10 ⇒ x = 105 = 2 saroj ' s present age = ( 5 x + 6 ) = 5 × 2 + 6 = 16 answer is c .

other

math_qa__PpJdNGWCMFumS8QJ

A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 70 km downstream. Answers: A) 4.25 hr B) 3.8 hr C) 8.25 hr D) 2.25 hr E) 2.50 hr

<gadget id="calculator">13 + 5</gadget> <output>18</output> <gadget id="calculator">70 / 18</gadget> <output>35/9 = around 3.888889</output> <result>B</result>

B

A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 70 km downstream.

divide(70, add(13, 5))

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

"speed of boat in still water = 13 km / hr speed of the stream = 5 km / hr speed downstream = ( 13 + 5 ) = 18 km / hr time taken to travel 70 km downstream = 70 ⠁ „ 18 = 3.8 hours answer is b"

physics

math_qa__FXRhJ1nDxd4OLaR4

If 60% of (x-y) = 20% of (x+y), then what percent of x is y? Choose one: A) 50 % B) 44.4 % C) 22.2 % D) 33.3 % E) 25 %

<gadget id="calculator">60 - 20</gadget> <output>40</output> <gadget id="calculator">60 + 20</gadget> <output>80</output> <gadget id="calculator">40 / 80</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">(1/2) * 100</gadget> <output>50</output> <result>A</result>

A

If 60% of (x-y) = 20% of (x+y), then what percent of x is y?

multiply(divide(subtract(60, 20), add(60, 20)), const_100)

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

"60 % of ( x - y ) = 20 % of ( x + y ) 60 / 100 ( x - y ) = 20 / 100 ( x + y ) 4 x = 8 y required percentage = y / x * 100 = 4 y / 8 y * 100 = 50 % answer is a"

general

math_qa__oSwqL1p0MT31hyD1

A and B undertake to do a piece of work for Rs. 600. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. !find the share of each. Choose the correct choice from the following options: A) 25 B) 50 C) 75 D) 80 E) none of them

<gadget id="calculator">4 + 3</gadget> <output>7</output> <gadget id="calculator">7 + 1</gadget> <output>8</output> <gadget id="calculator">1 / 8</gadget> <output>1/8 = around 0.125</output> <gadget id="calculator">(1/8) * 600</gadget> <output>75</output> <result>C</result>

C

A and B undertake to do a piece of work for Rs. 600. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. !find the share of each.

multiply(divide(const_1, add(add(const_4, const_3), const_1)), 600)

add(const_3,const_4)|add(#0,const_1)|divide(const_1,#1)|multiply(n0,#2)

c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 24 a : b : c = ratio of their 1 day ' s work = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . a ’ s share = rs . ( 600 * 4 / 8 ) = rs . 300 , b ' s share = rs . ( 600 * 3 / 8 ) = rs . 225 . c ' s share = rs . [ 600 - ( 300 + 225 » ) = rs . 75 . answer is c

physics

math_qa__i4toFzZqEscMLElq

How many even integers n, such that 20<=n<=220 are of the form 3k+4, where k is any natural number? Choose the most appropriate option. A) 28 B) 31 C) 34 D) 37 E) 40

<gadget id="calculator">220 - 2</gadget> <output>218</output> <gadget id="calculator">20 + 2</gadget> <output>22</output> <gadget id="calculator">218 - 22</gadget> <output>196</output> <gadget id="calculator">2 + 4</gadget> <output>6</output> <gadget id="calculator">196 / 6</gadget> <output>98/3 = around 32.666667</output> <gadget id="calculator">(98/3) + 1</gadget> <output>101/3 = around 33.666667</output> <result>C</result>

C

How many even integers n, such that 20<=n<=220 are of the form 3k+4, where k is any natural number?

add(divide(subtract(subtract(220, const_2), add(20, const_2)), add(const_2, 4)), const_1)

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

"the first number is 22 = 16 + 6 ( 1 ) . we can continue adding 6 to make a list : 22 , 28 , 34 , . . . the last number is 220 = 16 + 6 ( 34 ) there are 34 numbers in the list . the answer is c ."

general

math_qa__P6UYKizk9iZ2mAkT

The edges of three metal cubes are 1 cm, 3 cm, and 4 cm respectively. A new cube is made by melting these three cubes together. What is the edge of the new cube (in centimeters)? Select: A) 3.9 B) 4.2 C) 4.5 D) 4.8 E) 5.1

