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Calc-math_qa

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math_qa__tfcw3hOTiIK4H5aC

The average age of A, B and C is 25 years. If the average age of A and C is 29 years, what is the age of B in years ? Select A) 17 B) 35 C) 20 D) 32 E) 21

<gadget id="calculator">25 * 3</gadget> <output>75</output> <gadget id="calculator">29 * 2</gadget> <output>58</output> <gadget id="calculator">75 - 58</gadget> <output>17</output> <result>A</result>

A

The average age of A, B and C is 25 years. If the average age of A and C is 29 years, what is the age of B in years ?

subtract(multiply(25, const_3), multiply(29, const_2))

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

"age of b = age of ( a + b + c ) â € “ age of ( a + c ) = 25 ã — 3 â € “ 29 ã — 2 = 75 â € “ 58 = 17 years a"

general

math_qa__OlM3kyntGxrK8izG

A man walking at the rate of 6km per hour crosses a square field diagonally in 9 seconds the area of the field is Pick one: A) 110 sq . m B) 111.5 aq . m C) 112.5 sq . m D) 114 sq . m E) none of these

<gadget id="calculator">6 * 1_000</gadget> <output>6_000</output> <gadget id="calculator">360 * 10</gadget> <output>3_600</output> <gadget id="calculator">6_000 / 3_600</gadget> <output>5/3 = around 1.666667</output> <gadget id="calculator">(5/3) * 9</gadget> <output>15</output> <gadget id="calculator">15 ** 2</gadget> <output>225</output> <gadget id="calculator">225 / 2</gadget> <output>225/2 = around 112.5</output> <result>C</result>

C

A man walking at the rate of 6km per hour crosses a square field diagonally in 9 seconds the area of the field is

divide(power(multiply(divide(multiply(6, const_1000), multiply(const_360, const_10)), 9), const_2), const_2)

multiply(n0,const_1000)|multiply(const_10,const_360)|divide(#0,#1)|multiply(n1,#2)|power(#3,const_2)|divide(#4,const_2)

explanation : distance covered in 9 seconds = ( 6 × 1000 / 3600 ) × 9 = 15 m diagonal of square field = 15 m side of square = a then diagonal of that square = √ 2 a hence area of the square = a 2 = ( 152 ) / 2 = 112.5 sq . m answer : option c

geometry

math_qa__cIizWL6ET56PsEqq

In a college the ratio of the numbers of boys to the girls is 8:5. If there are 175 girls, the total number of students in the college is? Select: A) 562 B) 356 C) 455 D) 416 E) 512

<gadget id="calculator">8 / 5</gadget> <output>8/5 = around 1.6</output> <gadget id="calculator">(8/5) * 175</gadget> <output>280</output> <gadget id="calculator">280 + 175</gadget> <output>455</output> <result>C</result>

C

In a college the ratio of the numbers of boys to the girls is 8:5. If there are 175 girls, the total number of students in the college is?

add(multiply(divide(8, 5), 175), 175)

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

"let the number of boys and girls be 8 x and 5 x then , 5 x = 175 x = 35 total number of students = 13 x = 13 * 35 = 455 answer is c"

other

math_qa__GJEcmDNEO7eLT1QJ

I spend 40 hours a week (5 days) at work and like to organize my time so that I spend an equal number of hours on the two tasks I currently have. Currently, I am spending 5 hours a day on Task 1 and 3 on Task 2. How many hours a week less do I need to spend on Task 1 in order to evenly distribute my time? Choose the correct choice from the following choices. A) 5 B) 3 C) 7 D) 1 E) 6

<gadget id="calculator">40 / 2</gadget> <output>20</output> <gadget id="calculator">20 - 3</gadget> <output>17</output> <gadget id="calculator">20 - 5</gadget> <output>15</output> <gadget id="calculator">17 - 15</gadget> <output>2</output> <gadget id="calculator">2 + 3</gadget> <output>5</output> <result>A</result>

A

I spend 40 hours a week (5 days) at work and like to organize my time so that I spend an equal number of hours on the two tasks I currently have. Currently, I am spending 5 hours a day on Task 1 and 3 on Task 2. How many hours a week less do I need to spend on Task 1 in order to evenly distribute my time?

add(subtract(subtract(divide(40, const_2), 3), subtract(divide(40, const_2), 5)), 3)

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

5 x 5 = 25 25 - 5 = 20 the answer is a .

physics

math_qa__u5PUXbogyvNIoeLq

The area of a triangle is with base 4m and height 5m? Pick: A) 11 B) 10 C) 99 D) 17 E) 12

<gadget id="calculator">(4 * 5) / 2</gadget> <output>10</output> <result>B</result>

B

The area of a triangle is with base 4m and height 5m?

triangle_area(4, 5)

triangle_area(n0,n1)

1 / 2 * 4 * 5 = 10 m 2 answer : b

geometry

math_qa__xd0qdupiUZaz5PHQ

A pharmaceutical company received $5 million in royalties on the first $20 million in sales of and then $10 million in royalties on the next $108 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales? Choose one: A) 8 % B) 26 % C) 45 % D) 52 % E) 56 %

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

B

A pharmaceutical company received $5 million in royalties on the first $20 million in sales of and then $10 million in royalties on the next $108 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales?

multiply(divide(5, 20), const_100)

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

( 10 / 108 ) / ( 5 / 20 ) = 20 / 27 = 74 % it means that 10 / 108 represents only 74 % . therefore a decrease of 26 % . answer b

general

math_qa__ZP7VZaRcN2KwQBx8

Peter brought a scooter for a certain sum of money. He spent 10% of the cost on repairs and sold the scooter for a profit of $ 1100. How much did he spend on repairs if he made a profit of 20%? Choose the correct answer. A) 100 B) 200 C) 300 D) 400 E) 500

<gadget id="calculator">100 * 1_100</gadget> <output>110_000</output> <gadget id="calculator">110_000 / 20</gadget> <output>5_500</output> <gadget id="calculator">100 + 10</gadget> <output>110</output> <gadget id="calculator">5_500 / 110</gadget> <output>50</output> <gadget id="calculator">50 * 100</gadget> <output>5_000</output> <gadget id="calculator">5_500 - 5_000</gadget> <output>500</output> <result>E</result>

E

Peter brought a scooter for a certain sum of money. He spent 10% of the cost on repairs and sold the scooter for a profit of $ 1100. How much did he spend on repairs if he made a profit of 20%?

subtract(divide(multiply(const_100, 1100), 20), multiply(divide(divide(multiply(const_100, 1100), 20), add(const_100, const_10)), const_100))

add(const_10,const_100)|multiply(n1,const_100)|divide(#1,n2)|divide(#2,#0)|multiply(#3,const_100)|subtract(#2,#4)

e 500 let the c . p . be $ x . then , 20 % of x = 1100 20 / 100 * x = 1100 = > x = 5500 c . p . = $ 5500 , expenditure on repairs = 10 % actual price = $ ( 100 * 5500 ) / 110 = $ 5000 expenditures on repairs = ( 5500 - 5000 ) = $ 500 .

gain

math_qa__D1d19HQZCsn4eJVu

If the cost price of 19 articles is equal to the selling price of 16 articles, What is the percentage of profit or loss that the merchant makes? Choices: A) 18.75 % loss B) 18.75 % profit C) 33.33 % loss D) 30.33 % loss E) none of these

<gadget id="calculator">100 * 16</gadget> <output>1_600</output> <gadget id="calculator">1_600 / 19</gadget> <output>1_600/19 = around 84.210526</output> <gadget id="calculator">100 - (1_600/19)</gadget> <output>300/19 = around 15.789474</output> <gadget id="calculator">(300/19) / (1_600/19)</gadget> <output>3/16 = around 0.1875</output> <gadget id="calculator">100 * (3/16)</gadget> <output>75/4 = around 18.75</output> <result>B</result>

B

If the cost price of 19 articles is equal to the selling price of 16 articles, What is the percentage of profit or loss that the merchant makes?

multiply(const_100, divide(subtract(const_100, divide(multiply(const_100, 16), 19)), divide(multiply(const_100, 16), 19)))

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

"explanation : let cost price of 1 article be re . 1 . therefore , cost price of 19 articles = rs . 19 . selling price of 16 articles = rs . 19 therefore , selling price of 19 articles is : - = > 19 / 16 ã — 19 = > 22.56 . therefore , profit = selling price - cost price . = > 22.56 â ˆ ’ 19 = 3.56 . hence , the percentage of profit = profit x 100 / c . p . = > 3.56 / 19 ã — 100 . = > 18.75 % profit . answer : b"

gain

math_qa__shGXQdwFkKD1C0Nq

The mean of 40 observations was 100. It was found later that an observation 50 was wrongly taken as 75 The corrected new mean is Options: A) 125.8 B) 102.8 C) 99.375 D) 100.52 E) 122

<gadget id="calculator">100 * 40</gadget> <output>4_000</output> <gadget id="calculator">40 - 2</gadget> <output>38</output> <gadget id="calculator">38 - 75</gadget> <output>-37</output> <gadget id="calculator">4_000 + (-37)</gadget> <output>3_963</output> <gadget id="calculator">3_963 / 40</gadget> <output>3_963/40 = around 99.075</output> <result>C</result>

C

The mean of 40 observations was 100. It was found later that an observation 50 was wrongly taken as 75 The corrected new mean is

divide(add(multiply(100, 40), subtract(subtract(40, const_2), 75)), 40)

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

"explanation : correct sum = ( 100 * 40 + 50 - 75 ) = 3975 . correct mean = = 3975 / 40 = 99.375 answer : c"

general

math_qa__zwrh69qM3IA5z6ur

The entrance fee for a fair is $5 for persons under the age of 18, and 20% more for persons older. Each ride at the fair costs $0.50. If Joe goes with her 6 years old twin brothers, and they each took 3 rides in total. How much money does Joe end up spending at the fair? Choose the correct choice from the following answers A) 16 B) 20.5 C) 17.5 D) 20 E) 4.5

<gadget id="calculator">5 * 2</gadget> <output>10</output> <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">(6/5) * 5</gadget> <output>6</output> <gadget id="calculator">10 + 6</gadget> <output>16</output> <gadget id="calculator">3 * 3</gadget> <output>9</output> <gadget id="calculator">9 * 0.5</gadget> <output>4.5</output> <gadget id="calculator">16 + 4.5</gadget> <output>20.5</output> <result>B</result>

B

The entrance fee for a fair is $5 for persons under the age of 18, and 20% more for persons older. Each ride at the fair costs $0.50. If Joe goes with her 6 years old twin brothers, and they each took 3 rides in total. How much money does Joe end up spending at the fair?

add(add(multiply(5, const_2), multiply(add(divide(20, const_100), const_1), 5)), multiply(multiply(3, const_3), 0.5))

divide(n2,const_100)|multiply(n0,const_2)|multiply(n5,const_3)|add(#0,const_1)|multiply(n3,#2)|multiply(n0,#3)|add(#1,#5)|add(#6,#4)

total entrance fee is ( 2 * $ 5 ) + ( 1.20 * 5 ) = $ 16 total rides fee is ( 0.50 * 3 ) * 3 = $ 4.50 total money spent is $ 20.50 answer is b

general

math_qa__YES1xtOS0zijy0EV

In the manufacture of a certain product, 7 percent of the units produced are defective and 5 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale? Choose the correct choice from the following answers. A) 0.125 % B) 0.35 % C) 0.8 % D) 1.25 % E) 2.0 %

<gadget id="calculator">5 / 100</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">7 * (1/20)</gadget> <output>7/20 = around 0.35</output> <result>B</result>

B

In the manufacture of a certain product, 7 percent of the units produced are defective and 5 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?

multiply(7, divide(5, const_100))

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

"0.07 * 0.05 = 0.0035 = 0.35 % the answer is b ."

gain

math_qa__62qgsZZjSHYUsJYb

A bag contains 6 red, 5 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red? Choose the correct choice from the following answers A) 2 / 13 B) 3 / 17 C) 5 / 26 D) 5 / 21 E) 7 / 15

<gadget id="calculator">binomial(6, 2)</gadget> <output>15</output> <gadget id="calculator">6 + 5</gadget> <output>11</output> <gadget id="calculator">11 + 2</gadget> <output>13</output> <gadget id="calculator">binomial(13, 2)</gadget> <output>78</output> <gadget id="calculator">15 / 78</gadget> <output>5/26 = around 0.192308</output> <result>C</result>

