Datasets:

MU-NLPC

/

Calc-math_qa

like 4

Follow

NLP Centre, Faculty of Informatics, Masaryk University 14

math_qa__A3LCRTEgZLhZCvX9

Elvin's monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for Internet service. Elvin's total telephone bill for January was $48 and Elvin's total telephone bill for February was 90$. If Elvin's charge for the calls he made in February was twice the charge for the calls he made in January, what is Elvin's fixed monthly charge for Internet service? Select the correct option A) $ 5 B) $ 10 C) $ 14 D) $ 6 E) $ 28

<gadget id="calculator">48 * 2</gadget> <output>96</output> <gadget id="calculator">96 - 90</gadget> <output>6</output> <result>D</result>

D

Elvin's monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for Internet service. Elvin's total telephone bill for January was $48 and Elvin's total telephone bill for February was 90$. If Elvin's charge for the calls he made in February was twice the charge for the calls he made in January, what is Elvin's fixed monthly charge for Internet service?

subtract(multiply(48, const_2), 90)

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

"bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 48 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 90 i . e . x + y = 48 and 2 x + y = 90 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 90 - 48 i . e . x = 42 i . e . fixed monthly charge , y = 6 answer : option d"

general

math_qa__iwAEWXZeGwKcz5a3

In the recent, climate conference in New York, out of 500 men, 300 women, 500 children present inside the building premises, 10% of the men, 60% of the women and 70% of the children were Indians. Find the percentage of people who were not Indian? Pick one: A) 59.54 % B) 66.25 % C) 55.39 % D) 63.21 % E) 64.22 %

<gadget id="calculator">10 / 100</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">1 - (1/10)</gadget> <output>9/10 = around 0.9</output> <gadget id="calculator">500 * (9/10)</gadget> <output>450</output> <gadget id="calculator">60 / 100</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">1 - (3/5)</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">300 * (2/5)</gadget> <output>120</output> <gadget id="calculator">450 + 120</gadget> <output>570</output> <gadget id="calculator">70 / 100</gadget> <output>7/10 = around 0.7</output> <gadget id="calculator">1 - (7/10)</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">500 * (3/10)</gadget> <output>150</output> <gadget id="calculator">570 + 150</gadget> <output>720</output> <gadget id="calculator">500 + 300</gadget> <output>800</output> <gadget id="calculator">800 + 500</gadget> <output>1_300</output> <gadget id="calculator">720 / 1_300</gadget> <output>36/65 = around 0.553846</output> <gadget id="calculator">(36/65) * 100</gadget> <output>720/13 = around 55.384615</output> <result>C</result>

C

In the recent, climate conference in New York, out of 500 men, 300 women, 500 children present inside the building premises, 10% of the men, 60% of the women and 70% of the children were Indians. Find the percentage of people who were not Indian?

multiply(divide(add(add(multiply(500, subtract(const_1, divide(10, const_100))), multiply(300, subtract(const_1, divide(60, const_100)))), multiply(500, subtract(const_1, divide(70, const_100)))), add(add(500, 300), 500)), const_100)

add(n0,n1)|divide(n3,const_100)|divide(n4,const_100)|divide(n5,const_100)|add(n2,#0)|subtract(const_1,#1)|subtract(const_1,#2)|subtract(const_1,#3)|multiply(n0,#5)|multiply(n1,#6)|multiply(n2,#7)|add(#8,#9)|add(#11,#10)|divide(#12,#4)|multiply(#13,const_100)|

"solution : number of indians men present there = 500 * 10 / 100 = 50 indian women = 300 * 60 / 100 = 180 indian children = 500 * 70 / 100 = 350 . total member present in climate conference = 500 + 300 + 500 = 1300 total indian = 50 + 180 + 350 = 580 hence , % of indian present there = 580 * 100 / 1300 = 44.61 % % of people who were not indian = 100 - 44.61 = 55.39 % . answer c"

gain

math_qa__YG9QovKZx5llSaOM

Find k if 56 / k = 4. Select the correct option. A) 16 B) 17 C) 18 D) 14 E) 13

<gadget id="calculator">56 / 4</gadget> <output>14</output> <result>D</result>

D

Find k if 56 / k = 4.

divide(56, 4)

divide(n0,n1)|

"since 56 / k = 4 and 56 / 14 = 4 , then k = 14 correct answer d"

general

math_qa__gcIZDocP4UYYgXhx

A car traveled from San Diego to San Francisco at an average speed of 45 miles per hour. If the journey back took twice as long, what was the average speed of the trip? Choose the correct choice: A) 30 . B) 32 . C) 36 . D) 42 . E) 44 .

<gadget id="calculator">1 / 45</gadget> <output>1/45 = around 0.022222</output> <gadget id="calculator">(1/45) / 2</gadget> <output>1/90 = around 0.011111</output> <gadget id="calculator">(1/45) + (1/90)</gadget> <output>1/30 = around 0.033333</output> <gadget id="calculator">1 / (1/30)</gadget> <output>30</output> <result>A</result>

A

A car traveled from San Diego to San Francisco at an average speed of 45 miles per hour. If the journey back took twice as long, what was the average speed of the trip?

inverse(add(inverse(45), divide(inverse(45), const_2)))

inverse(n0)|divide(#0,const_2)|add(#1,#0)|inverse(#2)|

"let the time taken be = x one way distance = 45 x total distance traveled = 2 * 45 x = 90 x total time taken = x + 2 x = 3 x average speed = 90 x / 3 x = 30 answer : a"

physics

math_qa__hFP9KbnfH2o7rOvk

jack spent 1 / 6 of his lifetime in adolescence . his facial hair started growing after 1 / 12 more of his life . he successfully married his girlfriend diana after 1 / 7 more of his life . their son was born after 5 years from then . the son lived just 1 / 2 of what jack lived . jack dies 4 years after his son died . how long did jack live ? Choose the correct option A) 75 B) 90 C) 45 D) 80 E) 84

<gadget id="calculator">5 + 4</gadget> <output>9</output> <gadget id="calculator">1 / 6</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">1 / 12</gadget> <output>1/12 = around 0.083333</output> <gadget id="calculator">(1/6) + (1/12)</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">1 / 7</gadget> <output>1/7 = around 0.142857</output> <gadget id="calculator">(1/4) + (1/7)</gadget> <output>11/28 = around 0.392857</output> <gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">(11/28) + (1/2)</gadget> <output>25/28 = around 0.892857</output> <gadget id="calculator">1 - (25/28)</gadget> <output>3/28 = around 0.107143</output> <gadget id="calculator">9 / (3/28)</gadget> <output>84</output> <result>E</result>

E

jack spent 1 / 6 of his lifetime in adolescence . his facial hair started growing after 1 / 12 more of his life . he successfully married his girlfriend diana after 1 / 7 more of his life . their son was born after 5 years from then . the son lived just 1 / 2 of what jack lived . jack dies 4 years after his son died . how long did jack live ?

divide(add(5, 4), subtract(const_1, add(add(add(divide(1, 6), divide(1, 12)), divide(1, 7)), divide(1, 2))))

add(n6,n9)|divide(n0,n1)|divide(n0,n3)|divide(n0,n5)|divide(n0,n8)|add(#1,#2)|add(#5,#3)|add(#6,#4)|subtract(const_1,#7)|divide(#0,#8)

e 84 explanation : let us assume that jack lived for p years . p / 6 + p / 12 + p / 7 + 5 + p / 2 + 4 = x = > p = 84 . therefore , jack lived for 84 years .

general

math_qa__5vATcp7WmOHRxVUH

The price of a book is increased from $300 to $420. What is the % of increase in its price? Choose the correct choice from the following answers. A) 10 % B) 20 % C) 40 % D) 50 % E) 60 %

<gadget id="calculator">420 - 300</gadget> <output>120</output> <gadget id="calculator">120 / 300</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">(2/5) * 100</gadget> <output>40</output> <result>C</result>

C

The price of a book is increased from $300 to $420. What is the % of increase in its price?

multiply(divide(subtract(420, 300), 300), const_100)

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

"explanation : change in the price = rs 420 â € “ rs 300 = rs 120 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 120 300 ) * 100 = 40 % c"

gain

math_qa__0KMWPTHUwJIsSOWI

The total price of a basic computer and printer are $2,500. If the same printer had been purchased with an enhanced computer whose price was $500 more than the price of the basic computer, then the price of the printer would have been 1/8 of that total. What was the price of the basic computer? Choose the most appropriate option: A) 1500 B) 1600 C) 1750 D) 1900 E) 2125

<gadget id="calculator">1 / 4</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(1/4) * 1_000</gadget> <output>250</output> <gadget id="calculator">250 * 10</gadget> <output>2_500</output> <gadget id="calculator">500 + 2_500</gadget> <output>3_000</output> <gadget id="calculator">3_000 / 8</gadget> <output>375</output> <gadget id="calculator">2_500 - 375</gadget> <output>2_125</output> <result>E</result>

E

The total price of a basic computer and printer are $2,500. If the same printer had been purchased with an enhanced computer whose price was $500 more than the price of the basic computer, then the price of the printer would have been 1/8 of that total. What was the price of the basic computer?

subtract(multiply(multiply(const_0_25, const_1000), const_10), divide(add(500, multiply(multiply(const_0_25, const_1000), const_10)), 8))

multiply(const_0_25,const_1000)|multiply(#0,const_10)|add(n1,#1)|divide(#2,n3)|subtract(#1,#3)|