<gadget id="calculator">4 ** 3</gadget> <output>64</output> <gadget id="calculator">3 ** 3</gadget> <output>27</output> <gadget id="calculator">1 + 27</gadget> <output>28</output> <gadget id="calculator">64 + 28</gadget> <output>92</output> <gadget id="calculator">1 / 3</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">92 ** (1/3)</gadget> <output>92**(1/3) = around 4.514357</output> <result>C</result>

C

The edges of three metal cubes are 1 cm, 3 cm, and 4 cm respectively. A new cube is made by melting these three cubes together. What is the edge of the new cube (in centimeters)?

power(add(power(4, const_3), add(1, power(3, const_3))), const_0_33)

power(n1,const_3)|power(n2,const_3)|add(n0,#0)|add(#2,#1)|power(#3,const_0_33)

the total volume is 1 ^ 3 + 3 ^ 3 + 4 ^ 3 = 92 the edge of the new cube is the cube root of 92 which is about 4.5 cm . the answer is c .

physics

math_qa__II27iO3ktnzFafw9

An inspector rejects 10% of the meters as defective. How many will he examine to reject 12? Pick one: A) 100 B) 120 C) 250 D) 200 E) 160

<gadget id="calculator">12 * 100</gadget> <output>1_200</output> <gadget id="calculator">1_200 / 10</gadget> <output>120</output> <result>B</result>

B

An inspector rejects 10% of the meters as defective. How many will he examine to reject 12?

divide(multiply(12, const_100), 10)

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

"then , 10 % of x = 12 ( 10 / 100 ) x = 12 x = ( 12 * 100 * ) / 10 = 120 answer is b"

gain

math_qa__7djZvUPSvNC4YL7c

Car A runs at the speed of 50km/hr & reaches its destination in 6hr. Car B runs at the speed of 100 km/h & reaches its destination in 1h. What is the respective ratio of distances covered by Car A & Car B? Choose the most appropriate option A) 11 : 5 B) 3 : 1 C) 13 : 7 D) 15 : 7 E) 16 : 9

<gadget id="calculator">50 * 6</gadget> <output>300</output> <gadget id="calculator">100 * 1</gadget> <output>100</output> <gadget id="calculator">300 / 100</gadget> <output>3</output> <result>B</result>

B

Car A runs at the speed of 50km/hr & reaches its destination in 6hr. Car B runs at the speed of 100 km/h & reaches its destination in 1h. What is the respective ratio of distances covered by Car A & Car B?

divide(multiply(50, 6), multiply(100, 1))

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

"sol . distance travelled by car a = 50 × 6 = 300 km distance travelled by car b = 100 × 1 = 100 km ratio = 300 / 100 = 3 : 1 answer : b"

physics

math_qa__P4zM5av1AzEsrIEs

A cubical block of metal weighs 8 pounds. How much will another cube of the same metal weigh if its sides are twice as long? Choices: A) 48 B) 32 C) 24 D) 18 E) 64

<gadget id="calculator">2 * 4</gadget> <output>8</output> <gadget id="calculator">8 * 8</gadget> <output>64</output> <result>E</result>

E

A cubical block of metal weighs 8 pounds. How much will another cube of the same metal weigh if its sides are twice as long?

multiply(8, multiply(const_2, const_4))

multiply(const_2,const_4)|multiply(n0,#0)|

"for example our cube have a side 1 meter , so we have 1 cubical meter in this cube and this cubical meter weigth 6 pounds if we take cube with side 2 meters we will have 8 cubical meters in this cube 8 meters * 8 pounds = 64 pounds so answer is e and similar but more theoretical approach : if we have sides a and b than they have equal ration with their areas : a / b = a ^ 2 / b ^ 2 and they have equal ration with their volumes : a / b = a ^ 3 / b ^ 3 we have two sides 1 / 2 so their volume will be in ratio 1 / 8 weight of one cube * volume of another cube 8 * 8 = 64 so answer is e"

geometry

math_qa__MKbDo9Lp7NdvZSeE

Of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 20 grades are D's. What is the number of students in the course? Options: A) 80 B) 110 C) 160 D) 200 E) 400