C

A bag contains 6 red, 5 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?

divide(choose(6, 2), choose(add(add(6, 5), 2), 2))

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

"p ( both are red ) , = 6 c 213 c 2 = 6 c 213 c 2 = 5 / 26 c"

other

math_qa__fAMGb5tcU0yWQzmC

The cross-section of a cannel is a trapezium in shape. If the cannel is 6 m wide at the top and 4 m wide at the bottom and the area of cross-section is 10290 sq m, the depth of cannel is? Pick: A) 258 B) 260 C) 262 D) 264 E) 266

<gadget id="calculator">6 + 4</gadget> <output>10</output> <gadget id="calculator">10 / 2</gadget> <output>5</output> <gadget id="calculator">10_290 / 5</gadget> <output>2_058</output> <gadget id="calculator">2_058 / 4</gadget> <output>1_029/2 = around 514.5</output> <gadget id="calculator">(1_029/2) / 2</gadget> <output>1_029/4 = around 257.25</output> <result>A</result>

A

The cross-section of a cannel is a trapezium in shape. If the cannel is 6 m wide at the top and 4 m wide at the bottom and the area of cross-section is 10290 sq m, the depth of cannel is?

divide(divide(divide(10290, divide(add(6, 4), const_2)), const_4), const_2)

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

1 / 2 * d ( 6 + 4 ) = 10290 d = 258 answer : a

physics

math_qa__mSpui34jMMYh5mzr

A girl scout was selling boxes of cookies. In a month, she sold both boxes of chocolate chip cookies ($1.25 each) and boxes of plain cookies ($0.75 each). Altogether, she sold 1,585 boxes for a combined value of $1,586.25. How many boxes of plain cookies did she sell? Choose the correct answer A) 0 B) 233 C) 500 D) 695 E) 790

<gadget id="calculator">1_000 + 586.25</gadget> <output>1_586.25</output> <gadget id="calculator">1_586.25 / 2</gadget> <output>793.125</output> <result>E</result>

E

A girl scout was selling boxes of cookies. In a month, she sold both boxes of chocolate chip cookies ($1.25 each) and boxes of plain cookies ($0.75 each). Altogether, she sold 1,585 boxes for a combined value of $1,586.25. How many boxes of plain cookies did she sell?

divide(add(const_1000, 586.25), const_2)

add(n4,const_1000)|divide(#0,const_2)

let # plain cookies sold be x then # chocolate cookies = ( total cookies - x ) equating for x ( 0.75 ) * x + ( 1.25 ) * ( 1585 - x ) = 1586.25 = > x = 790 e

other

math_qa__eai09Hwf8tUysNnf

In what ratio P:Q should the Mixture P of milk and water in the ratio of 5:4 be mixed with another Mixture Q of milk and water in the ratio 2:7 so that the resultant mixture contains equal quantities of milk and water? Choose the correct choice: A) 3 : 2 B) 2 : 1 C) 4 : 3 D) 4 : 1 E) 5 : 1

<gadget id="calculator">4 + 7</gadget> <output>11</output> <gadget id="calculator">5 + 2</gadget> <output>7</output> <gadget id="calculator">11 - 7</gadget> <output>4</output> <gadget id="calculator">4 + 1</gadget> <output>5</output> <result>E</result>

E

In what ratio P:Q should the Mixture P of milk and water in the ratio of 5:4 be mixed with another Mixture Q of milk and water in the ratio 2:7 so that the resultant mixture contains equal quantities of milk and water?

add(subtract(add(4, 7), add(5, 2)), const_1)

add(n1,n3)|add(n0,n2)|subtract(#0,#1)|add(#2,const_1)

( 5 / 9 ) * p + ( 2 / 9 ) * q = ( 4 / 9 ) * p + ( 7 / 9 ) * q p = 5 q p / q = 5 / 1 the answer is e .

general

math_qa__AkEAJhWcEp1Ekt15

A certain company expects quarterly earnings of $0.80 per share of stock, half of which will be distributed as dividends to shareholders while the rest will be used for research and development. If earnings are greater than expected , shareholders will receive an additional $0.04 per share for each additional $0.10 of per share earnings. If quarterly earnings are $1.10 per share, what will be the dividend paid to a person who owns 500 shares of the company's stock? Choose the correct choice from the following answers: A) $ 260 B) $ 96 C) $ 26 D) $ 120 E) $ 240

<gadget id="calculator">0.8 / 2</gadget> <output>0.4</output> <gadget id="calculator">1.1 - 0.8</gadget> <output>0.3</output> <gadget id="calculator">0.3 * 10</gadget> <output>3</output> <gadget id="calculator">3 * 0.04</gadget> <output>0.12</output> <gadget id="calculator">0.4 + 0.12</gadget> <output>0.52</output> <gadget id="calculator">0.52 * 500</gadget> <output>260</output> <result>A</result>

A

A certain company expects quarterly earnings of $0.80 per share of stock, half of which will be distributed as dividends to shareholders while the rest will be used for research and development. If earnings are greater than expected , shareholders will receive an additional $0.04 per share for each additional $0.10 of per share earnings. If quarterly earnings are $1.10 per share, what will be the dividend paid to a person who owns 500 shares of the company's stock?

multiply(add(divide(0.80, const_2), multiply(multiply(subtract(1.10, 0.80), const_10), 0.04)), 500)

divide(n0,const_2)|subtract(n3,n0)|multiply(#1,const_10)|multiply(n1,#2)|add(#0,#3)|multiply(n4,#4)|

"eps actual > eps expected . each gets and additional . 12 per share . thus . 52 * 500 - - > $ 260 answer is a"

general

math_qa__njisCw9BjVEJk2hj

The positive integers s and t leave remainders of 2 and 3, respectively, when divided by 6. s > t. What is the remainder when s– t is divided by 6? Answers. A) 3 B) 1 C) 4 D) 2 E) 5

<gadget id="calculator">2 + 6</gadget> <output>8</output> <gadget id="calculator">8 - 3</gadget> <output>5</output> <result>E</result>

E

The positive integers s and t leave remainders of 2 and 3, respectively, when divided by 6. s > t. What is the remainder when s– t is divided by 6?

subtract(add(2, 6), 3)

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

let ' s test out some values of p and q that satisfy the given information . s leaves are remainder of 2 when divided by 6 so , s could equal 8 t leaves are remainder of 3 when divided by 6 so , t could equal 3 what is the remainder when s – t is divided by 6 ? so , s - t = 8 - 3 = 5 , and when we divide 5 by 6 , we get 0 with remainder 5 answer : e

general

math_qa__UdDImqzEZNVx7Npj

The sum of ages of 5 children born 2 years different each is 40 years. What is the age of the Elder child? Choose the correct option A) 12 B) 9 C) 10 D) 16 E) 17

<gadget id="calculator">2 + 4</gadget> <output>6</output> <gadget id="calculator">6 + 6</gadget> <output>12</output> <gadget id="calculator">4 + 4</gadget> <output>8</output> <gadget id="calculator">12 + 8</gadget> <output>20</output> <gadget id="calculator">20 + 40</gadget> <output>60</output> <gadget id="calculator">60 / 5</gadget> <output>12</output> <result>A</result>

A

The sum of ages of 5 children born 2 years different each is 40 years. What is the age of the Elder child?

divide(add(add(add(add(2, const_4), add(2, const_4)), add(const_4, const_4)), 40), 5)

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

"let the ages of children be x , ( x + 2 ) , ( x + 4 ) , ( x + 6 ) and ( x + 8 ) years . then , x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) + ( x + 8 ) = 40 5 x = 20 x = 4 . x + 8 = 4 + 8 = 12 answer : a"

general

math_qa__UNKGis15TG4wYw6P

Find large number from below question The difference of two no. is 1365. On dividing the larger no. by the smaller, we get 6 as quotient and the 15 as remainder? Select: A) 1234 B) 1456 C) 1256 D) 1456 E) 1635

<gadget id="calculator">1_365 - 15</gadget> <output>1_350</output> <gadget id="calculator">6 - 1</gadget> <output>5</output> <gadget id="calculator">1_350 / 5</gadget> <output>270</output> <gadget id="calculator">270 * 6</gadget> <output>1_620</output> <result>E</result>

E

Find large number from below question The difference of two no. is 1365. On dividing the larger no. by the smaller, we get 6 as quotient and the 15 as remainder?

multiply(divide(subtract(1365, 15), subtract(6, const_1)), 6)

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

"let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e"

general

math_qa__zOWkJpG3lCdb2CNS

The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 4% p.a. was Rs.326.40. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned. Select A) rs . 4326.40 B) rs . 4236.40 C) rs . 4136.40 D) rs . 4316.40 E) rs . 4136.40

<gadget id="calculator">4 / 100</gadget> <output>1/25 = around 0.04</output> <gadget id="calculator">1 + (1/25)</gadget> <output>26/25 = around 1.04</output> <gadget id="calculator">(26/25) ** 2</gadget> <output>676/625 = around 1.0816</output> <gadget id="calculator">(676/625) - 1</gadget> <output>51/625 = around 0.0816</output> <gadget id="calculator">326.4 / (51/625)</gadget> <output>4_000</output> <gadget id="calculator">4_000 + 326.4</gadget> <output>4_326.4</output> <result>A</result>

A

The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 4% p.a. was Rs.326.40. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.

add(divide(326.40, subtract(power(add(const_1, divide(4, const_100)), const_2), const_1)), 326.40)

divide(n0,const_100)|add(#0,const_1)|power(#1,const_2)|subtract(#2,const_1)|divide(n1,#3)|add(n1,#4)|

"let the sum be rs . p p { [ 1 + 4 / 100 ] 2 - 1 } = 326.40 p ( 4 / 100 ) ( 2 + 4 / 100 ) = 326.40 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 326.40 / ( 0.04 ) ( 2.04 ) = 4000 amount = 4000 + 326.40 = 4326.40 answer : a"

gain

math_qa__nbb0gRuZjL8hnQUx

James and David work at a grocery shop with 6 other workers. For an internal review, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that James and David will both be chosen? Choose the correct option. A) 1 / 20 B) 1 / 22 C) 1 / 23 D) 1 / 25 E) 1 / 15

<gadget id="calculator">1 / 6</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">6 - 1</gadget> <output>5</output> <gadget id="calculator">1 / 5</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(1/6) * (1/5)</gadget> <output>1/30 = around 0.033333</output> <gadget id="calculator">2 * (1/30)</gadget> <output>1/15 = around 0.066667</output> <result>E</result>

E

James and David work at a grocery shop with 6 other workers. For an internal review, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that James and David will both be chosen?

multiply(2, multiply(divide(const_1, 6), divide(const_1, subtract(6, const_1))))

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

"probability that james and david will both be chosen out of 6 workers = ( 2 / 6 ) * ( 1 / 5 ) = 1 / 15 answer e"

physics

math_qa__uMBGijGk4dGkzZr4

If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is - Choose the correct choice from the following: A) 8 / 13 B) 6 / 13 C) 3 / 13 D) 4 / 13 E) 1 / 13

<gadget id="calculator">3 / 52</gadget> <output>3/52 = around 0.057692</output> <gadget id="calculator">52 / 4</gadget> <output>13</output> <gadget id="calculator">13 / 52</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(3/52) + (1/4)</gadget> <output>4/13 = around 0.307692</output> <result>D</result>

D

If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is -

add(divide(const_3, const_52), divide(divide(const_52, const_4), const_52))

divide(const_3,const_52)|divide(const_52,const_4)|divide(#1,const_52)|add(#0,#2)

explanation : p ( s á ´ œ k ) = p ( s ) + p ( k ) - p ( s â ˆ © k ) , where s denotes spade and k denotes king . p ( s á ´ œ k ) = 13 / 52 + 4 / 52 - 1 / 52 = 4 / 13 answer : d

probability

math_qa__knCy1Ole8fxtGw9k

A man swims downstream 30 km and upstream 18 km taking 6 hours each time, what is the speed of the man in still water? Choose the correct choice. A) 7 B) 8 C) 5 D) 2 E) 4

<gadget id="calculator">18 / 6</gadget> <output>3</output> <gadget id="calculator">30 / 6</gadget> <output>5</output> <gadget id="calculator">3 + 5</gadget> <output>8</output> <gadget id="calculator">8 / 2</gadget> <output>4</output> <result>E</result>