"let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 1 / 8 of that new total price : p = 1 / 8 * $ 3,000 = $ 375 . plug this value in the first equation : c + 375 = $ 2,500 - - > c = $ 2,125 . answer : e ."

general

math_qa__hOD3tB1QQerQCl05

39! is divided by 41 then what is the remainder? Choose the correct choice. A) 1 B) 2 C) 4 D) 6 E) 7

<gadget id="calculator">factorial(39)</gadget> <output>20_397_882_081_197_443_358_640_281_739_902_897_356_800_000_000</output> <gadget id="calculator">20_397_882_081_197_443_358_640_281_739_902_897_356_800_000_000 % 41</gadget> <output>1</output> <result>A</result>

A

39! is divided by 41 then what is the remainder?

reminder(factorial(39), 41)

factorial(n0)|reminder(#0,n1)|

"substituting p = 41 in the wilson ' s theorem , we get 40 ! + 141 = 0 40 × 39 ! + 141 = 0 − 1 × 39 ! 41 = − 1 cancelling - 1 on both sides , 39 ! 41 = 1 a"

other

math_qa__QmOhLOLj6TvGgEKZ

If x is equal to the sum of the integers from 10 to 30, inclusive, and y is the number of even integers from 10 to 30, inclusive, what is the value of x + y? Pick one: A) 401 B) 411 C) 421 D) 431 E) 441

<gadget id="calculator">10 + 30</gadget> <output>40</output> <gadget id="calculator">40 / 2</gadget> <output>20</output> <gadget id="calculator">30 - 10</gadget> <output>20</output> <gadget id="calculator">20 + 1</gadget> <output>21</output> <gadget id="calculator">20 * 21</gadget> <output>420</output> <gadget id="calculator">20 / 2</gadget> <output>10</output> <gadget id="calculator">10 + 1</gadget> <output>11</output> <gadget id="calculator">420 + 11</gadget> <output>431</output> <result>D</result>

D

If x is equal to the sum of the integers from 10 to 30, inclusive, and y is the number of even integers from 10 to 30, inclusive, what is the value of x + y?

add(multiply(divide(add(10, 30), const_2), add(subtract(30, 10), const_1)), add(divide(subtract(30, 10), const_2), const_1))

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

"x = 10 + 11 + . . . + 30 = 21 ( 20 ) = 420 y = 11 x + y = 431 the answer is d ."

general

math_qa__dYhHUBapvuGJbnTk

The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is: Explanation: Choose the correct choice from the following answers: A) 101 B) 107 C) 111 D) 117 E) 121

<gadget id="calculator">37 ** 2</gadget> <output>1_369</output> <gadget id="calculator">4_107 / 1_369</gadget> <output>3</output> <gadget id="calculator">3 * 37</gadget> <output>111</output> <result>C</result>

C

The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is: Explanation:

multiply(divide(4107, power(37, const_2)), 37)

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

let the numbers be 37 a and 37 b . then , 37 a x 37 b = 4107 ab = 3 . now , co - primes with product 3 are ( 1 , 3 ) . so , the required numbers are ( 37 x 1 , 37 x 3 ) i . e . , ( 37 , 111 ) . greater number = 111 . answer : option c

general

math_qa__Dc5ugRWsmNNL75Te

If X and Y are sets of integers, X # Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 14 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X # Y consists of how many integers? Choose the most appropriate option. A) 6 B) 16 C) 20 D) 30 E) 174

<gadget id="calculator">18 - 6</gadget> <output>12</output> <gadget id="calculator">14 - 6</gadget> <output>8</output> <gadget id="calculator">12 + 8</gadget> <output>20</output> <result>C</result>

C

If X and Y are sets of integers, X # Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 14 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X # Y consists of how many integers?

add(subtract(18, 6), subtract(14, 6))

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

the number of integers that belong to set x only is 14 - 6 = 8 ; the number of integers that belong to set y only is 18 - 6 = 12 ; the number of integers that belong to set x or set y , but not both is 8 + 12 = 20 . answer : c .

other

math_qa__ZvjHyOetQdSA25t7

Find large no. from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 35 as remainder Choose the correct choice from the following answers: A) 1235 B) 1456 C) 1567 D) 1678 E) 1631

<gadget id="calculator">1_365 - 35</gadget> <output>1_330</output> <gadget id="calculator">6 - 1</gadget> <output>5</output> <gadget id="calculator">1_330 / 5</gadget> <output>266</output> <gadget id="calculator">266 * 6</gadget> <output>1_596</output> <gadget id="calculator">1_596 + 35</gadget> <output>1_631</output> <result>E</result>

E

Find large no. from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 35 as remainder

add(multiply(divide(subtract(1365, 35), subtract(6, const_1)), 6), 35)

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

"let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 35 5 x = 1330 x = 266 large number = 266 + 1365 = 1631 e"

general

math_qa__3PE1dHbJQrlaZq3E

n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2*n is divided by 4 ? Choose the correct choice from the following options. A) 8 B) 2 C) 6 D) 7 E) 1

<gadget id="calculator">3 * 2</gadget> <output>6</output> <gadget id="calculator">6 % 4</gadget> <output>2</output> <result>B</result>

B

n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2*n is divided by 4 ?

reminder(multiply(3, 2), 4)

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

explanation : let n = 4 * q + 3 . then , 2 * n = 8 * q + 6 = 4 ( 2 * q + 1 ) + 2 . thus when 2 * n is divided by 4 , the reminder is 2 . answer : b ) 2

general

math_qa__jEFaRRdfMqiWqt1i

A person want to give his money of $2700 to his 3 children A,B,C in the ratio 2:3:4. What is the B's share? Choose the correct choice from the following choices. A) $ 200 B) $ 900 C) $ 700 D) $ 600 E) $ 400

<gadget id="calculator">2 + 3</gadget> <output>5</output> <gadget id="calculator">5 + 4</gadget> <output>9</output> <gadget id="calculator">3 / 9</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">(1/3) * 2_700</gadget> <output>900</output> <result>B</result>

B

A person want to give his money of $2700 to his 3 children A,B,C in the ratio 2:3:4. What is the B's share?

multiply(divide(3, add(add(2, 3), 4)), 2700)

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

"b ' s share = 2700 * 3 / 9 = $ 900 answer is b"

other

math_qa__M7EwcRkph31sTbNI

The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 18. The larger of the two numbers is: Answers A) 276 B) 414 C) 322 D) 345 E) 355

<gadget id="calculator">23 * 18</gadget> <output>414</output> <result>B</result>

B

The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 18. The larger of the two numbers is:

multiply(23, 18)

multiply(n0,n2)|

"clearly , the numbers are ( 23 x 13 ) and ( 23 x 18 ) . larger number = ( 23 x 18 ) = 414 . answer : option b"

other

math_qa__WBshAUc74OO8c8CM

If 6^k = 4, then 6^(2k+3) = Choose the correct choice from the following choices. A) 2925 B) 3456 C) 4581 D) 3683 E) 1308

<gadget id="calculator">4 ** 2</gadget> <output>16</output> <gadget id="calculator">6 ** 3</gadget> <output>216</output> <gadget id="calculator">16 * 216</gadget> <output>3_456</output> <result>B</result>

B

If 6^k = 4, then 6^(2k+3) =

multiply(power(4, 2), power(6, 3))

power(n1,n3)|power(n0,n4)|multiply(#0,#1)

6 ^ k = 4 6 ^ 2 k = 4 ^ 2 6 ^ 2 k = 16 6 ^ ( 2 k + 3 ) = 6 ^ 2 k * 6 ^ 3 = 16 * 216 = 3456 answer : b

general

math_qa__UksrEUtr5gudhxQ3

A can finish a work in 18 days and B can do the same work in half the time taken by A. Then, working together, what part of the same work they can finish in a day? Answers: A) 1 / 9 B) 1 / 6 C) 1 / 2 D) 1 / 1 E) 1 / 4

<gadget id="calculator">18 / 2</gadget> <output>9</output> <gadget id="calculator">1 / 9</gadget> <output>1/9 = around 0.111111</output> <gadget id="calculator">1 / 18</gadget> <output>1/18 = around 0.055556</output> <gadget id="calculator">(1/9) + (1/18)</gadget> <output>1/6 = around 0.166667</output> <result>B</result>

B

A can finish a work in 18 days and B can do the same work in half the time taken by A. Then, working together, what part of the same work they can finish in a day?