<gadget id="calculator">1 / 5</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">1 / 4</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(1/5) + (1/4)</gadget> <output>9/20 = around 0.45</output> <gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">(9/20) + (1/2)</gadget> <output>19/20 = around 0.95</output> <gadget id="calculator">1 - (19/20)</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">20 / (1/20)</gadget> <output>400</output> <result>E</result>

E

Of the final grades received by the students in a certain math course, 1/5 are A's, 1/4 are B's, 1/2 are C's, and the remaining 20 grades are D's. What is the number of students in the course?

divide(20, subtract(1, add(add(divide(1, 5), divide(1, 4)), divide(1, 2))))

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

"we start by creating a variable for the total number of students in the math course . we can say : t = total number of students in the math course next , we can use variable t in an equation that we translate from the given information . we are given that , of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 20 grades are d ' s . since this represents all the grades in the class , it represents all the students in the class . thus we know : # a ’ s + # b ’ s + # c ’ s + # d ’ s = total number of students in the class 1 / 5 ( t ) + ¼ ( t ) + ½ ( t ) + 20 = t we can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have : 4 t + 5 t + 10 t + 400 = 20 t 19 t + 400 = 20 t 400 = t there are a total of 400 students in the math class . answer is e ."

general

math_qa__j0g1f8zIZqcFYjA6

How many pieces of 0.85 meteres can be cut from a rod 42.5 meteres long Choose the most appropriate option: A) 30 B) 40 C) 50 D) 60 E) 70

<gadget id="calculator">42.5 / 0.85</gadget> <output>50</output> <result>C</result>

C

How many pieces of 0.85 meteres can be cut from a rod 42.5 meteres long

divide(42.5, 0.85)

divide(n1,n0)

explanation : we need so simple divide 42.5 / 0.85 , = ( 4250 / 85 ) = 50 option c

physics

math_qa__h6QHzIi1p449FpJk

Ratio between Rahul and Deepak is 5:2, After 6 Years Rahul age will be 26 years. What is Deepak present age. Choose the correct choice from the following choices: A) 14 B) 15 C) 8 D) 22 E) 24

<gadget id="calculator">26 - 6</gadget> <output>20</output> <gadget id="calculator">20 * 2</gadget> <output>40</output> <gadget id="calculator">40 / 5</gadget> <output>8</output> <result>C</result>

C

Ratio between Rahul and Deepak is 5:2, After 6 Years Rahul age will be 26 years. What is Deepak present age.

divide(multiply(subtract(26, 6), 2), 5)

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

"explanation : present age is 5 x and 2 x , = > 5 x + 6 = 26 = > x = 4 so deepak age is = 2 ( 4 ) = 8 option c"

other

math_qa__p6wOMZ0kPcv2fblj

In what time will a train 400 m long cross an electric pole, it its speed be 144 km/hr? Choose the correct choice from the following options. A) 2.5 sec B) 12.9 sec C) 11.3 sec D) 21.9 sec E) 10.0 sec

<gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">144 * (5/18)</gadget> <output>40</output> <gadget id="calculator">400 / 40</gadget> <output>10</output> <result>E</result>

E

In what time will a train 400 m long cross an electric pole, it its speed be 144 km/hr?

divide(400, multiply(144, const_0_2778))

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

"speed = 144 * 5 / 18 = 40 m / sec time taken = 400 / 40 = 10.0 sec . answer : e"

physics

math_qa__ZCLVuRvlrs1JZU40

Set A consists of all the prime numbers between 62 and 85. What is the range of set A? Choose the correct choice: A) 12 B) 13 C) 16.6 D) 16 E) 23

<gadget id="calculator">85 - 2</gadget> <output>83</output> <gadget id="calculator">62 + 4</gadget> <output>66</output> <gadget id="calculator">66 + 1</gadget> <output>67</output> <gadget id="calculator">83 - 67</gadget> <output>16</output> <result>D</result>

D

Set A consists of all the prime numbers between 62 and 85. What is the range of set A?

subtract(subtract(85, const_2), add(add(62, const_4), const_1))