E

A man swims downstream 30 km and upstream 18 km taking 6 hours each time, what is the speed of the man in still water?

divide(add(divide(18, 6), divide(30, 6)), const_2)

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

"30 - - - 6 ds = 5 ? - - - - 1 18 - - - - 6 us = 3 ? - - - - 1 m = ? m = ( 5 + 3 ) / 2 = 4 answer : e"

physics

math_qa__YLGCyoqQvp6lOMTg

If the sum of the 4th term and the 12th term of an arithmetic progression is 16, what is the sum of the first 15 terms of the progression? Choose the correct choice from the following answers: A) 80 B) 100 C) 105 D) 120 E) 110

<gadget id="calculator">15 / 2</gadget> <output>15/2 = around 7.5</output> <gadget id="calculator">(15/2) * 16</gadget> <output>120</output> <result>D</result>

D

If the sum of the 4th term and the 12th term of an arithmetic progression is 16, what is the sum of the first 15 terms of the progression?

multiply(divide(15, const_2), 16)

divide(n3,const_2)|multiply(n2,#0)|

"4 th term + 12 th term = 16 i . e . , ( a + 3 d ) + ( a + 11 d ) = 16 now , sum of first 15 terms = ( 15 / 2 ) * [ 2 a + ( 15 - 1 ) d ] = ( 15 / 2 ) * [ 2 a + 14 d ] = ( 15 / 2 ) * 16 - - - - - - - - - - - - - - - from ( 1 ) = 120 answer : d"

general

math_qa__kr1ymx6e9h20eaBI

The side of a square is increased by 25% then how much % does its area increases? Pick one: A) 56.28 B) 56.25 C) 56.2 D) 56.24 E) 56.21

<gadget id="calculator">100 + 25</gadget> <output>125</output> <gadget id="calculator">125 ** 2</gadget> <output>15_625</output> <gadget id="calculator">100 ** 2</gadget> <output>10_000</output> <gadget id="calculator">15_625 - 10_000</gadget> <output>5_625</output> <gadget id="calculator">5_625 * 100</gadget> <output>562_500</output> <gadget id="calculator">562_500 / 10_000</gadget> <output>225/4 = around 56.25</output> <result>B</result>

B

The side of a square is increased by 25% then how much % does its area increases?

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

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

"a = 100 a 2 = 10000 a = 125 a 2 = 15625 - - - - - - - - - - - - - - - - 10000 - - - - - - - - - 5625 100 - - - - - - - ? = > 56.25 % answer : b"

geometry

math_qa__pwrapGi4kfvR7KN8

If x = 1- 2t and y = 2t - 2, then for what value of t does x = y? Choose the correct choice: A) 5 / 2 B) 3 / 2 C) 3 / 4 D) 2 / 5 E) 0

<gadget id="calculator">1 + 2</gadget> <output>3</output> <gadget id="calculator">2 + 2</gadget> <output>4</output> <gadget id="calculator">3 / 4</gadget> <output>3/4 = around 0.75</output> <result>C</result>

C

If x = 1- 2t and y = 2t - 2, then for what value of t does x = y?

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

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

"we are given x = 1 – 2 t and y = 2 t – 2 , and we need to determine the value for t when x = y . we should notice that both x and y are already in terms of t . thus , we can substitute 1 – 2 t for x and 2 t – 2 for y in the equation x = y . this gives us : 1 – 2 t = 2 t – 2 3 = 4 t 3 / 4 = t the answer is c ."

general

math_qa__cki6dpELsi0CBIN7

Pipes A and B can fill a tank in 6 and 4 hours. Pipe C can empty it in 12 hours. If all pipes are opened together, then the tank will be filled in? Choose the correct choice from the following: A) 3 hr B) 2 hr C) 1 hr D) 9 / 7 hr E) 5 / 3 hr

<gadget id="calculator">1 / 6</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">1 / 4</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(1/6) + (1/4)</gadget> <output>5/12 = around 0.416667</output> <gadget id="calculator">1 / 12</gadget> <output>1/12 = around 0.083333</output> <gadget id="calculator">(5/12) - (1/12)</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">1 / (1/3)</gadget> <output>3</output> <result>A</result>

A

Pipes A and B can fill a tank in 6 and 4 hours. Pipe C can empty it in 12 hours. If all pipes are opened together, then the tank will be filled in?

inverse(subtract(add(divide(const_1, 6), divide(const_1, 4)), divide(const_1, 12)))

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

net part filled in 1 hour = 1 / 6 + 1 / 4 - 1 / 12 = 1 / 3 the tank will be full in 3 hr answer is a

physics

math_qa__Ui7IRe3t0StIWoh1

hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is: Choose the correct option A) 720 B) 900 C) 1200 D) 1800 E) 2100

<gadget id="calculator">15 * 12</gadget> <output>180</output> <gadget id="calculator">180 * 2</gadget> <output>360</output> <gadget id="calculator">15 + 12</gadget> <output>27</output> <gadget id="calculator">27 * 2</gadget> <output>54</output> <gadget id="calculator">360 / 54</gadget> <output>20/3 = around 6.666667</output> <gadget id="calculator">180 * (20/3)</gadget> <output>1_200</output> <result>C</result>

C

hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:

multiply(multiply(15, 12), divide(multiply(multiply(15, 12), const_2), multiply(add(15, 12), const_2)))

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

2 ( 15 + 12 ) x h = 2 ( 15 x 12 ) h = 180 / 27 m = 20 / 3 m . volume = 15 x 12 x 20 / 3 m 3 answer : option c

geometry

math_qa__RpGkgco8M2NFhv3V

A candidate got 35% of the votes polled and he lost to his rival by 2370 votes. How many votes were cast? Choose the most appropriate option: A) 7500 B) 7900 C) 2665 D) 2888 E) 2661

<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">2_370 / (3/10)</gadget> <output>7_900</output> <result>B</result>

B

A candidate got 35% of the votes polled and he lost to his rival by 2370 votes. How many votes were cast?

divide(2370, 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 % - - - - - - - - - - 2370 100 % - - - - - - - - - ? = > 7900 answer : b"

gain

math_qa__uYq2CgZk1nZ6Ktj2

A cistern 6 m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the west surface is : Choose the correct choice from the following: A) 49 m 2 B) 50 m 2 C) 53.5 m 2 D) 55 m 2 E) none of these

<gadget id="calculator">25 / 100</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(1/4) + 1</gadget> <output>5/4 = around 1.25</output> <gadget id="calculator">(5/4) * 4</gadget> <output>5</output> <gadget id="calculator">(5/4) * 6</gadget> <output>15/2 = around 7.5</output> <gadget id="calculator">5 + (15/2)</gadget> <output>25/2 = around 12.5</output> <gadget id="calculator">2 * (25/2)</gadget> <output>25</output> <gadget id="calculator">4 * 6</gadget> <output>24</output> <gadget id="calculator">25 + 24</gadget> <output>49</output> <result>A</result>

A

A cistern 6 m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the west surface is :

add(multiply(const_2, add(multiply(add(divide(25, const_100), 1), 4), multiply(add(divide(25, const_100), 1), 6))), multiply(4, 6))

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

"solution area of the west surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 × 1.25 + 6 × 1.25 ) + 6 × 4 ] m 2 = 49 m 2 . answer a"

physics

math_qa__vmc4JQC2jM8S7soe

ABCD is a square. F and E are the midpoints of sides AD and CD, respectively. The area of triangle FED is 2 square inches. What is the area of square ABCD (in square inches)? Select the correct option A) 4 B) 8 C) 16 D) 32 E) 64

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

C

ABCD is a square. F and E are the midpoints of sides AD and CD, respectively. The area of triangle FED is 2 square inches. What is the area of square ABCD (in square inches)?

multiply(multiply(2, const_2), const_4)

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

area of fed = 2 sq inches = 1 / 2 * de * fd = 1 / 2 * de ^ 2 because the sides of a square are equal , hence half of the sides will also be equal . de ^ 2 = 4 de = fd = 2 hence the side of the square = 4 area if the square = 4 * 4 = 16 correct option : c

geometry

math_qa__VK32UPHVcBReCNj8

What profit percent is made by selling an article at a certain price, if by selling at 3/4rd of that price, there would be a loss of 20%? Choices: A) 20 % B) 29 % C) 7 % D) 27 % E) 28 %

<gadget id="calculator">100 - 20</gadget> <output>80</output> <gadget id="calculator">3 / 4</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">80 / (3/4)</gadget> <output>320/3 = around 106.666667</output> <gadget id="calculator">(320/3) - 100</gadget> <output>20/3 = around 6.666667</output> <result>C</result>

C

What profit percent is made by selling an article at a certain price, if by selling at 3/4rd of that price, there would be a loss of 20%?

subtract(divide(subtract(const_100, 20), divide(3, 4)), const_100)

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

"sp 2 = 3 / 4 sp 1 cp = 100 sp 2 = 80 3 / 4 sp 1 = 80 sp 1 = 107 100 - - - 107 = > 7 % answer : c"

gain

math_qa__32DJIW5v0g5Jyc6X

A money lender lent Rs. 1000 at 3% per year and Rs. 1400 at 3% per year. The amount should be returned to him when the total interest comes to Rs. 350. Find the number of years. Choose the correct choice from the following answers: A) 3.5 B) 3.75 C) 4 D) 4.25 E) 4.86

<gadget id="calculator">3 * 1_000</gadget> <output>3_000</output> <gadget id="calculator">3_000 / 100</gadget> <output>30</output> <gadget id="calculator">1_400 * 3</gadget> <output>4_200</output> <gadget id="calculator">4_200 / 100</gadget> <output>42</output> <gadget id="calculator">30 + 42</gadget> <output>72</output> <gadget id="calculator">350 / 72</gadget> <output>175/36 = around 4.861111</output> <result>E</result>

E

A money lender lent Rs. 1000 at 3% per year and Rs. 1400 at 3% per year. The amount should be returned to him when the total interest comes to Rs. 350. Find the number of years.

divide(350, add(divide(multiply(3, 1000), const_100), divide(multiply(1400, 3), const_100)))

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

( 1000 xtx 3 / 100 ) + ( 1400 xtx 3 / 100 ) = 350 â † ’ t = 4.86 answer e

gain

math_qa__fPkXiPIL5qFpkmmh

By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent of solution B. If 400 grams of solution A are mixed with 700 grams of solution B, then liquid X accounts for what percent of the weight of the resulting solution? Choose the correct answer: A) 1.58 % B) 1.98 % C) 10 % D) 15 % E) 19 %

<gadget id="calculator">400 * 0.8</gadget> <output>320</output> <gadget id="calculator">700 * 1.8</gadget> <output>1_260</output> <gadget id="calculator">320 + 1_260</gadget> <output>1_580</output> <gadget id="calculator">1_580 / 1_000</gadget> <output>79/50 = around 1.58</output> <result>A</result>

A

By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent of solution B. If 400 grams of solution A are mixed with 700 grams of solution B, then liquid X accounts for what percent of the weight of the resulting solution?

divide(add(multiply(400, 0.8), multiply(700, 1.8)), const_1000)

multiply(n0,n2)|multiply(n1,n3)|add(#0,#1)|divide(#2,const_1000)|

"i think there is a typo in question . it should have been ` ` by weight liquid ' x ' makes up . . . . . ` ` weight of liquid x = 0.8 % of weight of a + 1.8 % of weight of b when 400 gms of a and 700 gms of b is mixed : weight of liquid x = ( 0.8 * 400 ) / 100 + ( 1.8 * 700 ) / 100 = 15.8 gms % of liquid x in resultant mixture = ( 15.8 / 1000 ) * 100 = 1.58 % a"

gain

math_qa__qS2nVHPjfnjzDWL7

If a - b = 3 and a(power 2) + b(power 2) = 21, find the value of ab. Choose the correct option A) 5 B) 8 C) 4 D) 6 E) 3

<gadget id="calculator">3 ** 2</gadget> <output>9</output> <gadget id="calculator">21 - 9</gadget> <output>12</output> <gadget id="calculator">12 / 2</gadget> <output>6</output> <result>D</result>

D

If a - b = 3 and a(power 2) + b(power 2) = 21, find the value of ab.