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

divide(n0,const_2)|divide(const_1,n0)|divide(const_1,#0)|add(#2,#1)

given that b alone can complete the same work in days = half the time taken by a = 9 days a ’ s one day work = 1 / 18 b ’ s one day work = 1 / 9 ( a + b ) ’ s one day work = 1 / 18 + 1 / 9 = 1 / 6 answer : b .

physics

math_qa__dIeUP3w0svwaLZPz

An empty fuel tank with a capacity of 212 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 30 gallons of ethanol, how many gallons of fuel A were added? Answers A) 160 B) 98 C) 100 D) 80 E) 50

<gadget id="calculator">16 / 100</gadget> <output>4/25 = around 0.16</output> <gadget id="calculator">212 * (4/25)</gadget> <output>848/25 = around 33.92</output> <gadget id="calculator">(848/25) - 30</gadget> <output>98/25 = around 3.92</output> <gadget id="calculator">12 / 100</gadget> <output>3/25 = around 0.12</output> <gadget id="calculator">(4/25) - (3/25)</gadget> <output>1/25 = around 0.04</output> <gadget id="calculator">(98/25) / (1/25)</gadget> <output>98</output> <result>B</result>

B

An empty fuel tank with a capacity of 212 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 30 gallons of ethanol, how many gallons of fuel A were added?

divide(subtract(multiply(212, divide(16, const_100)), 30), subtract(divide(16, const_100), divide(12, const_100)))

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

"say there are a gallons of fuel a in the tank , then there would be 212 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 212 - a gallons of fuel b is 0.16 ( 212 - a ) ; since the total amount of ethanol is 30 gallons then 0.12 a + 0.16 ( 212 - a ) = 30 - - > a = 98 . answer : b ."

gain

math_qa__vvr3Mv1FrKLe4T1H

The weight of a hollow sphere is directly dependent on its surface area. The surface area of a sphere is 4π·R^2, where R is the radius of the sphere. If a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams, a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams R? Pick one: A) 16 B) r = 32 C) r = 64 D) 128 E) 512

<gadget id="calculator">8 * 4</gadget> <output>32</output> <result>B</result>

B

The weight of a hollow sphere is directly dependent on its surface area. The surface area of a sphere is 4π·R^2, where R is the radius of the sphere. If a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams, a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams R?

multiply(8, 4)

multiply(n0,n3)|

"weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )"

geometry

math_qa__nUswiNKZo3xj7ilu

10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 2 women and 10 children take to complete the work? Choose the correct choice from the following choices. A) 4 B) 5 C) 7 D) 8 E) 10

<gadget id="calculator">10 * 7</gadget> <output>70</output> <gadget id="calculator">2 / 70</gadget> <output>1/35 = around 0.028571</output> <gadget id="calculator">10 * 14</gadget> <output>140</output> <gadget id="calculator">10 / 140</gadget> <output>1/14 = around 0.071429</output> <gadget id="calculator">(1/35) + (1/14)</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">1 / (1/10)</gadget> <output>10</output> <result>E</result>

E

10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 2 women and 10 children take to complete the work?

inverse(add(divide(2, multiply(10, 7)), divide(10, multiply(10, 14))))

multiply(n0,n1)|multiply(n0,n3)|divide(n4,#0)|divide(n0,#1)|add(#2,#3)|inverse(#4)|

"1 women ' s 1 day work = 1 / 70 1 child ' s 1 day work = 1 / 140 ( 2 women + 10 children ) ' s 1 day work = ( 2 / 70 + 10 / 140 ) = 1 / 10 2 women and 10 children will complete the work in 10 days . e"

physics

math_qa__OCjX4WbKovSUrLM4

A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 660-mile journey? Assume that the train makes no intermediate stops. Choose one A) 8 B) 8.5 C) 11 D) 9.5 E) 10

<gadget id="calculator">10 + 20</gadget> <output>30</output> <gadget id="calculator">30 + 30</gadget> <output>60</output> <gadget id="calculator">660 / 60</gadget> <output>11</output> <result>C</result>

C

A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 660-mile journey? Assume that the train makes no intermediate stops.

divide(660, add(30, add(10, 20)))

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

a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 660 - mile journey ? assume that the train makes no intermediate stops . i think the easiest way to solve this problem would be simply to count the number of miles it travels per hour ( and in total ) hour miles / hour total miles 1 10 10 2 20 30 3 30 60 4 40 100 5 50 150 6 60 210 7 70 280 8 80 360 9 90 450 10 100 550 11 110 660 it takes a total of nine hours to cover the 660 mile distance . answer : c . 11

physics

math_qa__IRi4ja2SPUG7lLpL

Ramesh purchased a refrigerator for Rs. 14500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered? Choose the correct choice from the following. A) 34778 B) 26888 C) 20350 D) 17600 E) 12778

<gadget id="calculator">100 + 10</gadget> <output>110</output> <gadget id="calculator">14_500 * 100</gadget> <output>1_450_000</output> <gadget id="calculator">100 - 20</gadget> <output>80</output> <gadget id="calculator">1_450_000 / 80</gadget> <output>18_125</output> <gadget id="calculator">125 + 250</gadget> <output>375</output> <gadget id="calculator">18_125 + 375</gadget> <output>18_500</output> <gadget id="calculator">110 * 18_500</gadget> <output>2_035_000</output> <gadget id="calculator">2_035_000 / 100</gadget> <output>20_350</output> <result>C</result>

C

Ramesh purchased a refrigerator for Rs. 14500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered?

divide(multiply(add(const_100, 10), add(divide(multiply(14500, const_100), subtract(const_100, 20)), add(125, 250))), const_100)

add(n4,const_100)|add(n2,n3)|multiply(n0,const_100)|subtract(const_100,n1)|divide(#2,#3)|add(#1,#4)|multiply(#0,#5)|divide(#6,const_100)|

"price at which the tv set is bought = rs . 14,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 18125 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 18125 + 375 = rs . 18500 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 18500 * 110 / 100 = rs . 20350 answer : c"

gain

math_qa__00DW5uguhWSJ8DPk

Approximately how many revolutions will be made by a car tire with a 13-inch diameter if the car travels 1⁄2 mile? Choose the correct choice from the following choices: A) 120 B) 180 C) 772 D) 720 E) 1,440

<gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">3 * 2</gadget> <output>6</output> <gadget id="calculator">6 / 10</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">(3/5) + 1</gadget> <output>8/5 = around 1.6</output> <gadget id="calculator">(8/5) / 10</gadget> <output>4/25 = around 0.16</output> <gadget id="calculator">(4/25) + 4</gadget> <output>104/25 = around 4.16</output> <gadget id="calculator">(104/25) / 10</gadget> <output>52/125 = around 0.416</output> <gadget id="calculator">(52/125) + 1</gadget> <output>177/125 = around 1.416</output> <gadget id="calculator">(177/125) / 10</gadget> <output>177/1_250 = around 0.1416</output> <gadget id="calculator">(177/1_250) + 3</gadget> <output>3_927/1_250 = around 3.1416</output> <gadget id="calculator">(3_927/1_250) * 13</gadget> <output>51_051/1_250 = around 40.8408</output> <gadget id="calculator">6 * 10</gadget> <output>60</output> <gadget id="calculator">60 + 3</gadget> <output>63</output> <gadget id="calculator">63 * 10</gadget> <output>630</output> <gadget id="calculator">630 + 3</gadget> <output>633</output> <gadget id="calculator">633 * 10</gadget> <output>6_330</output> <gadget id="calculator">6_330 + 3</gadget> <output>6_333</output> <gadget id="calculator">6_333 + 2</gadget> <output>6_335</output> <gadget id="calculator">6_335 * 10</gadget> <output>63_350</output> <gadget id="calculator">(51_051/1_250) / 63_350</gadget> <output>7_293/11_312_500 = around 0.000645</output> <gadget id="calculator">(1/2) / (7_293/11_312_500)</gadget> <output>5_656_250/7_293 = around 775.572467</output> <result>C</result>

C

Approximately how many revolutions will be made by a car tire with a 13-inch diameter if the car travels 1⁄2 mile?

divide(divide(1, 2), divide(multiply(add(divide(add(divide(add(divide(add(divide(multiply(const_3, 2), const_10), 1), const_10), const_4), const_10), 1), const_10), const_3), 13), multiply(add(add(multiply(add(multiply(add(multiply(multiply(const_3, 2), const_10), const_3), const_10), const_3), const_10), const_3), 2), const_10)))

divide(n1,n2)|multiply(n2,const_3)|divide(#1,const_10)|multiply(#1,const_10)|add(#2,n1)|add(#3,const_3)|divide(#4,const_10)|multiply(#5,const_10)|add(#6,const_4)|add(#7,const_3)|divide(#8,const_10)|multiply(#9,const_10)|add(#10,n1)|add(#11,const_3)|add(#13,n2)|divide(#12,const_10)|add(#15,const_3)|multiply(#14,const_10)|multiply(n0,#16)|divide(#18,#17)|divide(#0,#19)|

"diameter of car tire = 13 inches radius of car tire = 6.5 inches = 6.5 * 2.54 cm = 16.51 cm circumference of the car tire = 2 * pi * 16.51 = 2 * 3.14 * 16.51 = 103.68 cm distance traveled by car = . 5 mile = . 5 * 1.6 km = . 8 km = 800 m = 8 * 10 ^ 4 cm number of revolutions = distance traveled / circumference of tire = 8 * 10 ^ 4 / 103.68 = 771.60 since the answer choices are far apart we should use estimation in this question . ideally , in the gmat the conversion between units would be provided . answer c"

general

math_qa__dFbenCGZpPDewg2z

If x/y = 2/5, then (x + y)/(x - y) = ? Select. A) 5 B) 1 / 5 C) - 1 / 6 D) - 1 / 5 E) - 7 / 3

<gadget id="calculator">2 + 5</gadget> <output>7</output> <gadget id="calculator">2 - 5</gadget> <output>-3</output> <gadget id="calculator">7 / (-3)</gadget> <output>-7/3 = around -2.333333</output> <result>E</result>

E

If x/y = 2/5, then (x + y)/(x - y) = ?