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

the range of a set of data is the difference between the highest and lowest values in the set in this set , highest number = 83 lowest number = 67 range = highest - lowest = 83 - 67 = 16 option d

general

math_qa__Ehcgvgv3EZsDzVb8

s(n) is a n-digit number formed by attaching the first n perfect squares, in order, into one integer. For example, s(1) = 1, s(2) = 14, s(3) = 149, s(4) = 14916, s(5) = 1491625, etc. How many digits W are in s(99)? Pick one: A) w = 350 B) w = 353 C) w = 354 D) 356 E) 357

<gadget id="calculator">60 + 4</gadget> <output>64</output> <gadget id="calculator">64 + 4</gadget> <output>68</output> <gadget id="calculator">68 * 4</gadget> <output>272</output> <gadget id="calculator">68 + 272</gadget> <output>340</output> <gadget id="calculator">3 * 1</gadget> <output>3</output> <gadget id="calculator">3 * 2</gadget> <output>6</output> <gadget id="calculator">6 * 2</gadget> <output>12</output> <gadget id="calculator">3 + 12</gadget> <output>15</output> <gadget id="calculator">340 + 15</gadget> <output>355</output> <result>B</result>

B

s(n) is a n-digit number formed by attaching the first n perfect squares, in order, into one integer. For example, s(1) = 1, s(2) = 14, s(3) = 149, s(4) = 14916, s(5) = 1491625, etc. How many digits W are in s(99)?

add(add(add(add(const_60, 4), 4), multiply(add(add(const_60, 4), 4), 4)), add(multiply(3, 1), multiply(multiply(3, 2), 2)))

add(n6,const_60)|multiply(n0,n4)|multiply(n2,n4)|add(n6,#0)|multiply(n2,#2)|add(#1,#4)|multiply(n6,#3)|add(#3,#6)|add(#7,#5)|

"focus on the points where the number of digits in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square . 10 , 11 , 12 , . . . 31 - three digit squares . to get 31 , think of 1000 - the first 4 digit number . it is not a perfect square but 900 is 30 ^ 2 . 32 ^ 2 = 2 ^ 10 = 1024 , the first 4 digit square . 32 - 99 - four digit squares . to get 99 , think of 10,000 - the first 5 digit number which is 100 ^ 2 . so number of digits in s ( 99 ) = 3 * 1 + 6 * 2 + 22 * 3 + 68 * 4 = 3 + 12 + 66 + 272 = 353 . b"

general

math_qa__OsXt9vOwt10gngmA

A candidate got 35% of the votes and lost to the rival by 1650 votes. How many votes were cast? Choose the correct choice from the following answers A) 5000 B) 5500 C) 6000 D) 6500 E) 7000

<gadget id="calculator">35 / 100</gadget> <output>7/20 = around 0.35</output> <gadget id="calculator">1 - (7/20)</gadget> <output>13/20 = around 0.65</output> <gadget id="calculator">(13/20) - (7/20)</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">1_650 / (3/10)</gadget> <output>5_500</output> <result>B</result>

B

A candidate got 35% of the votes and lost to the rival by 1650 votes. How many votes were cast?

divide(1650, subtract(subtract(const_1, divide(35, const_100)), divide(35, const_100)))

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

"35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % = 1650 10 % = 550 100 % of the votes = 5500 answer : b"

gain

math_qa__qHLrSTUUan0MPid1

The total age of A and B is 10 years more than the total age of B and C. C is how many years younger than A.? Choose the correct choice from the following answers: A) 16 B) 12 C) 10 D) 20 E) 10

<gadget id="calculator">10 * 1</gadget> <output>10</output> <result>C</result>

C

The total age of A and B is 10 years more than the total age of B and C. C is how many years younger than A.?

multiply(10, const_1)

multiply(n0,const_1)|

"( a + b ) - ( b - c ) = 10 a - c = 10 answer is c"

general

math_qa__ryCY45z7DyitdmJ0

Excluding stoppages, the speed of a train is 67 kmph and including stoppages it is 51 kmph. Of how many minutes does the train stop per hour? Choose the correct answer A) 82 B) 17 C) 14 D) 82 E) 18

<gadget id="calculator">51 / 67</gadget> <output>51/67 = around 0.761194</output> <gadget id="calculator">60 * (51/67)</gadget> <output>3_060/67 = around 45.671642</output> <gadget id="calculator">60 - (3_060/67)</gadget> <output>960/67 = around 14.328358</output> <result>C</result>

C

Excluding stoppages, the speed of a train is 67 kmph and including stoppages it is 51 kmph. Of how many minutes does the train stop per hour?