divide(subtract(21, power(3, 2)), 2)

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

"2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 21 - 9 = 12 ab = 6 . answer is d ."

general

math_qa__WS8Obs61JwQoYnKq

Out of 460 students of a school, 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket ? Choose the correct choice from the following answers: A) 120 B) 150 C) 100 D) 180 E) 90

<gadget id="calculator">175 + 325</gadget> <output>500</output> <gadget id="calculator">460 - 50</gadget> <output>410</output> <gadget id="calculator">500 - 410</gadget> <output>90</output> <result>E</result>

E

Out of 460 students of a school, 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket ?

subtract(add(175, 325), subtract(460, 50))

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

"n ( a ) = 325 , n ( b ) = 175 , n ( aub ) = 460 - 50 = 410 . required number = n ( anb ) = n ( a ) + n ( b ) - n ( aub ) = 325 + 175 - 410 = 90 . answer is e"

other

math_qa__IfPyIhDgGNZHr9Or

In a 8 x 8 chess board what is the total number of squares. Pick one: A) 238 B) 204 C) 678 D) 169 E) 161

<gadget id="calculator">8 + 1</gadget> <output>9</output> <gadget id="calculator">8 * 9</gadget> <output>72</output> <gadget id="calculator">8 * 2</gadget> <output>16</output> <gadget id="calculator">16 + 1</gadget> <output>17</output> <gadget id="calculator">72 * 17</gadget> <output>1_224</output> <gadget id="calculator">8 - 2</gadget> <output>6</output> <gadget id="calculator">1_224 / 6</gadget> <output>204</output> <result>B</result>

B

In a 8 x 8 chess board what is the total number of squares.

divide(multiply(multiply(8, add(8, const_1)), add(multiply(8, const_2), const_1)), subtract(8, const_2))

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

ans : the total number of squares in a n x n chess board is equal to ` ` the sum of first n natural number squares ' ' i . e . , n ( n + 1 ) ( 2 n + 1 ) 6 n ( n + 1 ) ( 2 n + 1 ) 6 so substituting 8 in the above formula we get 204 answer : b

general

math_qa__JgdNbAIR5NXSagU5

In a division, divident is 686, divisior is 36 and quotient is 19. Find the remainder. Choose the correct choice from the following answers: A) 4 B) 3 C) 2 D) 5 E) 6

<gadget id="calculator">686 % 36</gadget> <output>2</output> <result>C</result>

C

In a division, divident is 686, divisior is 36 and quotient is 19. Find the remainder.

reminder(686, 36)

reminder(n0,n1)|

"explanation : 686 = 36 x 19 + r 686 = 684 + r r = 686 - 684 = 2 answer : option c"

general

math_qa__c9Sxvly2GcpRbYfc

A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is : Choose the correct choice from the following answers A) 1 / 4 B) 1 / 10 C) 7 / 15 D) 8 / 15 E) 9 / 15

<gadget id="calculator">1 / 15</gadget> <output>1/15 = around 0.066667</output> <gadget id="calculator">1 / 20</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">(1/15) + (1/20)</gadget> <output>7/60 = around 0.116667</output> <gadget id="calculator">(7/60) * 4</gadget> <output>7/15 = around 0.466667</output> <gadget id="calculator">1 - (7/15)</gadget> <output>8/15 = around 0.533333</output> <result>D</result>

D

A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :

subtract(const_1, multiply(add(divide(const_1, 15), divide(const_1, 20)), 4))

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

"explanation : a ' s 1 day ' s work = 1 / 15 b ' s 1 day ' s work = 1 / 20 ( a + b ) ' s 1 day ' s work = ( 1 / 15 + 1 / 20 ) = 7 / 60 ( a + b ) ' s 4 day ' s work = 7 / 60 x 4 = 7 / 15 therefore , remaining work = 1 - 7 / 15 = 8 / 15 answer is d"

physics

math_qa__1UhvdKu9zKYainWi

Rakesh credits 15% of his salary in his fixed deposit account and spends 30% of the remaining amount on groceries. If the cash in hand is Rs.2380, what is his salary? Answers. A) rs . 3500 B) rs . 4000 C) rs . 4500 D) rs . 5000 E) none

<gadget id="calculator">100 - 15</gadget> <output>85</output> <gadget id="calculator">85 / 100</gadget> <output>17/20 = around 0.85</output> <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">(17/20) * (7/10)</gadget> <output>119/200 = around 0.595</output> <gadget id="calculator">2_380 / (119/200)</gadget> <output>4_000</output> <result>B</result>

B

Rakesh credits 15% of his salary in his fixed deposit account and spends 30% of the remaining amount on groceries. If the cash in hand is Rs.2380, what is his salary?

divide(2380, multiply(divide(subtract(const_100, 15), const_100), divide(subtract(const_100, 30), const_100)))

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

explanation : let salary be rs . x . then , x - 15 % of x - 30 % of 85 % of x = 2380 or x - 15 x / 100 − 30 × 85 × x / 100 × 100 = 2380 or 200 x - 30 x - 51 x = 2380 × 2002380 × 200 or 119 x = 2380 × 2002380 × 200 or x 2380 × 200 / 119 = 4000 correct option : b

gain

math_qa__XpoBHhHmJ7tGFi33

If a light flashes every 6 seconds, how many times will it flash in ¾ of an hour? Options: A) 451 times B) 638 times C) 838 times D) 436 times E) 435 times

<gadget id="calculator">3_600 / 4</gadget> <output>900</output> <gadget id="calculator">900 * 3</gadget> <output>2_700</output> <gadget id="calculator">2_700 / 6</gadget> <output>450</output> <result>A</result>

A

If a light flashes every 6 seconds, how many times will it flash in ¾ of an hour?

divide(multiply(divide(const_3600, const_4), const_3), 6)

divide(const_3600,const_4)|multiply(#0,const_3)|divide(#1,n0)

there are 60 minutes in an hour . in ¾ of an hour there are ( 60 * ¾ ) minutes = 45 minutes . in ¾ of an hour there are ( 60 * 45 ) seconds = 2700 seconds . light flashed for every 6 seconds . in 2700 seconds 2700 / 6 = 450 times . the count start after the first flash , the light will flashes 451 times in ¾ of an hour . answer : a

physics

math_qa__1UiW2MAg1HCZuB58

By selling an article at Rs.400, a profit of 60% is made. Find its cost price? Select the correct option: A) 228 B) 267 C) 287 D) 250 E) 811

<gadget id="calculator">400 * 100</gadget> <output>40_000</output> <gadget id="calculator">100 + 60</gadget> <output>160</output> <gadget id="calculator">40_000 / 160</gadget> <output>250</output> <result>D</result>

D

By selling an article at Rs.400, a profit of 60% is made. Find its cost price?

divide(multiply(400, const_100), add(const_100, 60))

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

"sp = 400 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 400 * [ 100 / ( 100 + 60 ) ] = 400 * [ 100 / 160 ] = rs . 250 answer : d"

gain

math_qa__vBVvGQCHuUe5e4AH

While working alone at their constant rates, computer X can process 240 files in 12 hours, and computer Y can process 240 files in 3 hours. If all files processed by these computers are the same size, how many hours would it take the two computers, working at the same time at their respective constant rates, to process a total of 240 files? Choose the correct choice from the following choices. A) 1.6 B) 1.8 C) 2 D) 2.2 E) 2.4

<gadget id="calculator">240 / 12</gadget> <output>20</output> <gadget id="calculator">240 / 3</gadget> <output>80</output> <gadget id="calculator">20 + 80</gadget> <output>100</output> <gadget id="calculator">240 / 100</gadget> <output>12/5 = around 2.4</output> <result>E</result>

E

While working alone at their constant rates, computer X can process 240 files in 12 hours, and computer Y can process 240 files in 3 hours. If all files processed by these computers are the same size, how many hours would it take the two computers, working at the same time at their respective constant rates, to process a total of 240 files?

divide(240, add(divide(240, 12), divide(240, 3)))

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

"both computers together process files at a rate of 240 / 12 + 240 / 3 = 20 + 80 = 100 files per hour . the time required to process 240 files is 240 / 100 = 2.4 hours the answer is e ."

physics

math_qa__qYnjE1bKKNKz1NQm

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

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

D

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

divide(divide(300, 5), 3)

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

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

physics

math_qa__oHneS0C7eSbIjqY3

The average marks of a class of 24 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students? Choose the correct choice from the following choices: A) 52.2 B) 59.5 C) 52.8 D) 53.5 E) 52.1

<gadget id="calculator">24 * 40</gadget> <output>960</output> <gadget id="calculator">50 * 60</gadget> <output>3_000</output> <gadget id="calculator">960 + 3_000</gadget> <output>3_960</output> <gadget id="calculator">24 + 50</gadget> <output>74</output> <gadget id="calculator">3_960 / 74</gadget> <output>1_980/37 = around 53.513514</output> <result>D</result>

D

The average marks of a class of 24 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?

divide(add(multiply(24, 40), multiply(50, 60)), add(24, 50))

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

"sum of the marks for the class of 24 students = 24 * 40 = 960 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 74 students = 960 + 3000 = 3960 average marks of all the students = 3960 / 74 = 53.5 answer : d"

general

math_qa__7MmYyT8a1TszCCVB

Each month a retailer sells 100 identical items. On each item he makes a profit of $30 that constitutes 10% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount? Choose the correct choice from the following answers: A) 191 B) 213 C) 221 D) 223 E) 226

<gadget id="calculator">100 * 30</gadget> <output>3_000</output> <gadget id="calculator">3_000 / 10</gadget> <output>300</output> <gadget id="calculator">300 + 30</gadget> <output>330</output> <gadget id="calculator">330 * 5</gadget> <output>1_650</output> <gadget id="calculator">1_650 / 100</gadget> <output>33/2 = around 16.5</output> <gadget id="calculator">30 - (33/2)</gadget> <output>27/2 = around 13.5</output> <gadget id="calculator">3_000 / (27/2)</gadget> <output>2_000/9 = around 222.222222</output> <result>D</result>

D

Each month a retailer sells 100 identical items. On each item he makes a profit of $30 that constitutes 10% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount?

divide(multiply(100, 30), subtract(30, divide(multiply(add(divide(multiply(100, 30), 10), 30), 5), 100)))

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

"for this question , we ' ll need the following formula : sell price = cost + profit we ' re told that the profit on 1 item is $ 20 and that this represents 10 % of the cost : sell price = cost + $ 30 sell price = $ 300 + $ 30 thus , the sell price is $ 330 for each item . selling all 100 items gives the retailer . . . 100 ( $ 30 ) = $ 2,000 of profit if the retailer offers a 5 % discount on the sell price , then the equation changes . . . 5 % ( 330 ) = $ 16.5 discount $ 313.5 = $ 300 + $ 13.5 now , the retailer makes a profit of just $ 13.5 per item sold . to earn $ 2,000 in profit , the retailer must sell . . . . $ 13.5 ( x ) = $ 2,000 x = 2,000 / 13.5 x = 222.222222 items you ' ll notice that this is not among the answer choices . . . . 221 and 223 are . selling 221 items would get us 9 ( 221 ) = $ 1989 which is not enough money . to get back to at least $ 2,000 , we need to sell 223 items . final answer : d"

gain

math_qa__CdsAvxquVusrb1G5

If X gets 25% more than Y and Y gets 20% more than Z, the share of Z out of Rs. 555 will be: Choose the correct choice from the following answers: A) rs . 300 B) rs . 200 C) rs . 240 D) rs . 150 E) none of these

<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">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">(5/4) * (6/5)</gadget> <output>3/2 = around 1.5</output> <gadget id="calculator">(3/2) + (6/5)</gadget> <output>27/10 = around 2.7</output> <gadget id="calculator">(27/10) + 1</gadget> <output>37/10 = around 3.7</output> <gadget id="calculator">555 / (37/10)</gadget> <output>150</output> <result>D</result>

D

If X gets 25% more than Y and Y gets 20% more than Z, the share of Z out of Rs. 555 will be:

divide(555, add(add(multiply(add(const_1, divide(25, const_100)), add(const_1, divide(20, const_100))), add(const_1, divide(20, const_100))), const_1))