divide(add(2, 5), subtract(2, 5))

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

any x and y satisfying x / y = 2 / 5 should give the same value for ( x + y ) / ( x - y ) . say x = 2 and y = 5 , then ( x + y ) / ( x - y ) = ( 2 + 5 ) / ( 2 - 5 ) = - 7 / 3 . answer : e .

general

math_qa__Vrhm2XhhXJAyYHs1

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

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

B

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

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

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

"back - solving is the best way to solve this problem . you basically need 12 combinations ( including single colors ) if we start from option 1 - > 1 = > 4 c 2 + 4 = 10 ( not enough ) 2 = > 5 c 2 + 5 = 15 ( enough ) since the minimum number is asked . it should be 5 . answer - b"

general

math_qa__rOTDmLOfak6e5NeQ

An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 27 metre of cloth ? Choose the correct choice from the following choices. A) 211 seconds B) 195 seconds C) 155 seconds D) 115 seconds E) 115 seconds

<gadget id="calculator">27 / 0.128</gadget> <output>210.9375</output> <result>A</result>

A

An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 27 metre of cloth ?

divide(27, 0.128)

divide(n1,n0)|

"explanation : let the time required by x seconds . then , more cloth means more time ( direct proportion ) so , 0.128 : 1 : : 27 : x = > x = { \ color { blue } \ frac { 27 \ times 1 } { 0.128 } } = > x = 210.94 so time will be approx 211 seconds answer : a"

physics

math_qa__CwXOxjoSq0kygy3K

1*2+ 2*2^2+ 3*2^3+ 4*2^4……………………+2012*2^2012 Choose the correct choice from the following options. A) 8100312 B) 8100313 C) 8100412 D) 8200312 E) 8300312

<gadget id="calculator">2_012 + 1</gadget> <output>2_013</output> <gadget id="calculator">2 * 2_013</gadget> <output>4_026</output> <gadget id="calculator">4_026 * 2_012</gadget> <output>8_100_312</output> <result>A</result>

A

1*2+ 2*2^2+ 3*2^3+ 4*2^4……………………+2012*2^2012

multiply(multiply(2, add(2012, const_1)), 2012)

add(n11,const_1)|multiply(n1,#0)|multiply(n11,#1)

take 2 outside as common we get 2 ( 1 + 2 * 1 ^ 2 + 3 * 1 ^ 3 + . . . . . . . . . 2012 * 1 ^ 2012 ) then 2 ( 1 + 2 + . . . . . 2012 ) we get 8100312 answer : a

general

math_qa__jlIoH3J5WkezwOZD

Stock / Number of shares V ------------ 68 W ---------- 112 X ------------ 56 Y ------------ 94 Z ------------ 45 The table shows the number of shares of each of the 5 stocks owned by Mr Sami. If Mr. Sami was to sell 20 shares of Stock X and buy 23 shares of stock Y, what would be the increase in the range of the numbers of shares of the 5 stocks owned by Mr. Sami? Choose the correct choice from the following choices A) 4 B) 6 C) 9 D) 14 E) 20

<gadget id="calculator">94 + 23</gadget> <output>117</output> <gadget id="calculator">56 - 20</gadget> <output>36</output> <gadget id="calculator">117 - 36</gadget> <output>81</output> <gadget id="calculator">112 - 45</gadget> <output>67</output> <gadget id="calculator">81 - 67</gadget> <output>14</output> <result>D</result>

D

Stock / Number of shares V ------------ 68 W ---------- 112 X ------------ 56 Y ------------ 94 Z ------------ 45 The table shows the number of shares of each of the 5 stocks owned by Mr Sami. If Mr. Sami was to sell 20 shares of Stock X and buy 23 shares of stock Y, what would be the increase in the range of the numbers of shares of the 5 stocks owned by Mr. Sami?

subtract(subtract(add(94, 23), subtract(56, 20)), subtract(112, 45))

add(n3,n7)|subtract(n2,n6)|subtract(n1,n4)|subtract(#0,#1)|subtract(#3,#2)

based on the original number of shares , the range would be : 112 - 45 = 67 however , the prompt tells us that two of the values in the table are going to change . after the changes , the values will be : v 68 w 112 x 36 y 117 z 45 now the range is 117 - 36 = 81 the increase in the range requires us to compare thenewrange to theoldrange : 81 - 67 = 14 d

general

math_qa__TFLzheZX2QuszuFi

The mean of 50 observations was 32. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is Choices A) 35.2 B) 32.5 C) 36.5 D) 39.1 E) none

<gadget id="calculator">32 * 50</gadget> <output>1_600</output> <gadget id="calculator">50 - 2</gadget> <output>48</output> <gadget id="calculator">48 - 23</gadget> <output>25</output> <gadget id="calculator">1_600 + 25</gadget> <output>1_625</output> <gadget id="calculator">1_625 / 50</gadget> <output>65/2 = around 32.5</output> <result>B</result>

B

The mean of 50 observations was 32. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is

divide(add(multiply(32, 50), subtract(subtract(50, const_2), 23)), 50)

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

"sol . therefore correct sum = ( 32 × 50 + 48 – 23 ) = 1625 . therefore correct mean = 1625 / 50 = 32.5 . answer b"

general

math_qa__odNlKBttlo9vBoRr

0.009/x=0.05. find the value of X Choose the correct choice from the following options. A) 0.00018 B) 0.09 C) 0.018 D) 0.18 E) 90

<gadget id="calculator">0.009 / 0.05</gadget> <output>0.18</output> <result>D</result>

D

0.009/x=0.05. find the value of X

divide(0.009, 0.05)

divide(n0,n1)|

"x = 0.009 / 0.18 = 0.05 answer : d"

general

math_qa__1PWVD2OPETWQo8uI

By selling an article at Rs.700, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%? Options. A) s . 600 B) s . 480 C) s . 500 D) s . 450 E) s . 420

<gadget id="calculator">700 * 100</gadget> <output>70_000</output> <gadget id="calculator">25 + 100</gadget> <output>125</output> <gadget id="calculator">70_000 / 125</gadget> <output>560</output> <gadget id="calculator">560 * 25</gadget> <output>14_000</output> <gadget id="calculator">14_000 / 100</gadget> <output>140</output> <gadget id="calculator">560 - 140</gadget> <output>420</output> <result>E</result>

E

By selling an article at Rs.700, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?

subtract(divide(multiply(700, const_100), add(25, const_100)), divide(multiply(divide(multiply(700, const_100), add(25, const_100)), 25), const_100))

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

"sp = 700 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 700 * [ 100 / 125 ] = 560 loss = 25 % = 25 % of 560 = rs . 140 sp = cp - loss = 560 - 140 = rs . 420 answer : e"

gain

math_qa__b4kZkShWLyd34uuk

In a office work is distribute between p persons. If 1/6 members are absent then work increased for each person is? Choose the correct choice from the following options. A) 10 % B) 14.28 % C) 15 % D) 16 % E) 20 %

<gadget id="calculator">100 * 6</gadget> <output>600</output> <gadget id="calculator">6 - 1</gadget> <output>5</output> <gadget id="calculator">600 / 5</gadget> <output>120</output> <gadget id="calculator">120 - 100</gadget> <output>20</output> <result>E</result>

E

In a office work is distribute between p persons. If 1/6 members are absent then work increased for each person is?

subtract(divide(multiply(const_100, 6), subtract(6, 1)), const_100)

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

let total % of work is 100 % total person = p 1 / 6 person are absent of total person . so absent person is 1 / 6 p ie p / 6 . left person is , p - p / 6 = 5 p / 6 . p person do the work 100 % 1 person do the work 100 * p % 5 p / 6 person do the work ( 100 * p * 6 ) / 5 p % = 120.00 % work increased for each person is = ( 120 - 100 ) % = 20 % answer : e

general

math_qa__E274uDDnd3ZT5wPA

A cistern which could be filled in 9 hours takes 1 hour more to be filled owing to a leak in its bottom.If the cistern is full, in what time will the leak empty it? Choose the correct choice from the following A) 50 hours B) 62 hours C) 90 hours D) 75 hours E) 100 hours

<gadget id="calculator">1 / 9</gadget> <output>1/9 = around 0.111111</output> <gadget id="calculator">1 / 10</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">(1/9) - (1/10)</gadget> <output>1/90 = around 0.011111</output> <gadget id="calculator">1 / (1/90)</gadget> <output>90</output> <result>C</result>

C

A cistern which could be filled in 9 hours takes 1 hour more to be filled owing to a leak in its bottom.If the cistern is full, in what time will the leak empty it?

inverse(subtract(divide(const_1, 9), divide(const_1, const_10)))

divide(const_1,n0)|divide(const_1,const_10)|subtract(#0,#1)|inverse(#2)|

"let the leak empty the full cistern in x hours 9 x / x - 9 = 9 + 1 x = 90 hours answer is c"

physics

math_qa__fj6wkXrqwlm8MKxB

The total marks obtained by a student in Mathematics and Physics is 60 and his score in Chemistry is 10 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together. Choose the correct answer: A) 35 B) 30 C) 25 D) data inadequate E) none of these .