subtract(const_60, multiply(const_60, divide(51, 67)))

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

"explanation : t = 16 / 67 * 60 = 14 answer : option c"

physics

math_qa__TMveR1X7Y2A9S0L5

The average runs of a cricket player of 8 innings was 24. How many runs must he make in his next innings so as to increase his average of runs by 8? Choose the correct choice from the following answers. A) 12 B) 42 C) 64 D) 96 E) 84

<gadget id="calculator">8 + 1</gadget> <output>9</output> <gadget id="calculator">24 + 8</gadget> <output>32</output> <gadget id="calculator">9 * 32</gadget> <output>288</output> <gadget id="calculator">24 * 8</gadget> <output>192</output> <gadget id="calculator">288 - 192</gadget> <output>96</output> <result>D</result>

D

The average runs of a cricket player of 8 innings was 24. How many runs must he make in his next innings so as to increase his average of runs by 8?

subtract(multiply(add(8, const_1), add(24, 8)), multiply(24, 8))

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

"explanation : average after 9 innings = 32 required number of runs = ( 32 * 9 ) – ( 24 * 8 ) = 288 – 192 = 96 answer d"

general

math_qa__exqOVCABrDTYKKoI

If Jack walked 4 miles in 1 hour and 15 minutes, what was his rate of walking in miles per hour? Choose the correct choice from the following choices A) 3.2 B) 4.5 C) 6 D) 6.25 E) 15

<gadget id="calculator">4 * 60</gadget> <output>240</output> <gadget id="calculator">15 + 60</gadget> <output>75</output> <gadget id="calculator">240 / 75</gadget> <output>16/5 = around 3.2</output> <result>A</result>

A

If Jack walked 4 miles in 1 hour and 15 minutes, what was his rate of walking in miles per hour?

divide(multiply(4, const_60), add(15, const_60))

add(n2,const_60)|multiply(n0,const_60)|divide(#1,#0)

distance walked in 1 hour and 15 mins = 4 miles speed per hour = distance / time = 4 / ( 5 / 4 ) = 3.2 miles per hour answer a

physics

math_qa__W9qb7vZAVO8WccKK

Yesterday it took Robert 6 hours to drive from City A to City B. Today it took Robert 4.5 hours to drive back from City В to City A along the same route. If he had saved 30 minutes in both trips, the speed for the round trip would be 90 miles per hour. What is the distance between city A and city B? Choices: A) 90 B) 120 C) 150 D) 440 E) 430

<gadget id="calculator">6 + 4.5</gadget> <output>10.5</output> <gadget id="calculator">10.5 - 1</gadget> <output>9.5</output> <gadget id="calculator">90 * 9.5</gadget> <output>855</output> <gadget id="calculator">855 / 2</gadget> <output>855/2 = around 427.5</output> <result>E</result>

E

Yesterday it took Robert 6 hours to drive from City A to City B. Today it took Robert 4.5 hours to drive back from City В to City A along the same route. If he had saved 30 minutes in both trips, the speed for the round trip would be 90 miles per hour. What is the distance between city A and city B?

divide(multiply(90, subtract(add(6, 4.5), const_1)), const_2)

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

2 d / 90 = 9.5 ( because time = 6 + 4.5 - 1 hrs ) = > d = 430 answer - e

physics

math_qa__Sn63ytXcNjf6UzT3

A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is : Choose the correct option A) 251 B) 253 C) 255 D) 257 E) 260

<gadget id="calculator">10 / 2</gadget> <output>5</output> <gadget id="calculator">5 - 3</gadget> <output>2</output> <gadget id="calculator">100 * 2</gadget> <output>200</output> <gadget id="calculator">5 * 10</gadget> <output>50</output> <gadget id="calculator">200 + 50</gadget> <output>250</output> <gadget id="calculator">250 + 3</gadget> <output>253</output> <result>B</result>

B

A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is :

add(add(multiply(const_100, subtract(divide(10, const_2), 3)), multiply(divide(10, const_2), 10)), 3)