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

"z share = z , y = 1.2 z x = 1.25 ã — 1.2 z , x + y + z = 555 ( 1.25 ã — 1.2 + 1.2 + 1 ) z = 55 3.7 z = 555 , z = 150 answer : . d"

general

math_qa__FUiyeEglx1ky1YAv

The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 972 sq m, then what is the breadth of the rectangular plot? Choose the correct option: A) 16 B) 17 C) 18 D) 19 E) 14

<gadget id="calculator">972 / 3</gadget> <output>324</output> <gadget id="calculator">324 ** (1/2)</gadget> <output>18</output> <result>C</result>

C

The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 972 sq m, then what is the breadth of the rectangular plot?

sqrt(divide(972, const_3))

divide(n0,const_3)|sqrt(#0)|

"let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 972 3 b 2 = 972 b 2 = 324 b = 18 m . answer : option c"

geometry

math_qa__ugWkIAMzsXviIZre

If the radius of a circle is increased by 12%, then the area of the circle Pick: A) decreases by 25.44 % B) increases by 25.44 % C) no change in area D) decreases by 12 % E) none

<gadget id="calculator">12 / 100</gadget> <output>3/25 = around 0.12</output> <gadget id="calculator">(3/25) + 1</gadget> <output>28/25 = around 1.12</output> <gadget id="calculator">(28/25) ** 2</gadget> <output>784/625 = around 1.2544</output> <gadget id="calculator">(784/625) - 1</gadget> <output>159/625 = around 0.2544</output> <gadget id="calculator">(159/625) * 100</gadget> <output>636/25 = around 25.44</output> <result>B</result>

B

If the radius of a circle is increased by 12%, then the area of the circle

multiply(subtract(power(add(divide(12, const_100), const_1), const_2), const_1), const_100)

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

a 1 = pi ( 100 ) ^ 2 a 2 = pi ( 112 ) ^ 2 so ( a 2 - a 1 ) / a 1 * 100 = 25.44 answer : b

geometry

math_qa__WTJrC7BF1falOb7j

A grocer has a sale of Rs. 2500, Rs. 6500, Rs. 9855, Rs. 7230 and Rs. 7000 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 7500? Choose the correct choice: A) s . 49180 B) s . 49910 C) s . 11915 D) s 6997 E) s . 5000

<gadget id="calculator">5 + 1</gadget> <output>6</output> <gadget id="calculator">6 * 7_500</gadget> <output>45_000</output> <gadget id="calculator">2_500 + 6_500</gadget> <output>9_000</output> <gadget id="calculator">9_000 + 9_855</gadget> <output>18_855</output> <gadget id="calculator">18_855 + 7_230</gadget> <output>26_085</output> <gadget id="calculator">26_085 + 7_000</gadget> <output>33_085</output> <gadget id="calculator">45_000 - 33_085</gadget> <output>11_915</output> <result>C</result>

C

A grocer has a sale of Rs. 2500, Rs. 6500, Rs. 9855, Rs. 7230 and Rs. 7000 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 7500?

subtract(multiply(add(5, const_1), 7500), add(add(add(add(2500, 6500), 9855), 7230), 7000))

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

total sale for 5 months = rs . ( 2500 + 6500 + 9855 + 7230 + 7000 ) = rs . 33085 . required sale = rs . [ ( 7500 x 6 ) - 33085 ] = rs . ( 45000 - 33085 ) = rs . 11915 . c

general

math_qa__tYtItDGgw2rB9ZH6

A cyclist bikes x distance at 20 miles per hour and returns over the same path at 16 miles per hour. What is the cyclist's average rate for the round trip in miles per hour? Choose the correct choice from the following: A) 17.6 B) 17.3 C) 8.6 D) 17.2 E) 9.0

<gadget id="calculator">20 + 16</gadget> <output>36</output> <gadget id="calculator">36 / 2</gadget> <output>18</output> <result>A</result>

A

A cyclist bikes x distance at 20 miles per hour and returns over the same path at 16 miles per hour. What is the cyclist's average rate for the round trip in miles per hour?

divide(add(20, 16), const_2)

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

"distance = d 1 = x miles speed = s 1 = 20 miles per hour time = t 1 = distance / speed = x / 20 2 . going from b to a distance = d 2 = x miles speed = s 2 = 16 miles per hour time = t 2 = distance / speed = x / 16 3 . average speed = total distance / total time total distance = x + x = 2 x total time = x / 20 + x / 16 = 9 x / 80 speed = 2 x / ( 9 x / 80 ) = 160 / 9 = 17.6 answer : a"

physics

math_qa__7wzO00izHoP6wGtx

If a is an integer greater than 6 but less than 17 and b is an integer greater than 3 but less than 29, what is the range of a/b? Choose the correct option: A) 15 / 4 B) 13 / 2 C) 9 / 7 D) 1 / 5 E) 7 / 6

<gadget id="calculator">17 - 1</gadget> <output>16</output> <gadget id="calculator">3 + 1</gadget> <output>4</output> <gadget id="calculator">16 / 4</gadget> <output>4</output> <gadget id="calculator">6 + 1</gadget> <output>7</output> <gadget id="calculator">29 - 1</gadget> <output>28</output> <gadget id="calculator">7 / 28</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">4 - (1/4)</gadget> <output>15/4 = around 3.75</output> <result>A</result>

A

If a is an integer greater than 6 but less than 17 and b is an integer greater than 3 but less than 29, what is the range of a/b?

subtract(divide(subtract(17, const_1), add(3, const_1)), divide(add(6, const_1), subtract(29, const_1)))

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

"the way to approach this problem is 6 < a < 17 and 3 < b < 29 minimum possible value of a is 7 and maximum is 16 minimum possible value of b is 4 and maximum is 28 range = max a / min b - min a / max b ( highest - lowest ) 16 / 4 - 7 / 28 = 15 / 4 hence a"

general

math_qa__B63I0QukBFlosesa

Increasing the original price of a certain item by 25 percent and then increasing the new price by 25 percent is equivalent to increasing the original price by what percent? Choose the correct choice: A) 31.25 B) 37.5 C) 50.0 D) 52.5 E) 56.25

<gadget id="calculator">25 / 100</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(1/4) + 1</gadget> <output>5/4 = around 1.25</output> <gadget id="calculator">(5/4) * (5/4)</gadget> <output>25/16 = around 1.5625</output> <gadget id="calculator">(25/16) - 1</gadget> <output>9/16 = around 0.5625</output> <gadget id="calculator">(9/16) * 100</gadget> <output>225/4 = around 56.25</output> <result>E</result>

E

Increasing the original price of a certain item by 25 percent and then increasing the new price by 25 percent is equivalent to increasing the original price by what percent?

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

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

"soln : - x * 1.25 * 1.25 = 1.5625 x so there is a net increase of 56.25 % . answer e ."

gain

math_qa__hRbJ12ezypbutt82

Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 61900. What is his profit percent? Pick: A) 22 B) 77 C) 18 D) 99 E) 12.5

<gadget id="calculator">42_000 + 13_000</gadget> <output>55_000</output> <gadget id="calculator">61_900 - 55_000</gadget> <output>6_900</output> <gadget id="calculator">6_900 / 55_000</gadget> <output>69/550 = around 0.125455</output> <gadget id="calculator">(69/550) * 100</gadget> <output>138/11 = around 12.545455</output> <result>E</result>

E

Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 61900. What is his profit percent?

multiply(divide(subtract(61900, add(42000, 13000)), add(42000, 13000)), const_100)

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

"total cp = rs . 42000 + rs . 13000 = rs . 55000 and sp = rs . 61900 profit ( % ) = ( 61900 - 55000 ) / 55000 * 100 = 12.5 % answer : e"

gain

math_qa__rtp1mZGdoV1BiQjZ

Increasing the original price of an article by 5 percent and then increasing the new price by 5 percent is equivalent to increasing the original price by Select the correct option: A) 10.25 % B) 12.5 % C) 14.75 % D) 15.15 % E) 16.25 %

<gadget id="calculator">5 / 100</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">1 + (1/20)</gadget> <output>21/20 = around 1.05</output> <gadget id="calculator">(21/20) * (21/20)</gadget> <output>441/400 = around 1.1025</output> <gadget id="calculator">(441/400) - 1</gadget> <output>41/400 = around 0.1025</output> <gadget id="calculator">100 * (41/400)</gadget> <output>41/4 = around 10.25</output> <result>A</result>

A

Increasing the original price of an article by 5 percent and then increasing the new price by 5 percent is equivalent to increasing the original price by

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

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

"1.05 * 1.05 * x = 1.1025 * x the answer is a ."

gain

math_qa__i1VuMWZ0f6OYI8J9

there are 1200 jelly beans divided between two jars , jar x and jar y . if there are 400 fewer jelly beans in jar x than 3 times the number of beans in jar y , how many beans are in jar x ? Choices: A) 650 B) 700 C) 750 D) 800 E) 850

<gadget id="calculator">1_200 + 400</gadget> <output>1_600</output> <gadget id="calculator">1_600 / 4</gadget> <output>400</output> <gadget id="calculator">1_200 - 400</gadget> <output>800</output> <result>D</result>

D

there are 1200 jelly beans divided between two jars , jar x and jar y . if there are 400 fewer jelly beans in jar x than 3 times the number of beans in jar y , how many beans are in jar x ?

subtract(1200, divide(add(1200, 400), const_4))

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

x + y = 1200 so y = 1200 - x x = 3 y - 400 x = 3 ( 1200 - x ) - 400 4 x = 3200 x = 800 the answer is d .

general

math_qa__P4e6qbK4BeVsOTLT

If x is 20 percent more than y and y is 70 percent less than z, then x is what percent of z? Pick one: A) 500 % B) 250 % C) 500 / 3 % D) 36 % E) 60 %

<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">100 - 70</gadget> <output>30</output> <gadget id="calculator">(6/5) * 30</gadget> <output>36</output> <result>D</result>

D

If x is 20 percent more than y and y is 70 percent less than z, then x is what percent of z?

multiply(add(const_1, divide(20, const_100)), subtract(const_100, 70))

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

z = 100 ; y = 30 so x = 36 x as % of z = 36 / 100 * 100 = > 36 % answer will be ( d )

general

math_qa__9oTo2d7f1SQ3DnZy

How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language? Pick one. A) 321 B) 65 C) 120 D) 100 E) 80

<gadget id="calculator">1 * 1_000</gadget> <output>1_000</output> <gadget id="calculator">1_000 * 1_000</gadget> <output>1_000_000</output> <gadget id="calculator">10 * 1_000</gadget> <output>10_000</output> <gadget id="calculator">1_000_000 / 10_000</gadget> <output>100</output> <result>D</result>

D

How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?

divide(multiply(multiply(1, const_1000), const_1000), multiply(const_10, const_1000))

multiply(n0,const_1000)|multiply(const_10,const_1000)|multiply(#0,const_1000)|divide(#2,#1)

1 million distinct 3 digit initials are needed . let the number of required alphabets in the language be ‘ n ’ . therefore , using ‘ n ’ alphabets we can form n * n * n = n 3 distinct 3 digit initials . note distinct initials is different from initials where the digits are different . for instance , aaa and bbb are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different . this n 3 different initials = 1 million i . e . n 3 = 106 ( 1 million = 106 ) = > n 3 = ( 102 ) 3 = > n = 102 = 100 hence , the language needs to have a minimum of 100 alphabets to achieve the objective . ans : d

general

math_qa__2cDzmyxcaNXlwLxh

Bruce purchased 8kg of grapes at the rate of 70 per kg and 11 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper? Choose the correct choice from the following options A) 1040 B) 1165 C) 1055 D) 1065 E) 1075

<gadget id="calculator">8 * 70</gadget> <output>560</output> <gadget id="calculator">11 * 55</gadget> <output>605</output> <gadget id="calculator">560 + 605</gadget> <output>1_165</output> <result>B</result>

B

Bruce purchased 8kg of grapes at the rate of 70 per kg and 11 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?

add(multiply(8, 70), multiply(11, 55))

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

"cost of 8 kg grapes = 70 × 8 = 560 . cost of 11 kg of mangoes = 55 × 11 = 605 . total cost he has to pay = 560 + 605 = 1165 b"

gain

math_qa__AN6xXnsNY3M6kexe

A 56 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? Choose the correct option: A) 8 B) 12 C) 13 D) 14 E) 16