<gadget id="calculator">60 + 10</gadget> <output>70</output> <gadget id="calculator">70 / 2</gadget> <output>35</output> <result>A</result>

A

The total marks obtained by a student in Mathematics and Physics is 60 and his score in Chemistry is 10 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.

divide(add(60, 10), const_2)

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

"let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 60 and c - p = 10 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 60 + 10 ) / 2 = 35 . answer : a"

general

math_qa__gGgmlbPGBIB2uEz2

If the given two numbers are respectively 5% and 25% of a third number, then what percentage is the first of the second ? Select the correct option: A) 20 % B) 25 % C) 18 % D) 30 % E) none of these

<gadget id="calculator">5 / 100</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">25 / 100</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(1/20) / (1/4)</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(1/5) * 100</gadget> <output>20</output> <result>A</result>

A

If the given two numbers are respectively 5% and 25% of a third number, then what percentage is the first of the second ?

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

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

"here , l = 5 and m = 25 therefore , first number = l / m x 100 % of second number = 5 / 25 x 100 % of second number = 20 % of second number answer : a"

gain

math_qa__IqZ7YPAqWNuqiKyg

Starting from his house one day, a student walk at a speed of 2 kmph and reaches his school 10 minutes late. Next he increased his speed by 1 kmph and reaches the school 10 minutes early. How far is the school from his house? Choose the correct answer. A) 1 km B) 2 km C) 3 km D) 4 km E) 5 km

<gadget id="calculator">10 + 10</gadget> <output>20</output> <gadget id="calculator">20 / 60</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">(1/3) * 2</gadget> <output>2/3 = around 0.666667</output> <gadget id="calculator">2 + 1</gadget> <output>3</output> <gadget id="calculator">(2/3) * 3</gadget> <output>2</output> <result>B</result>

B

Starting from his house one day, a student walk at a speed of 2 kmph and reaches his school 10 minutes late. Next he increased his speed by 1 kmph and reaches the school 10 minutes early. How far is the school from his house?

multiply(multiply(divide(add(10, 10), const_60), 2), add(2, 1))

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

let the distance be x km difference in timings = 20 min = 20 / 60 = 1 / 3 hr x / 2 - x / 3 = 1 / 3 x = 2 km answer is b

physics

math_qa__TFStvrB1xIVlQhr3

If 23 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect? Choices: A) 176 B) 253 C) 342 D) 458 E) 560

<gadget id="calculator">factorial(23)</gadget> <output>25_852_016_738_884_976_640_000</output> <gadget id="calculator">23 - 2</gadget> <output>21</output> <gadget id="calculator">factorial(21)</gadget> <output>51_090_942_171_709_440_000</output> <gadget id="calculator">factorial(2)</gadget> <output>2</output> <gadget id="calculator">51_090_942_171_709_440_000 * 2</gadget> <output>102_181_884_343_418_880_000</output> <gadget id="calculator">25_852_016_738_884_976_640_000 / 102_181_884_343_418_880_000</gadget> <output>253</output> <result>B</result>

B

If 23 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?

divide(factorial(23), multiply(factorial(subtract(23, const_2)), factorial(const_2)))

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

"if two lines are not parallel , then they will intersect in exactly one point . lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel . we are also given that no three lines are concurrent . this means that no three lines intersect at the same point . so every pair of two lines we select will have a unique point of intersection which they will not share with any third line . the number of ways to select 2 lines from 23 lines is 23 c 2 = 253 the answer is b ."

physics

math_qa__r1lxPLR16gtXKCee

The sum of the non-prime numbers between 20 and 30, non-inclusive, is Choose the correct choice from the following: A) 173 B) 185 C) 197 D) 209 E) 221

<gadget id="calculator">20 + 1</gadget> <output>21</output> <gadget id="calculator">21 + 1</gadget> <output>22</output> <gadget id="calculator">21 + 22</gadget> <output>43</output> <gadget id="calculator">22 + 2</gadget> <output>24</output> <gadget id="calculator">43 + 24</gadget> <output>67</output> <gadget id="calculator">24 + 1</gadget> <output>25</output> <gadget id="calculator">67 + 25</gadget> <output>92</output> <gadget id="calculator">25 + 1</gadget> <output>26</output> <gadget id="calculator">92 + 26</gadget> <output>118</output> <gadget id="calculator">26 + 1</gadget> <output>27</output> <gadget id="calculator">118 + 27</gadget> <output>145</output> <gadget id="calculator">27 + 1</gadget> <output>28</output> <gadget id="calculator">145 + 28</gadget> <output>173</output> <result>A</result>

A

The sum of the non-prime numbers between 20 and 30, non-inclusive, is

add(add(add(add(add(add(add(20, const_1), add(add(20, const_1), const_1)), add(add(add(20, const_1), const_1), const_2)), add(add(add(add(20, const_1), const_1), const_2), const_1)), add(add(add(add(add(20, const_1), const_1), const_2), const_1), const_1)), add(add(add(add(add(add(20, const_1), const_1), const_2), const_1), const_1), const_1)), add(add(add(add(add(add(add(20, const_1), const_1), const_2), const_1), const_1), const_1), const_1))

add(n0,const_1)|add(#0,const_1)|add(#0,#1)|add(#1,const_2)|add(#2,#3)|add(#3,const_1)|add(#4,#5)|add(#5,const_1)|add(#6,#7)|add(#7,const_1)|add(#8,#9)|add(#9,const_1)|add(#10,#11)|

"sum of consecutive integers from 21 to 29 , inclusive = = = = > ( a 1 + an ) / 2 * # of terms = ( 21 + 29 ) / 2 * 9 = 25 * 9 = 225 sum of non - prime numbers b / w 20 and 30 , non inclusive = = = > 225 - 52 ( i . e . , 23 + 29 , being the prime # s in the range ) = 173 answer : a"

general

math_qa__ny9avWyY5wmkMLGi

There are 60 supermarkets in the FGH chain. All of them are either in the US or Canada. If there are 22 more FGH supermarkets in the US than in Canada, how many FGH supermarkets are there in the US? Answers A) 20 B) 31 C) 41 D) 53 E) 64

<gadget id="calculator">60 + 22</gadget> <output>82</output> <gadget id="calculator">82 / 2</gadget> <output>41</output> <result>C</result>

C

There are 60 supermarkets in the FGH chain. All of them are either in the US or Canada. If there are 22 more FGH supermarkets in the US than in Canada, how many FGH supermarkets are there in the US?

divide(add(60, 22), const_2)

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

"x + ( x - 22 ) = 60 - - > x = 41 . answer : c ."

general

math_qa__IM6e7nenobTmR3OI

A salt manufacturing company produced a total of 1000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its ave66rage daily production for that year? Choose the correct choice from the following answers: A) 51 B) 53 C) 55 D) 56 E) 57

<gadget id="calculator">1_000 * 2</gadget> <output>2_000</output> <gadget id="calculator">12 - 1</gadget> <output>11</output> <gadget id="calculator">11 * 100</gadget> <output>1_100</output> <gadget id="calculator">2_000 + 1_100</gadget> <output>3_100</output> <gadget id="calculator">3_100 * 12</gadget> <output>37_200</output> <gadget id="calculator">37_200 / 2</gadget> <output>18_600</output> <gadget id="calculator">3 * 100</gadget> <output>300</output> <gadget id="calculator">2 * 3</gadget> <output>6</output> <gadget id="calculator">6 * 10</gadget> <output>60</output> <gadget id="calculator">300 + 60</gadget> <output>360</output> <gadget id="calculator">2 + 3</gadget> <output>5</output> <gadget id="calculator">360 + 5</gadget> <output>365</output> <gadget id="calculator">18_600 / 365</gadget> <output>3_720/73 = around 50.958904</output> <result>A</result>

A

A salt manufacturing company produced a total of 1000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its ave66rage daily production for that year?

divide(divide(multiply(add(multiply(1000, const_2), multiply(subtract(const_12, const_1), 100)), const_12), const_2), add(add(multiply(const_3, const_100), multiply(multiply(const_2, const_3), const_10)), add(const_2, const_3)))

add(const_2,const_3)|multiply(n0,const_2)|multiply(const_100,const_3)|multiply(const_2,const_3)|subtract(const_12,const_1)|multiply(n1,#4)|multiply(#3,const_10)|add(#1,#5)|add(#2,#6)|add(#8,#0)|multiply(#7,const_12)|divide(#10,const_2)|divide(#11,#9)

total production of salt by the company in that year = 1000 + 1100 + 1200 + . . . . + 2100 = 18600 . average monthly production of salt for that year = 18600 / 365 â ‰ ˆ 51 answer : a

general

math_qa__hSF9f5vimeUaKtkr

How much water should be added to 15 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ? Choose the correct choice from the following choices: A) 25 liters B) 27 liters C) 30 liters D) 32 liters E) 35 liters

<gadget id="calculator">2 * 100</gadget> <output>200</output> <gadget id="calculator">75 / 100</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">(3/4) * 20</gadget> <output>15</output> <gadget id="calculator">20 - 15</gadget> <output>5</output> <gadget id="calculator">200 / 5</gadget> <output>40</output> <gadget id="calculator">40 - 15</gadget> <output>25</output> <result>A</result>

A

How much water should be added to 15 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ?

subtract(divide(multiply(const_2, const_100), subtract(20, multiply(divide(75, const_100), 20))), 15)