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

"let the middle digit be x . then , 2 x = 10 or x = 5 . so , the number is either 253 or 352 . since the number increases on reversing the digits , so the hundred ' s digits is smaller than the unit ' s digit . hence , required number = 253 . option b"

general

math_qa__d4zFLFwr4e12Txpw

How many seconds will a train 110 meters long take to cross a railway platform 165 meters long if the speed of the train is 132 kmph? Options: A) 6 sec B) 7.5 sec C) 8 sec D) 3 sec E) 10 sec

<gadget id="calculator">165 + 110</gadget> <output>275</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">132 * (5/18)</gadget> <output>110/3 = around 36.666667</output> <gadget id="calculator">275 / (110/3)</gadget> <output>15/2 = around 7.5</output> <result>B</result>

B

How many seconds will a train 110 meters long take to cross a railway platform 165 meters long if the speed of the train is 132 kmph?

divide(add(165, 110), multiply(132, const_0_2778))

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

"d = 110 + 165 = 275 s = 132 * 5 / 18 = 110 / 3 mps t = 275 * 3 / 110 = 7.5 sec b ) 7.5 sec"

physics

math_qa__eRPLE2du8sp6kYyy

2 trains starting at the same time from 2 stations 200 km apart and going in opposite direction cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds Options. A) 11 : 9 B) 13 : 9 C) 17 : 9 D) 21 : 9 E) none of these

<gadget id="calculator">200 - 110</gadget> <output>90</output> <gadget id="calculator">90 / 110</gadget> <output>9/11 = around 0.818182</output> <gadget id="calculator">1 / (9/11)</gadget> <output>11/9 = around 1.222222</output> <result>A</result>

A

2 trains starting at the same time from 2 stations 200 km apart and going in opposite direction cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds

inverse(divide(subtract(200, 110), 110))

subtract(n2,n3)|divide(#0,n3)|inverse(#1)|

"explanation : we know total distance is 200 km if both trains crossed each other at a distance of 110 km then one train covered 110 km and other 90 km [ 110 + 90 = 200 km ] so ratio of their speed = 110 : 90 = 11 : 9 option a"

physics

math_qa__4alYBgonc1dC3KEa

A work can be finished in 13 days by ten women. The same work can be finished in fifteen days by ten men. The ratio between the capacity of a man and a woman is Pick one. A) 14 : 13 B) 13 : 15 C) 12 : 13 D) 13 : 12 E) 14 : 15

<gadget id="calculator">13 + 2</gadget> <output>15</output> <gadget id="calculator">15 * 10</gadget> <output>150</output> <gadget id="calculator">1 / 150</gadget> <output>1/150 = around 0.006667</output> <gadget id="calculator">13 * 10</gadget> <output>130</output> <gadget id="calculator">1 / 130</gadget> <output>1/130 = around 0.007692</output> <gadget id="calculator">(1/150) / (1/130)</gadget> <output>13/15 = around 0.866667</output> <result>B</result>

B

A work can be finished in 13 days by ten women. The same work can be finished in fifteen days by ten men. The ratio between the capacity of a man and a woman is

divide(divide(const_1, multiply(add(13, const_2), const_10)), divide(const_1, multiply(13, const_10)))

add(n0,const_2)|multiply(n0,const_10)|divide(const_1,#1)|multiply(#0,const_10)|divide(const_1,#3)|divide(#4,#2)

work done by 10 women in 1 day = 1 / 13 work done by 1 woman in 1 day = 1 / ( 13 ã — 10 ) work done by 16 men in 1 day = 1 / 15 work done by 1 man in 1 day = 1 / ( 15 ã — 10 ) ratio of the capacity of a man and woman = 1 / ( 15 ã — 10 ) : 1 / ( 13 ã — 10 ) = 1 / 15 : 1 / 13 = 1 / 15 : 1 / 13 = 13 : 15 answer is b .

physics

math_qa__rp7FpNVx0MdgbF8V

If 213 × 16 = 3408, then 1.6 × 213.0 is equal to : Choose the correct choice from the following answers: A) 0.3408 B) 3.408 C) 34.08 D) 340.8 E) none of these

<gadget id="calculator">1.6 * 213</gadget> <output>340.8</output> <result>D</result>

D

If 213 × 16 = 3408, then 1.6 × 213.0 is equal to :

multiply(1.6, 213)

multiply(n0,n3)

solution 1.6 × 21.3 = ( 16 / 10 x 213 ) = ( 16 x 213 / 10 ) = 3408 / 10 = 340.8 . answer d

general