<gadget id="calculator">10 - 8</gadget> <output>2</output> <gadget id="calculator">56 * 2</gadget> <output>112</output> <gadget id="calculator">112 / 8</gadget> <output>14</output> <result>D</result>

D

A 56 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(56, subtract(10, 8)), 8)

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

"amount of salt = 5.6 assume x gallons of water are added . 5.6 / 56 + x = 8 / 100 560 = 8 x + 448 8 x = 112 x = 14 correct option : d"

general

math_qa__sjWDCCZigteiQEkC

A, B and C invest in the ratio of 3 : 4: 5. The percentage of return on their investments are in the ratio of 6 : 5 : 4. Find the total earnings, If B earns Rs. 120 more than A : Choose one. A) 2348 B) 3480 C) 2767 D) 1998 E) 2771

<gadget id="calculator">3 * 6</gadget> <output>18</output> <gadget id="calculator">4 * 5</gadget> <output>20</output> <gadget id="calculator">18 + 20</gadget> <output>38</output> <gadget id="calculator">5 * 4</gadget> <output>20</output> <gadget id="calculator">38 + 20</gadget> <output>58</output> <gadget id="calculator">20 - 18</gadget> <output>2</output> <gadget id="calculator">120 / 2</gadget> <output>60</output> <gadget id="calculator">58 * 60</gadget> <output>3_480</output> <result>B</result>

B

A, B and C invest in the ratio of 3 : 4: 5. The percentage of return on their investments are in the ratio of 6 : 5 : 4. Find the total earnings, If B earns Rs. 120 more than A :

multiply(add(add(multiply(3, 6), multiply(4, 5)), multiply(5, 4)), divide(120, subtract(multiply(4, 5), multiply(3, 6))))

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

"explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \ inline \ frac { 18 xy } { 100 } \ inline \ frac { 20 xy } { 100 } \ inline \ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \ inline \ frac { 58 xy } { 100 } b ' s earnings - a ' s earnings = \ inline \ frac { 2 xy } { 100 } = 120 total earning = \ inline \ frac { 58 xy } { 100 } = 3480 answer : b ) rs . 3480"

general

math_qa__kSmNMuG1QeipXraF

Two numbers have a H.C.F of 16 and a product of two numbers is 2560. Find the L.C.M of the two numbers? Choose the correct choice from the following options. A) 140 B) 150 C) 160 D) 170 E) 180

<gadget id="calculator">2_560 / 16</gadget> <output>160</output> <result>C</result>

C

Two numbers have a H.C.F of 16 and a product of two numbers is 2560. Find the L.C.M of the two numbers?

divide(2560, 16)

divide(n1,n0)|

"l . c . m of two numbers is given by ( product of the two numbers ) / ( h . c . f of the two numbers ) = 2560 / 16 = 160 . answer : c"

physics

math_qa__m6CXaWnbHcRiCChv

In an examination, there were 2,000 candidates, out of which 900 candidates were girls and rest were Boys. If 38% of the boys and 32% of the girls passed, then the total percentage of failed candidates is? Choose the correct choice from the following answers: A) 35.67 % B) 64.75 % C) 68.57 % D) 69.57 % E) none of these

<gadget id="calculator">100 * 10</gadget> <output>1_000</output> <gadget id="calculator">2 * 1_000</gadget> <output>2_000</output> <gadget id="calculator">38 / 100</gadget> <output>19/50 = around 0.38</output> <gadget id="calculator">2_000 - 900</gadget> <output>1_100</output> <gadget id="calculator">(19/50) * 1_100</gadget> <output>418</output> <gadget id="calculator">2_000 - 418</gadget> <output>1_582</output> <gadget id="calculator">32 / 100</gadget> <output>8/25 = around 0.32</output> <gadget id="calculator">(8/25) * 900</gadget> <output>288</output> <gadget id="calculator">1_582 - 288</gadget> <output>1_294</output> <gadget id="calculator">1_294 / 2_000</gadget> <output>647/1_000 = around 0.647</output> <gadget id="calculator">(647/1_000) * 100</gadget> <output>647/10 = around 64.7</output> <result>B</result>

B

In an examination, there were 2,000 candidates, out of which 900 candidates were girls and rest were Boys. If 38% of the boys and 32% of the girls passed, then the total percentage of failed candidates is?

multiply(divide(subtract(subtract(multiply(const_2, multiply(const_100, const_10)), multiply(divide(38, const_100), subtract(multiply(const_2, multiply(const_100, const_10)), 900))), multiply(divide(32, const_100), 900)), multiply(const_2, multiply(const_100, const_10))), const_100)

divide(n2,const_100)|divide(n3,const_100)|multiply(const_10,const_100)|multiply(#2,const_2)|multiply(n1,#1)|subtract(#3,n1)|multiply(#0,#5)|subtract(#3,#6)|subtract(#7,#4)|divide(#8,#3)|multiply(#9,const_100)|

"girls = 900 , boys = 1100 passed = ( 38 % of 1100 ) + ( 32 % of 900 ) = 418 + 288 = 706 failed = 2000 - 706 = 1294 failed % = [ ( 1294 / 2000 ) x 100 ] % = 64.7 % . answer : b"

general

math_qa__7TmAUWlJin8mobl9

An article is bought for Rs.600 and sold for Rs.450, find the loss percent? Options. A) 16 % B) 18 % C) 19 % D) 20 % E) 25 %

<gadget id="calculator">450 * 100</gadget> <output>45_000</output> <gadget id="calculator">45_000 / 600</gadget> <output>75</output> <gadget id="calculator">100 - 75</gadget> <output>25</output> <result>E</result>

E

An article is bought for Rs.600 and sold for Rs.450, find the loss percent?

subtract(const_100, divide(multiply(450, const_100), 600))

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

"600 - - - - 150 100 - - - - ? = > 16 2 / 3 % answer : e"

gain

math_qa__CHbOMXdmcRGhvMda

A man rows his boat 60 km downstream and 30 km upstream taking 3 hrs each time. Find the speed of the stream ? Choose the correct option A) 5 kmph B) 6 kmph C) 8 kmph D) 1 kmph E) 2 kmph

<gadget id="calculator">60 / 3</gadget> <output>20</output> <gadget id="calculator">30 / 3</gadget> <output>10</output> <gadget id="calculator">20 - 10</gadget> <output>10</output> <gadget id="calculator">10 / 2</gadget> <output>5</output> <result>A</result>

A

A man rows his boat 60 km downstream and 30 km upstream taking 3 hrs each time. Find the speed of the stream ?

divide(subtract(divide(60, 3), divide(30, 3)), const_2)

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

explanation : speed of the boat downstream = speed of the boat upstream \ small \ therefore the speed of the stream = answer : a

physics

math_qa__Rr1ljqSKMkYGga5C

The ratio of the amount of the oil bill for the month of February to the amount of the oil bill for the month of January was 3:2. If the oil bill for February had been $10 more, the corresponding ratio would have been 5:3. How much was the oil bill for January? Choose the correct choice from the following choices: A) $ 60 B) $ 80 C) $ 100 D) $ 120 E) $ 140

<gadget id="calculator">5 / 3</gadget> <output>5/3 = around 1.666667</output> <gadget id="calculator">3 / 2</gadget> <output>3/2 = around 1.5</output> <gadget id="calculator">(5/3) - (3/2)</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">10 / (1/6)</gadget> <output>60</output> <result>A</result>

A

The ratio of the amount of the oil bill for the month of February to the amount of the oil bill for the month of January was 3:2. If the oil bill for February had been $10 more, the corresponding ratio would have been 5:3. How much was the oil bill for January?

divide(10, subtract(divide(5, 3), divide(3, 2)))

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

"3 : 2 = 9 : 6 and 5 : 3 = 10 : 6 . an increase in $ 10 increases the ratio by 1 : 6 . therefore , january ' s bill was 6 ( $ 10 ) = $ 60 . the answer is a ."

general

math_qa__nWsoXSB11UjYMOIw

What is the average (arithmetic mean) of all multiples of 10 from 10 to 600 inclusive? Pick one: A) 190 B) 195 C) 305 D) 205 E) 210

<gadget id="calculator">10 + 600</gadget> <output>610</output> <gadget id="calculator">600 - 10</gadget> <output>590</output> <gadget id="calculator">590 / 10</gadget> <output>59</output> <gadget id="calculator">59 + 1</gadget> <output>60</output> <gadget id="calculator">610 * 60</gadget> <output>36_600</output> <gadget id="calculator">36_600 / 2</gadget> <output>18_300</output> <gadget id="calculator">18_300 / 60</gadget> <output>305</output> <result>C</result>

C

What is the average (arithmetic mean) of all multiples of 10 from 10 to 600 inclusive?

divide(divide(multiply(add(10, 600), add(divide(subtract(600, 10), 10), const_1)), const_2), add(divide(subtract(600, 10), 10), const_1))

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

"this question can be solved with the average formula and ' bunching . ' we ' re asked for the average of all of the multiples of 10 from 10 to 600 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 60 ( 10 ) = 600 so we know that there are 60 total numbers . we can now figure out the sum of those numbers with ' bunching ' : 10 + 600 = 610 20 + 590 = 610 30 + 580 = 610 etc . since there are 60 total terms , this pattern will create 30 ' pairs ' of 610 . thus , since the average = ( sum of terms ) / ( number of terms ) , we have . . . ( 30 ) ( 610 ) / ( 60 ) = 305 final answer : c"

general

math_qa__lLHVaGH5mt9U7Lc4

A $74.95 lawn chair was sold for $59.95 at a special sale. By approximately what percent was the price decreased? Choose the most appropriate option. A) 15 % B) 20 % C) 25 % D) 60 % E) 80 %

<gadget id="calculator">74.95 - 59.95</gadget> <output>15</output> <gadget id="calculator">15 / 74.95</gadget> <output>0.200133</output> <gadget id="calculator">0.200133 * 100</gadget> <output>20.0133</output> <result>B</result>

B

A $74.95 lawn chair was sold for $59.95 at a special sale. By approximately what percent was the price decreased?

multiply(divide(subtract(74.95, 59.95), 74.95), const_100)

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

"listed selling price of chair = 74.95 $ discounted selling price of chair = 59.95 $ discount = 74.95 - 59.95 = 15 $ % decrease in price of chair = ( 15 / 74.95 ) * 100 % = 20 % approx answer b"

general

math_qa__oHBNuCDPLB2puukT

If Rs. 595 be divided among A, B, C in such a way that A gets 2/3 of what B gets and B gets 1/4 of what C gets, then their shares are respectively? Choose the correct option: A) s . 420 B) s . 360 C) s . 389 D) s . 368 E) s . 323

<gadget id="calculator">2 / 3</gadget> <output>2/3 = around 0.666667</output> <gadget id="calculator">1 / 4</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(2/3) * (1/4)</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">(1/6) + (1/4)</gadget> <output>5/12 = around 0.416667</output> <gadget id="calculator">(5/12) + 1</gadget> <output>17/12 = around 1.416667</output> <gadget id="calculator">595 / (17/12)</gadget> <output>420</output> <result>A</result>

A

If Rs. 595 be divided among A, B, C in such a way that A gets 2/3 of what B gets and B gets 1/4 of what C gets, then their shares are respectively?

divide(595, add(add(multiply(divide(2, 3), divide(1, 4)), divide(1, 4)), 1))

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

"( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 595 * 2 / 17 = rs . 70 b ' s share = 595 * 3 / 17 = rs . 105 c ' s share = 595 * 12 / 17 = rs . 420 . answer : a"

general

math_qa__jQhBKGpIm2Dn1sH2

A part-time employee’s hourly wage was increased by 50%. She decided to decrease the number of hours worked per week so that her total income did not change. By approximately what percent should the number of hours worked be decreased? Choose the correct choice from the following options. A) 9 % B) 15 % C) 25 % D) 33 % E) 50 %

<gadget id="calculator">50 / 100</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">50 + 100</gadget> <output>150</output> <gadget id="calculator">150 / 100</gadget> <output>3/2 = around 1.5</output> <gadget id="calculator">(1/2) / (3/2)</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">(1/3) * 100</gadget> <output>100/3 = around 33.333333</output> <result>D</result>

D

A part-time employee’s hourly wage was increased by 50%. She decided to decrease the number of hours worked per week so that her total income did not change. By approximately what percent should the number of hours worked be decreased?