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

"let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 15 + x ) ) ) 2 = 5 % * ( 15 + x ) - - - - - - - - > x = 25 ans a"

general

math_qa__YuSwxv65N0zPkfwF

In a sample of 800 high school students in which all students are either freshmen, sophomores, juniors, or seniors, 27 percent are juniors and 75 percent are not sophomores. If there are 160 seniors, how many more freshmen than sophomores are there among the sample of students? Options: A) 12 B) 18 C) 24 D) 30 E) 36

<gadget id="calculator">160 / 800</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(1/5) * 100</gadget> <output>20</output> <gadget id="calculator">100 - 20</gadget> <output>80</output> <gadget id="calculator">80 - 27</gadget> <output>53</output> <gadget id="calculator">100 - 75</gadget> <output>25</output> <gadget id="calculator">53 - 25</gadget> <output>28</output> <gadget id="calculator">28 * 800</gadget> <output>22_400</output> <gadget id="calculator">22_400 / 100</gadget> <output>224</output> <gadget id="calculator">25 * 800</gadget> <output>20_000</output> <gadget id="calculator">20_000 / 100</gadget> <output>200</output> <gadget id="calculator">224 - 200</gadget> <output>24</output> <result>C</result>

C

In a sample of 800 high school students in which all students are either freshmen, sophomores, juniors, or seniors, 27 percent are juniors and 75 percent are not sophomores. If there are 160 seniors, how many more freshmen than sophomores are there among the sample of students?

subtract(divide(multiply(subtract(subtract(subtract(const_100, multiply(divide(160, 800), const_100)), 27), subtract(const_100, 75)), 800), const_100), divide(multiply(subtract(const_100, 75), 800), const_100))

divide(n3,n0)|subtract(const_100,n2)|multiply(#0,const_100)|multiply(n0,#1)|divide(#3,const_100)|subtract(const_100,#2)|subtract(#5,n1)|subtract(#6,#1)|multiply(n0,#7)|divide(#8,const_100)|subtract(#9,#4)|

"200 are sophomores . the number of freshmen is 600 - 160 - 0.27 ( 800 ) = 224 the answer is c ."

gain

math_qa__jSGrHP54SsUzCbqW

A train 440 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going? Choose the correct choice A) 80 B) 26 C) 24 D) 54 E) 15

<gadget id="calculator">60 + 6</gadget> <output>66</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">66 * (5/18)</gadget> <output>55/3 = around 18.333333</output> <gadget id="calculator">440 / (55/3)</gadget> <output>24</output> <result>C</result>

C

A train 440 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?

divide(440, multiply(add(60, 6), const_0_2778))

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

"speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 440 * 3 / 55 = 24 sec . answer : c"

physics

math_qa__WUMiP8Dcm1mQQvRd

find two integers, neither of which ends in a zero, and whose product is exactly 1,00,000 Choose the correct choice from the following: A) 64 and 15,625 B) 32 and 3,125 C) 64 and 15,620 D) 64 and 15,635 E) 64 and 16,625

<gadget id="calculator">100 * 100</gadget> <output>10_000</output> <gadget id="calculator">10_000 * 100</gadget> <output>1_000_000</output> <gadget id="calculator">3 * 12</gadget> <output>36</output> <gadget id="calculator">36 - 4</gadget> <output>32</output> <gadget id="calculator">1_000_000 / 32</gadget> <output>31_250</output> <gadget id="calculator">1_000_000 / 31_250</gadget> <output>32</output> <result>B</result>

B

find two integers, neither of which ends in a zero, and whose product is exactly 1,00,000

divide(multiply(multiply(const_100, const_100), const_100), divide(multiply(multiply(const_100, const_100), const_100), subtract(multiply(const_3, const_12), const_4)))

multiply(const_100,const_100)|multiply(const_12,const_3)|multiply(#0,const_100)|subtract(#1,const_4)|divide(#2,#3)|divide(#2,#4)

1 , 00,000 = 10 ^ 5 = 10 x 10 x 10 x 10 x 10 = ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) = ( 2 ^ 5 ) x ( 5 ^ 5 ) = 32 x 3125 so the numbers are 32 and 3,125 answer : b

general

math_qa__lIUTcKk2caykbbf8

A man starts walking at 3 pm . ha walks at a speed of 4 km/hr on level ground and at a speed of 3 km/hr on uphill , 6 km/hr downhill and then 4 km/hr on level ground to reach home at 9 pm. What is the distance covered on one way Choose the correct choice from the following options: A) 10 km B) 12 km C) 14 km D) 16 km E) 18 km

<gadget id="calculator">6 / 2</gadget> <output>3</output> <gadget id="calculator">4 * 3</gadget> <output>12</output> <result>B</result>

B

A man starts walking at 3 pm . ha walks at a speed of 4 km/hr on level ground and at a speed of 3 km/hr on uphill , 6 km/hr downhill and then 4 km/hr on level ground to reach home at 9 pm. What is the distance covered on one way

multiply(4, divide(6, const_2))

divide(n3,const_2)|multiply(n1,#0)

avg speed = 2 * 3 * 6 / ( 3 + 6 ) = 4 so speed of man = 4 km / hr distance = 4 * 6 = 24 km since we want one way distance it will be 24 / 2 = 12 km answer : b

physics

math_qa__tr1VGObjGwm5Ygvy

A train 175 m long running at 36 kmph crosses a platform in 40 sec. What is the length of the platform? Choose the correct answer A) 271 B) 266 C) 225 D) 277 E) 232

<gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">36 * (5/18)</gadget> <output>10</output> <gadget id="calculator">40 * 10</gadget> <output>400</output> <gadget id="calculator">400 - 175</gadget> <output>225</output> <result>C</result>

C

A train 175 m long running at 36 kmph crosses a platform in 40 sec. What is the length of the platform?

subtract(multiply(40, multiply(36, const_0_2778)), 175)

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

"length of the platform = 36 * 5 / 18 * 40 = 400 – 175 = 225 answer : c"

physics

math_qa__FqKmXKTf5DjPXXfq

The population of a town increases 22% and 25% respectively in two consecutive years. After the growth the present population of the town is 1220. Then what is the population of the town 2 years ago? Choose the correct answer. A) 600 B) 700 C) 800 D) 900 E) 1000

<gadget id="calculator">22 / 100</gadget> <output>11/50 = around 0.22</output> <gadget id="calculator">1 + (11/50)</gadget> <output>61/50 = around 1.22</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">(61/50) * (5/4)</gadget> <output>61/40 = around 1.525</output> <gadget id="calculator">1_220 / (61/40)</gadget> <output>800</output> <result>C</result>

C

The population of a town increases 22% and 25% respectively in two consecutive years. After the growth the present population of the town is 1220. Then what is the population of the town 2 years ago?

divide(1220, multiply(add(const_1, divide(22, 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)|

"explanation : formula : ( after = 100 denominator ago = 100 numerator ) 1220 * 100 / 122 * 100 / 125 = 800 answer : option c"

gain

math_qa__zzG88oKVYpycGkiE

in how many v ways can a 4 - letter password be chosen , using the letters a , b , c , d , e , and / or f , such that at least one letter is repeated within the password ? Choose the correct choice from the following. A) 720 B) 864 C) 900 D) 936 E) 1296

<gadget id="calculator">4 + 2</gadget> <output>6</output> <gadget id="calculator">6 ** 4</gadget> <output>1_296</output> <gadget id="calculator">factorial(6)</gadget> <output>720</output> <gadget id="calculator">factorial(2)</gadget> <output>2</output> <gadget id="calculator">factorial(4)</gadget> <output>24</output> <gadget id="calculator">2 * 24</gadget> <output>48</output> <gadget id="calculator">720 / 48</gadget> <output>15</output> <gadget id="calculator">15 * 24</gadget> <output>360</output> <gadget id="calculator">1_296 - 360</gadget> <output>936</output> <result>D</result>

D

in how many v ways can a 4 - letter password be chosen , using the letters a , b , c , d , e , and / or f , such that at least one letter is repeated within the password ?

subtract(power(add(4, const_2), 4), multiply(divide(factorial(add(4, const_2)), multiply(factorial(const_2), factorial(4))), factorial(4)))

add(n0,const_2)|factorial(const_2)|factorial(n0)|factorial(#0)|multiply(#1,#2)|power(#0,n0)|divide(#3,#4)|multiply(#6,#2)|subtract(#5,#7)

total number of four letter passwords = 6 * 6 * 6 * 6 = 1296 - - - - - - ( 1 ) total number of passwords in which no letter repeats = 6 c 4 * 4 ! = 15 * 24 = 360 - - - - - - ( 2 ) therefore required value v = ( 1 ) - ( 2 ) = 1296 - 360 = 936 . d

general

math_qa__yU067VZUkvPR6zSy

The average expenditure of a labourer for 6 months was 85 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income is Choose the correct choice from the following. A) 70 B) 72 C) 75 D) 78 E) none of the above

<gadget id="calculator">85 * 6</gadget> <output>510</output> <gadget id="calculator">60 * 4</gadget> <output>240</output> <gadget id="calculator">510 + 240</gadget> <output>750</output> <gadget id="calculator">750 + 30</gadget> <output>780</output> <gadget id="calculator">6 + 4</gadget> <output>10</output> <gadget id="calculator">780 / 10</gadget> <output>78</output> <result>D</result>

D

The average expenditure of a labourer for 6 months was 85 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income is

divide(add(add(multiply(85, 6), multiply(60, 4)), 30), add(6, 4))

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

"income of 6 months = ( 6 × 85 ) – debt = 510 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 780 average monthly income = 780 ÷ 10 = 78 answer d"

general

math_qa__u1TKtlTvQNia6NLa

A sum of money is sufficient to pay B's wages for 12 days and C's wages for 24 days. The same money is sufficient to pay the wages of both for? Pick one: A) 6 B) 7 C) 8 D) 9 E) 10

<gadget id="calculator">1 / 24</gadget> <output>1/24 = around 0.041667</output> <gadget id="calculator">1 / 12</gadget> <output>1/12 = around 0.083333</output> <gadget id="calculator">(1/24) + (1/12)</gadget> <output>1/8 = around 0.125</output> <gadget id="calculator">1 / (1/8)</gadget> <output>8</output> <result>C</result>

C

A sum of money is sufficient to pay B's wages for 12 days and C's wages for 24 days. The same money is sufficient to pay the wages of both for?

inverse(add(divide(const_1, 24), divide(const_1, 12)))

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

let the total money be $ x b ' s 1 day work = $ x / 12 c ' s 1 day work = $ x / 24 a + b 1 day work = $ x / 8 money is sufficient to pay the wages of both for 8 days answer is c

general

math_qa__GHrEt3c4l2PbDpAv

Jonathan, Matthew and Zac are picking strawberries from their yard. Together they have picked a total of 550 strawberries. Jonathan and Matthew have picked 350 strawberries together. Matthew and Zac have picked 250 strawberries together. How many strawberries has Zac picked by himself? Choose the correct choice from the following: A) 100 B) 200 C) 350 D) 50 E) 250

<gadget id="calculator">350 + 250</gadget> <output>600</output> <gadget id="calculator">550 - 600</gadget> <output>-50</output> <gadget id="calculator">-(-50)</gadget> <output>50</output> <gadget id="calculator">4 * 50</gadget> <output>200</output> <result>B</result>

B

Jonathan, Matthew and Zac are picking strawberries from their yard. Together they have picked a total of 550 strawberries. Jonathan and Matthew have picked 350 strawberries together. Matthew and Zac have picked 250 strawberries together. How many strawberries has Zac picked by himself?

multiply(const_4, negate(subtract(550, add(350, 250))))

add(n1,n2)|subtract(n0,#0)|negate(#1)|multiply(#2,const_4)

jonathan = matthew + zac = 550 strawberries j + m = 350 m + z = 250 use j + m = 350 to plug into the original formula ( j + m ) + z = 550 350 + z = 550 subtract 350 from each side z = 200 answer : b

general

math_qa__HfCCKVO0rHHRLHMX

In a certain Parallelogram the degree measure of one angle exceeds that of the other by 70 what is the degree measure of the smaller angle? Answers A) 55 B) 80 C) 85 D) 90 E) 95

<gadget id="calculator">3_600 / 10</gadget> <output>360</output> <gadget id="calculator">70 * 2</gadget> <output>140</output> <gadget id="calculator">360 - 140</gadget> <output>220</output> <gadget id="calculator">220 / 4</gadget> <output>55</output> <result>A</result>

A

In a certain Parallelogram the degree measure of one angle exceeds that of the other by 70 what is the degree measure of the smaller angle?

divide(subtract(divide(const_3600, const_10), multiply(70, const_2)), const_4)

divide(const_3600,const_10)|multiply(n0,const_2)|subtract(#0,#1)|divide(#2,const_4)

in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 ° ) . given : x + ( x + 70 ) = 180 - - > x = 55 . answer : a .

geometry

math_qa__fbFzbCba1Oj3G3eq

A candidate got 35% of the votes and lost to the rival by 1350 votes. How many votes were cast? Choose the correct choice from the following choices: A) 4000 B) 4500 C) 5000 D) 5500 E) 6000

<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_350 / (3/10)</gadget> <output>4_500</output> <result>B</result>

B

A candidate got 35% of the votes and lost to the rival by 1350 votes. How many votes were cast?

divide(1350, 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 % = 1350 10 % = 450 100 % of the votes = 4500 answer : b"

gain

math_qa__ZpivYNSqxaADIT8T

A zeebra chases a tiger 5 hours after the tiger runs. zeebra takes 6 hours to reach the tiger. If the average speed of the zeebra is 55 kmph, what s the average speed of the tiger? Choose the correct choice A) 35 kmph B) 32 kmph C) 30 kmph D) 31 kmph E) 20 kmph

<gadget id="calculator">55 * 6</gadget> <output>330</output> <gadget id="calculator">5 + 6</gadget> <output>11</output> <gadget id="calculator">330 / 11</gadget> <output>30</output> <result>C</result>

C

A zeebra chases a tiger 5 hours after the tiger runs. zeebra takes 6 hours to reach the tiger. If the average speed of the zeebra is 55 kmph, what s the average speed of the tiger?

divide(multiply(55, 6), add(5, 6))

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

tiger take 11 hours and zeebra take 6 hours . . . then distance chased by them is 55 * 6 . so speed of tiger is ( 55 * 6 ) / 11 = 30 kmph . answer is c

physics

math_qa__NcsZIECL6eCKtDUC

If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 4 flips but not on the last flip? Choose the correct choice. A) 1 / 2 B) 1 / 4 C) 1 / 8 D) 1 / 16 E) 1 / 32

<gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">(1/2) ** 5</gadget> <output>1/32 = around 0.03125</output> <result>E</result>

E

If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 4 flips but not on the last flip?

power(divide(1, 2), 5)

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

p ( hhhht ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 the answer is e .

probability

math_qa__u1TDiTtSgCJ350KO

The average age of students of a class is 15.8 years. The average age of boys in the class is 16.2 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is: Options: A) 2 : 5 B) 2 : 3 C) 2 : 4 D) 1 : 1 E) 2 : 9

<gadget id="calculator">15.8 - 15.4</gadget> <output>0.4</output> <gadget id="calculator">16.2 - 15.8</gadget> <output>0.4</output> <gadget id="calculator">0.4 / 0.4</gadget> <output>1</output> <result>D</result>

D

The average age of students of a class is 15.8 years. The average age of boys in the class is 16.2 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is:

divide(subtract(15.8, 15.4), subtract(16.2, 15.8))

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

"let the ratio be k : 1 . then , k * 16.2 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.2 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.4 = 1 / 1 required ratio = 1 / 1 : 1 = 1 : 1 . answer : d"

general

math_qa__OkPIQilrpC93K2Ht

A number is doubled and 9 is added. If resultant is trebled, it becomes 75. What is that number Choose the correct option. A) 8 B) 10 C) 12 D) 14 E) 15

<gadget id="calculator">3 * 9</gadget> <output>27</output> <gadget id="calculator">75 - 27</gadget> <output>48</output> <gadget id="calculator">3 * 2</gadget> <output>6</output> <gadget id="calculator">48 / 6</gadget> <output>8</output> <result>A</result>

A

A number is doubled and 9 is added. If resultant is trebled, it becomes 75. What is that number

divide(subtract(75, multiply(const_3, 9)), multiply(const_3, const_2))

multiply(n0,const_3)|multiply(const_2,const_3)|subtract(n1,#0)|divide(#2,#1)|

"explanation : = > 3 ( 2 x + 9 ) = 75 = > 2 x + 9 = 25 = > x = 8 answer : option a"

general

math_qa__pbTFvkf2HKDXaEQI

(112 x 5^4) = ? Select. A) 70000 B) 80000 C) 90000 D) 90090 E) 100000

<gadget id="calculator">4 + 1</gadget> <output>5</output> <gadget id="calculator">5 ** 4</gadget> <output>625</output> <gadget id="calculator">112 * 625</gadget> <output>70_000</output> <result>A</result>

A

(112 x 5^4) = ?

multiply(112, power(add(const_4, const_1), const_4))

add(const_1,const_4)|power(#0,const_4)|multiply(n0,#1)|

"( 112 x 54 ) = 112 x 10 4 = 112 x 104 = 1120000 = 70000 2 24 16 a )"

general

math_qa__pqYcBDTejuOdquqq

x+(1/x) = 2 find x^2 + (1/x^2) Choose the correct choice from the following answers: A) 2 B) 3.25 C) 4.25 D) 5.25 E) 6.25

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

A

x+(1/x) = 2 find x^2 + (1/x^2)

subtract(power(2, 2), 2)

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

"squaring on both sides ( x + 1 / x ) ^ 2 = 2 ^ 2 x ^ 2 + 1 / x ^ 2 = 4 - 2 x ^ 2 + 1 / x ^ 2 = 2 answer : a"

general

math_qa__sXOhhyP3otuAimSb

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

<gadget id="calculator">12 - 3</gadget> <output>9</output> <gadget id="calculator">9 / 12</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">9 - 1</gadget> <output>8</output> <gadget id="calculator">12 - 1</gadget> <output>11</output> <gadget id="calculator">8 / 11</gadget> <output>8/11 = around 0.727273</output> <gadget id="calculator">(3/4) * (8/11)</gadget> <output>6/11 = around 0.545455</output> <result>C</result>

C

In a box of 12 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?

multiply(divide(subtract(12, 3), 12), divide(subtract(subtract(12, 3), const_1), subtract(12, const_1)))