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

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

let ' s plug in somenicenumbers and see what ' s needed . let ' s say the employee used to make $ 1 / hour and worked 100 hours / week so , the total weekly income was $ 100 / week after the 50 % wage increase , the employee makes $ 1.50 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.50 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.50 to get : new # of hours = 100 / 1.50 ≈ 67 hours so , the number of hours decreases from 100 hours to ( approximately ) 67 hours . this represents a 33 % decrease ( approximately ) . answer : d

general

math_qa__x3YXPXwSnbSafwVB

Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 3% sugar by weight. To make a delicious and healthy mixture that is 5% sugar, what should be the ratio of Cereal A to Cereal B, by weight? Pick one: A) 2 : 5 B) 2 : 7 C) 1 : 6 D) 1 : 4 E) 1 : 3

<gadget id="calculator">5 - 3</gadget> <output>2</output> <gadget id="calculator">10 - 5</gadget> <output>5</output> <gadget id="calculator">2 / 5</gadget> <output>2/5 = around 0.4</output> <result>A</result>

A

Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 3% sugar by weight. To make a delicious and healthy mixture that is 5% sugar, what should be the ratio of Cereal A to Cereal B, by weight?

divide(subtract(5, 3), subtract(10, 5))

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

"ratio of a / ratio of b = ( average wt of mixture - wt of b ) / ( wt of a - average wt of mixture ) = > ratio of a / ratio of b = ( 5 - 3 ) / ( 10 - 5 ) = 2 / 5 so they should be mixed in the ratio 2 : 5 answer - a"

general

math_qa__S12obfr8Ps8mjscE

The Q train leaves station A moving at a constant speed, and passes by stations B and C, in this order. It takes the Q train 7 hours to reach station B, and 5 additional hours to reach station C. The distance between stations A and B is m kilometers longer than the distance between stations B and C. What is the distance between stations A and C in terms of m? Choose the correct answer. A) 1.8 m B) 6 m C) 7 m D) 9 m E) 12 m

<gadget id="calculator">5 / 7</gadget> <output>5/7 = around 0.714286</output> <gadget id="calculator">1 - (5/7)</gadget> <output>2/7 = around 0.285714</output> <gadget id="calculator">2 / (2/7)</gadget> <output>7</output> <gadget id="calculator">7 - 1</gadget> <output>6</output> <result>B</result>

B

The Q train leaves station A moving at a constant speed, and passes by stations B and C, in this order. It takes the Q train 7 hours to reach station B, and 5 additional hours to reach station C. The distance between stations A and B is m kilometers longer than the distance between stations B and C. What is the distance between stations A and C in terms of m?

subtract(divide(const_2, subtract(const_1, divide(5, 7))), const_1)

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

the reason it is failing for you is that you chose incorrect numbers . if the question says it q took 7 hrs to reach from a to b and 5 hrs to reach from b to c at a constant speed . it shows that distance ab and bc should be in ratio of 7 / 5 . if you take such numbers you can solve problem . ab = 7 , bc = 5 therefore ab - bc = 2 but from question , ab - bc = m = > m = 2 now total distance = ab + bc = 12 substitute 12 to get answer in terms of m total distance = 12 = 6 m ans b

physics

math_qa__eq9QcFkFMxeeoDyx

A room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room. Choose the correct choice from the following A) 107 B) 117 C) 127 D) 137 E) 147

<gadget id="calculator">6 * 100</gadget> <output>600</output> <gadget id="calculator">600 + 24</gadget> <output>624</output> <gadget id="calculator">4 * 100</gadget> <output>400</output> <gadget id="calculator">400 + 32</gadget> <output>432</output> <gadget id="calculator">624 * 432</gadget> <output>269_568</output> <gadget id="calculator">gcd(624, 432)</gadget> <output>48</output> <gadget id="calculator">48 * 48</gadget> <output>2_304</output> <gadget id="calculator">269_568 / 2_304</gadget> <output>117</output> <result>B</result>

B

A room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room.

divide(multiply(add(multiply(6, const_100), 24), add(multiply(4, const_100), 32)), multiply(gcd(add(multiply(6, const_100), 24), add(multiply(4, const_100), 32)), gcd(add(multiply(6, const_100), 24), add(multiply(4, const_100), 32))))

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

"let us calculate both the length and width of the room in centimeters . length = 6 meters and 24 centimeters = 624 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 624 and 432 = 48 thus , the number of square tiles required = ( 624 x 432 ) / ( 48 x 48 ) = 13 x 9 = 117 answer : b"

general

math_qa__4igCRV1Q0wOkRfU1

How many integers are between 8 and 122/7, inclusive? Choose the correct answer. A) 8 B) 10 C) 12 D) 15 E) 16

<gadget id="calculator">122 / 7</gadget> <output>122/7 = around 17.428571</output> <gadget id="calculator">(122/7) - 8</gadget> <output>66/7 = around 9.428571</output> <gadget id="calculator">(66/7) + 1</gadget> <output>73/7 = around 10.428571</output> <result>B</result>

B

How many integers are between 8 and 122/7, inclusive?

add(subtract(divide(122, 7), 8), const_1)

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

122 / 7 = 17 . xx we are not concerned about the exact value of 122 / 7 as we just need the integers . the different integers between 8 and 122 / 7 would be 8 , 9 , 10 , 11 , 12,13 , 14,15 , 16,17 total number of integers = 10 option b

general

math_qa__O2WiadPTlxBnkm4U

There are 60 supermarkets in the FGH chain. All of them are either in the US or Canada. If there are 14 more FGH supermarkets in the US than in Canada, how many FGH supermarkets are there in the US? Choose the correct choice. A) 20 B) 37 C) 42 D) 53 E) 64

<gadget id="calculator">60 + 14</gadget> <output>74</output> <gadget id="calculator">74 / 2</gadget> <output>37</output> <result>B</result>

B

There are 60 supermarkets in the FGH chain. All of them are either in the US or Canada. If there are 14 more FGH supermarkets in the US than in Canada, how many FGH supermarkets are there in the US?

divide(add(60, 14), const_2)

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

"x + ( x - 14 ) = 60 - - > x = 37 . answer : b ."

general

math_qa__H32Yn6ITOrigR4mc

The cricket team of 11members is 26yrs old & the wicket keeper is 3 yrs older. If the ages ofthese 2are excluded, the average age of theremaining players is 1 year less than the average age of the whole team. What is the average age of the team ? Choose the correct choice from the following answers: A) 18 B) 21 C) 23 D) 25 E) 27

<gadget id="calculator">26 + 3</gadget> <output>29</output> <gadget id="calculator">29 + 26</gadget> <output>55</output> <gadget id="calculator">11 - 2</gadget> <output>9</output> <gadget id="calculator">55 - 9</gadget> <output>46</output> <gadget id="calculator">11 - 9</gadget> <output>2</output> <gadget id="calculator">46 / 2</gadget> <output>23</output> <result>C</result>

C

The cricket team of 11members is 26yrs old & the wicket keeper is 3 yrs older. If the ages ofthese 2are excluded, the average age of theremaining players is 1 year less than the average age of the whole team. What is the average age of the team ?

divide(subtract(add(add(26, 3), 26), subtract(11, 2)), subtract(11, subtract(11, 2)))

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

"let the average age of the whole team be x years . 11 x - ( 26 + 29 ) = 9 ( x - 1 ) = > 11 x - 9 x = 46 = > 2 x = 46 = > x = 23 . so , average age of the team is 23 years . c"

general

math_qa__rSqMKzs2ClsVDHAb

The true discount on a bill of Rs. 2160 is Rs. 360. What is the banker's discount? Choose the correct choice from the following choices. A) rs . 432 B) rs . 422 C) rs . 412 D) rs . 442 E) none of these

<gadget id="calculator">2_160 - 360</gadget> <output>1_800</output> <gadget id="calculator">360 / 1_800</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(1/5) * 2_160</gadget> <output>432</output> <result>A</result>

A

The true discount on a bill of Rs. 2160 is Rs. 360. What is the banker's discount?

multiply(divide(360, subtract(2160, 360)), 2160)

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

"explanation : f = rs . 2160 td = rs . 360 pw = f - td = 2160 - 360 = rs . 1800 true discount is the simple interest on the present value for unexpired time = > simple interest on rs . 1800 for unexpired time = rs . 360 banker ' s discount is the simple interest on the face value of the bill for unexpired time = simple interest on rs . 2160 for unexpired time = 360 / 1800 × 2160 = 15 × 2160 = rs . 432 answer : option a"

gain

math_qa__pFLZrOg8rtFbG0UT

If the cost price is 82% of the selling price, then what is the profit percent? Choose the correct choice: A) 5 % B) 22 % C) 13 % D) 21 % E) 19 %

<gadget id="calculator">100 - 82</gadget> <output>18</output> <gadget id="calculator">18 / 82</gadget> <output>9/41 = around 0.219512</output> <gadget id="calculator">(9/41) * 100</gadget> <output>900/41 = around 21.95122</output> <result>B</result>

B

If the cost price is 82% of the selling price, then what is the profit percent?

multiply(divide(subtract(const_100, 82), 82), const_100)

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

"let s . p . = $ 100 c . p . = $ 82 profit = $ 18 profit % = 18 / 82 * 100 = 25 / 6 = 22 % approximately answer is b"

gain

math_qa__8Vag4jvcdJejLRkV

If 0.5% of A =85 paise, then the value of A is ? Choose the correct choice from the following answers A) rs . 170 B) rs . 17 C) rs . 1.70 D) rs . 4.25 E) none

<gadget id="calculator">85 / 0.5</gadget> <output>170</output> <result>A</result>

A

If 0.5% of A =85 paise, then the value of A is ?

divide(85, 0.5)

divide(n1,n0)|

"answer ∵ 0.5 / 100 of a = 85 / 100 ∴ a = rs . ( 85 / 0.5 ) = rs . 170 correct option : a"

gain

math_qa__G4851NemFiDIYXqr

Find the compound interest on $1200 for 5 years at 20% p.a. if CI is component yearly? Choose the correct choice from the following options: A) $ 120 B) $ 150 C) $ 1786 D) $ 250 E) $ 300

<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">(6/5) ** 5</gadget> <output>7_776/3_125 = around 2.48832</output> <gadget id="calculator">1_200 * (7_776/3_125)</gadget> <output>373_248/125 = around 2_985.984</output> <gadget id="calculator">(373_248/125) - 1_200</gadget> <output>223_248/125 = around 1_785.984</output> <result>C</result>

C

Find the compound interest on $1200 for 5 years at 20% p.a. if CI is component yearly?

subtract(multiply(1200, power(add(const_1, divide(20, const_100)), 5)), 1200)

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

"a = p ( 1 + r / 100 ) ^ t = 1200 ( 1 + 20 / 100 ) ^ 5 = $ 2986 ci = $ 1786 answer is c"

gain

math_qa__iJGOt4GSI71VSajQ

A certain class of students is being divided into teams. The class can either be divided into 12 teams with an equal number of players on each team or 24 teams with an equal number of players on each team. What is the lowest possible number of students in the class? Choose one: A) 24 B) 36 C) 48 D) 60 E) 72

<gadget id="calculator">lcm(12, 24)</gadget> <output>24</output> <result>A</result>

A

A certain class of students is being divided into teams. The class can either be divided into 12 teams with an equal number of players on each team or 24 teams with an equal number of players on each team. What is the lowest possible number of students in the class?

lcm(12, 24)

lcm(n0,n1)|

"let total no of students in the class be n so , we are told that n is divisible by both 12 24 so , lets find the least common multiple of 12 24 , ie 24 so our answer is ( a ) 24"

general

math_qa__wO9nbyAqri6M7Mdg

A group of 6 children and 10 adults are going to the zoo. Child tickets cost $10, and adult tickets cost $16. How much will the zoo tickets cost in all? Pick one: A) $ 220 B) $ 340 C) $ 150 D) $ 100 E) $ 120

<gadget id="calculator">6 * 10</gadget> <output>60</output> <gadget id="calculator">10 * 16</gadget> <output>160</output> <gadget id="calculator">60 + 160</gadget> <output>220</output> <result>A</result>

A

A group of 6 children and 10 adults are going to the zoo. Child tickets cost $10, and adult tickets cost $16. How much will the zoo tickets cost in all?

add(multiply(6, 10), multiply(10, 16))