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

"# defective pens = 3 # good pens = 9 probability of the 1 st pen being good = # of favorable outcomes / # of total outcomes = 9 / 12 probability of the 2 nd pen being good = # of remaining favorable outcomes / # of total remaining outcomes = 8 / 11 total probability = 9 / 12 * 8 / 11 = 6 / 11 answer will be c"

general

math_qa__A6upx2893fTXu3ZT

If a sum of money doubles itself in 15 years at simple interest, the ratepercent per annum is Select the correct option. A) 12 B) 12.5 C) 6.67 D) 13.5 E) 14

<gadget id="calculator">15 / 100</gadget> <output>3/20 = around 0.15</output> <gadget id="calculator">2 / (3/20)</gadget> <output>40/3 = around 13.333333</output> <gadget id="calculator">(40/3) / 2</gadget> <output>20/3 = around 6.666667</output> <result>C</result>

C

If a sum of money doubles itself in 15 years at simple interest, the ratepercent per annum is

divide(divide(const_2, divide(15, const_100)), const_2)

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

"explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 15 ) = 6.67 option c"

gain

math_qa__OX3ddDTJvymWvplK

Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.883. Find the cost of each ice-cream cup? Pick one. A) 25 B) 76 C) 29 D) 12 E) 20

<gadget id="calculator">16 * 6</gadget> <output>96</output> <gadget id="calculator">883 - 96</gadget> <output>787</output> <gadget id="calculator">5 * 45</gadget> <output>225</output> <gadget id="calculator">787 - 225</gadget> <output>562</output> <gadget id="calculator">7 * 70</gadget> <output>490</output> <gadget id="calculator">562 - 490</gadget> <output>72</output> <gadget id="calculator">72 / 6</gadget> <output>12</output> <result>D</result>

D

Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.883. Find the cost of each ice-cream cup?

divide(subtract(subtract(subtract(883, multiply(16, 6)), multiply(5, 45)), multiply(7, 70)), 6)

multiply(n0,n3)|multiply(n1,n5)|multiply(n2,n6)|subtract(n7,#0)|subtract(#3,#1)|subtract(#4,#2)|divide(#5,n3)|

"explanation : let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 883 96 + 225 + 490 + 6 x = 883 6 x = 72 = > x = 12 . answer : d"

general

math_qa__a91lXlCn6oKcujL0

Drum X is 1/2 full of oil and drum Y, which has twice the capacity of drum X, is 1/3 full of oil. If all of the oil in drum X is poured into drum Y, then drum Y will be filled to what capacity? Select A) 2 / 3 B) 5 / 6 C) 7 / 12 D) 11 / 12 E) 17 / 24

<gadget id="calculator">1 / 3</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">(1/3) * 12</gadget> <output>4</output> <gadget id="calculator">12 / 2</gadget> <output>6</output> <gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">6 * (1/2)</gadget> <output>3</output> <gadget id="calculator">4 + 3</gadget> <output>7</output> <gadget id="calculator">7 / 12</gadget> <output>7/12 = around 0.583333</output> <result>C</result>

C

Drum X is 1/2 full of oil and drum Y, which has twice the capacity of drum X, is 1/3 full of oil. If all of the oil in drum X is poured into drum Y, then drum Y will be filled to what capacity?

divide(add(multiply(divide(1, 3), const_12), multiply(divide(const_12, 2), divide(1, 2))), const_12)

divide(n0,n3)|divide(const_12,n1)|divide(n0,n1)|multiply(#0,const_12)|multiply(#1,#2)|add(#3,#4)|divide(#5,const_12)|

"( 1 / 2 ) x = ( 1 / 4 ) y ( 1 / 4 ) y + ( 1 / 3 ) y = ( 7 / 12 ) y the answer is c ."

general

math_qa__7K5uG9WHnkrYvpDx

A train 160 m long passes a man,running at 6 kmph in the direction opposite to that of the train,in 6 seconds.The speed of the train is Choose the correct answer. A) 54 kmph B) 60 kmph C) 66 kmph D) 72 kmph E) 90 kmph

<gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">6 * (5/18)</gadget> <output>5/3 = around 1.666667</output> <gadget id="calculator">(5/3) * 6</gadget> <output>10</output> <gadget id="calculator">160 - 10</gadget> <output>150</output> <gadget id="calculator">150 / 6</gadget> <output>25</output> <gadget id="calculator">25 / (5/18)</gadget> <output>90</output> <result>E</result>

E

A train 160 m long passes a man,running at 6 kmph in the direction opposite to that of the train,in 6 seconds.The speed of the train is

divide(divide(subtract(160, multiply(multiply(6, const_0_2778), 6)), 6), const_0_2778)

multiply(n1,const_0_2778)|multiply(n1,#0)|subtract(n0,#1)|divide(#2,n1)|divide(#3,const_0_2778)|

"speed of train relative to man : 160 / 6 * 18 / 5 km / hr = 96 km / hr let speed of train = x therefore x + 6 = 96 x = 96 - 6 x = 90 km / hr answer : e"

physics

math_qa__QTZpTYHhu08BCZFS

If 9 engines consume 24 metric tonnes of coal, when each is working 8 hoursday, bow much coal will be required for 8 engines, each running 13hours a day, it being given that 3 engines of former type consume as much as 4 engines of latter type? Options: A) 22 B) 24 C) 26 D) 28 E) none of them

<gadget id="calculator">3 * 24</gadget> <output>72</output> <gadget id="calculator">9 * 8</gadget> <output>72</output> <gadget id="calculator">72 / 72</gadget> <output>1</output> <gadget id="calculator">1 * 2</gadget> <output>2</output> <gadget id="calculator">13 * 2</gadget> <output>26</output> <result>C</result>

C

If 9 engines consume 24 metric tonnes of coal, when each is working 8 hoursday, bow much coal will be required for 8 engines, each running 13hours a day, it being given that 3 engines of former type consume as much as 4 engines of latter type?

multiply(13, multiply(divide(multiply(3, 24), multiply(9, 8)), const_2))

multiply(n1,n5)|multiply(n0,n2)|divide(#0,#1)|multiply(#2,const_2)|multiply(n4,#3)

let 3 engines of former type consume 1 unit in 1 hour . then , 4 engines of latter type consume 1 unit in 1 hour . therefore 1 engine of former type consumes ( 1 / 3 ) unit in 1 hour . 1 engine of latter type consumes ( 1 / 4 ) unit in 1 hour . let the required consumption of coal be x units . less engines , less coal consumed ( direct proportion ) more working hours , more coal consumed ( direct proportion ) less rate of consumption , less coal consumed ( direct prportion ) number of engines 9 : 8 working hours 8 : 13 } : : 24 : x rate of consumption ( 1 / 3 ) : ( 1 / 4 ) [ 9 x 8 x ( 1 / 3 ) x x ) = ( 8 x 13 x ( 1 / 4 ) x 24 ) = 24 x = 624 = x = 26 . hence , the required consumption of coal = 26 metric tonnes . answer is c .

physics

math_qa__7zjCs7Z7cpO52SMT

If 16 percent of the students at a certain school went to a camping trip and took more than $100, and 75 percent of the students who went to the camping trip did not take more than $100, what percentage of the students at the school went to the camping trip? Pick A) 95 B) 90 C) 85 D) 80 E) 64

<gadget id="calculator">100 - 75</gadget> <output>25</output> <gadget id="calculator">25 / 100</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">16 / (1/4)</gadget> <output>64</output> <result>E</result>

E

If 16 percent of the students at a certain school went to a camping trip and took more than $100, and 75 percent of the students who went to the camping trip did not take more than $100, what percentage of the students at the school went to the camping trip?

divide(16, divide(subtract(100, 75), 100))

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

"let x be the number of students in the school . 0.16 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.16 x / 0.25 = 0.64 x students went to the camping which is 64 % . the answer is e"

general

math_qa__4RWmpq5XZaBJoQF9

Average of 10 matches is 32, How many runs one should should score to increase his average by 6 runs. Options A) 70 B) 76 C) 78 D) 98 E) 88

<gadget id="calculator">32 + 6</gadget> <output>38</output> <gadget id="calculator">10 + 1</gadget> <output>11</output> <gadget id="calculator">38 * 11</gadget> <output>418</output> <gadget id="calculator">10 * 32</gadget> <output>320</output> <gadget id="calculator">418 - 320</gadget> <output>98</output> <result>D</result>

D

Average of 10 matches is 32, How many runs one should should score to increase his average by 6 runs.

subtract(multiply(add(32, 6), add(10, const_1)), multiply(10, 32))

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

"explanation : average after 11 innings should be 38 so , required score = ( 11 * 38 ) - ( 10 * 32 ) = 418 - 320 = 98 answer : option d"

general

math_qa__LjvIhIZGvHzCVMPZ

Solve below question 2x + 1 = -23 Pick A) - 8 B) - 9 C) - 12 D) - 4 E) 12

<gadget id="calculator">23 + 1</gadget> <output>24</output> <gadget id="calculator">-24</gadget> <output>-24</output> <gadget id="calculator">(-24) / 2</gadget> <output>-12</output> <result>C</result>

C

Solve below question 2x + 1 = -23

divide(negate(add(23, 1)), 2)

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

1 . subtract 1 from both sides : 2 x + 1 - 1 = - 23 - 1 2 . simplify both sides : 2 x = - 24 3 . divide both sides by 2 : 4 . simplify both sides : x = - 12 c

general