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

step 1 : find the cost of the children ' s tickets . 6 × $ 10 = $ 60 step 2 : find the cost of the adults ' tickets . 10 × $ 16 = $ 160 step 3 : find the total cost . $ 60 + $ 160 = $ 220 the zoo tickets will cost $ 220 . answer is a .

general

math_qa__LEWOgnt09JHa2bbv

Tourist purchased a total of 30 travelers checks in $50 and $100 denominations. The total worth of the travelers checks is $1800. How many checks of $50 denominations can he spend so that average amount (arithmetic mean) of the remaining travelers checks is $62.5? Select A) 6 B) 12 C) 15 D) 20 E) 24

<gadget id="calculator">62.5 * 30</gadget> <output>1_875</output> <gadget id="calculator">1_875 - 1_800</gadget> <output>75</output> <gadget id="calculator">62.5 - 50</gadget> <output>12.5</output> <gadget id="calculator">75 / 12.5</gadget> <output>6</output> <result>A</result>

A

Tourist purchased a total of 30 travelers checks in $50 and $100 denominations. The total worth of the travelers checks is $1800. How many checks of $50 denominations can he spend so that average amount (arithmetic mean) of the remaining travelers checks is $62.5?

divide(subtract(multiply(62.5, 30), 1800), subtract(62.5, 50))

multiply(n0,n5)|subtract(n5,n1)|subtract(#0,n3)|divide(#2,#1)|

"you could set - up a quick table and brute force the answer . a 6 * 50 300 1800 - 300 1500 24 62.50 b 16 * 50 600 1800 - 600 1200 18 66.67 c 15 * 50 750 1800 - 750 1050 15 70.00 d 20 * 50 1000 1800 - 1000 800 10 80.00 e 24 * 50 1200 1800 - 1200 600 6 100.00 answer is a"

general

math_qa__T39ixuKsopvQprl1

What will be the compound interest on Rs. 40000 after 3 years at the rate of 12 % per annum Pick. A) rs 16123.20 B) rs 16123.30 C) rs 16197.12 D) rs 16123.50 E) none of these

<gadget id="calculator">4 * 100</gadget> <output>400</output> <gadget id="calculator">400 * 100</gadget> <output>40_000</output> <gadget id="calculator">12 / 100</gadget> <output>3/25 = around 0.12</output> <gadget id="calculator">1 + (3/25)</gadget> <output>28/25 = around 1.12</output> <gadget id="calculator">(28/25) ** 3</gadget> <output>21_952/15_625 = around 1.404928</output> <gadget id="calculator">40_000 * (21_952/15_625)</gadget> <output>1_404_928/25 = around 56_197.12</output> <gadget id="calculator">(1_404_928/25) - 40_000</gadget> <output>404_928/25 = around 16_197.12</output> <result>C</result>

C

What will be the compound interest on Rs. 40000 after 3 years at the rate of 12 % per annum

subtract(multiply(multiply(multiply(const_4, const_100), const_100), power(add(const_1, divide(12, const_100)), 3)), multiply(multiply(const_4, const_100), const_100))

divide(n2,const_100)|multiply(const_100,const_4)|add(#0,const_1)|multiply(#1,const_100)|power(#2,n1)|multiply(#3,#4)|subtract(#5,#3)|

"explanation : ( 40000 × ( 1 + 12 / 100 ) 3 ) = > 40000 × 28 / 25 × 28 / 25 × 28 / 25 = > 56197.12 so compound interest will be 56197.12 - 40000 = rs 16197.12 option c"

gain

math_qa__JA9zFuCW3Vpkbmtv

Working alone, printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 16, 10, and 20 hours, respectively. What is the ratio of the time it takes printer X to do the job, working alone at its rate, to the time it takes printers Y and Z to do the job, working together at their individual rates? Choices: A) 7 / 4 B) 10 / 3 C) 12 / 5 D) 15 / 7 E) 18 / 11

<gadget id="calculator">1 / 10</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">1 / 20</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">(1/10) + (1/20)</gadget> <output>3/20 = around 0.15</output> <gadget id="calculator">1 / (3/20)</gadget> <output>20/3 = around 6.666667</output> <gadget id="calculator">16 / (20/3)</gadget> <output>12/5 = around 2.4</output> <result>C</result>

C

Working alone, printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 16, 10, and 20 hours, respectively. What is the ratio of the time it takes printer X to do the job, working alone at its rate, to the time it takes printers Y and Z to do the job, working together at their individual rates?

divide(16, divide(const_1, add(divide(const_1, 10), divide(const_1, 20))))

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

"the time it takes printer x is 16 hours . the combined rate of y and z is 1 / 10 + 1 / 20 = 3 / 20 the time it takes y and z is 20 / 3 the ratio of times is 16 / ( 20 / 3 ) = 3 * 16 / 20 = 12 / 5 the answer is c ."

general

math_qa__YeOc8NwwhlFAD3l2

The average weight of 10 oarsmen in a boat is increased by 1.8kg when one of the crew, who weight 53kg is replaced by a new man. Find the weight of the new man. Choose the correct choice from the following answers A) 59 kg B) 62 kg C) 74 kg D) 85 kg E) 71 kg

<gadget id="calculator">1.8 * 10</gadget> <output>18</output> <gadget id="calculator">18 + 53</gadget> <output>71</output> <result>E</result>

E

The average weight of 10 oarsmen in a boat is increased by 1.8kg when one of the crew, who weight 53kg is replaced by a new man. Find the weight of the new man.

add(multiply(1.8, 10), 53)

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

"total weight increased = 1.8 * 10 = 18 kg weight of the new man = 53 + 18 = 71 kg answer is e"

general

math_qa__JDqfkFCCAlXxn4Hv

In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (7, 0), (0, -3.5), (-7, 0)? Options: A) 56 B) 88 C) 112 D) 49 E) 120

<gadget id="calculator">7 * 2</gadget> <output>14</output> <gadget id="calculator">3.5 * 2</gadget> <output>7</output> <gadget id="calculator">(14 * 7) / 2</gadget> <output>49</output> <result>D</result>

D

In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (7, 0), (0, -3.5), (-7, 0)?

rhombus_area(multiply(7, const_2), multiply(3.5, const_2))

multiply(n2,const_2)|multiply(n1,const_2)|rhombus_area(#0,#1)|

"area of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 7 + 7 = 14 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 14 * 7 = 49 d is the answer"

geometry

math_qa__NvT9Q0nV72K3TUF4

A man is walking at the rate of 7 km/hr crosses a bridge in 15 minutes. The length of the bridge is Pick. A) 1000 meters B) 1050 meters C) 1200 meters D) 1750 meters E) none of these

<gadget id="calculator">15 / 60</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">7 * (1/4)</gadget> <output>7/4 = around 1.75</output> <gadget id="calculator">(7/4) * 1_000</gadget> <output>1_750</output> <result>D</result>

D

A man is walking at the rate of 7 km/hr crosses a bridge in 15 minutes. The length of the bridge is

multiply(multiply(7, divide(15, const_60)), const_1000)

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

"explanation : we need to get the answer in meters . so we will first of change distance from km / hour to meter / sec by multiplying it with 5 / 18 and also change 15 minutes to seconds by multiplying it with 60 . speed = 7 â ˆ — 5 / 18 = 35 / 18 m / sec time = 15 â ˆ — 60 seconds = 900 seconds distance = time â ˆ — speed / distance = 35 / 18 â ˆ — 900 = 1750 meter option d"

gain

math_qa__bY8rCAz2pODzeOvf

If two sides of a triangle are 6 and 13, respectively, which of the following could NOT be the area of this triangle? Choose the correct choice. A) 40 B) 6 C) 17 D) 29 E) 38

<gadget id="calculator">6 * 13</gadget> <output>78</output> <gadget id="calculator">78 / 2</gadget> <output>39</output> <result>A</result>

A

If two sides of a triangle are 6 and 13, respectively, which of the following could NOT be the area of this triangle?

divide(multiply(6, 13), const_2)

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

for this question it would be helpful to know the largest area that this triangle could be , given the two sides of 6 and 12 . we know that the area of a triangle will be maximized when two sides are perpendicular to each other ( consult bunuel ' s drawing above ) . thus we have a max area being equal to one half the base times the height , either ( . 5 ) 13 * 6 - or - ( . 5 ) 6 * 13 will result in a maximum area of 39 for the triangle ; therefore , the triangle could never have an area of 40 . a

geometry

math_qa__3vKKg4aiXUubmZ23

Average expenditure of a person for the first 3 days of a week is Rs. 350 and for the next 4 days is Rs. 420. Average expenditure of the man for the whole week is: Choose the correct choice from the following answers: A) 350 B) 370 C) 390 D) 430 E) none

<gadget id="calculator">420 - 350</gadget> <output>70</output> <gadget id="calculator">4 * 70</gadget> <output>280</output> <gadget id="calculator">3 + 4</gadget> <output>7</output> <gadget id="calculator">280 / 7</gadget> <output>40</output> <gadget id="calculator">350 + 40</gadget> <output>390</output> <result>C</result>

C

Average expenditure of a person for the first 3 days of a week is Rs. 350 and for the next 4 days is Rs. 420. Average expenditure of the man for the whole week is:

add(350, divide(multiply(4, subtract(420, 350)), add(3, 4)))

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

"explanation : assumed mean = rs . 350 total excess than assumed mean = 4 × ( rs . 420 - rs . 350 ) = rs . 280 therefore , increase in average expenditure = rs . 280 / 7 = rs . 40 therefore , average expenditure for 7 days = rs . 350 + rs . 40 = rs . 390 correct option : c"

general

math_qa__Gm3MTcDK8tnYSmbJ

Compound interest of Rs.1000 at 10% per annum for 1 1/2years will be (interest compounded half yearly). Select A) rs . 473 B) rs . 374 C) rs . 495 D) rs . 157 E) none of the above

<gadget id="calculator">10 / 2</gadget> <output>5</output> <gadget id="calculator">5 / 100</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">1 + (1/20)</gadget> <output>21/20 = around 1.05</output> <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) * 2</gadget> <output>3</output> <gadget id="calculator">(21/20) ** 3</gadget> <output>9_261/8_000 = around 1.157625</output> <gadget id="calculator">1_000 * (9_261/8_000)</gadget> <output>9_261/8 = around 1_157.625</output> <gadget id="calculator">(9_261/8) - 1_000</gadget> <output>1_261/8 = around 157.625</output> <result>D</result>

D

Compound interest of Rs.1000 at 10% per annum for 1 1/2years will be (interest compounded half yearly).

subtract(multiply(1000, power(add(1, divide(divide(10, 2), const_100)), multiply(add(1, divide(1, 2)), 2))), 1000)

divide(n1,n4)|divide(n2,n4)|add(n2,#1)|divide(#0,const_100)|add(#3,n2)|multiply(#2,n4)|power(#4,#5)|multiply(n0,#6)|subtract(#7,n0)|

"10 % interest per annum will be 5 % interest half yearly for 3 terms ( 1 1 / 2 years ) so compound interest = 3000 [ 1 + ( 5 / 100 ) ] ^ 3 - 1000 = 1000 [ ( 21 / 20 ) ^ 3 - 1 ] = 1000 ( 9261 - 8000 ) / 8000 = 1 * 1261 / 8 = 157 answer : d"

gain

math_qa__0RdR9xp95OepWyOb

Susan drove an average speed of 30 miles per hour for the first 40 miles of a trip then at a average speed of 15 miles/hr for the remaining 40 miles of the trip if she made no stops during the trip what was susan's avg speed in miles/hr for the entire trip Choose the correct choice from the following A) 35 B) 20 C) 45 D) 50 E) 55

<gadget id="calculator">40 + 40</gadget> <output>80</output> <gadget id="calculator">40 / 30</gadget> <output>4/3 = around 1.333333</output> <gadget id="calculator">40 / 15</gadget> <output>8/3 = around 2.666667</output> <gadget id="calculator">(4/3) + (8/3)</gadget> <output>4</output> <gadget id="calculator">80 / 4</gadget> <output>20</output> <result>B</result>

B

Susan drove an average speed of 30 miles per hour for the first 40 miles of a trip then at a average speed of 15 miles/hr for the remaining 40 miles of the trip if she made no stops during the trip what was susan's avg speed in miles/hr for the entire trip

divide(add(40, 40), add(divide(40, 30), divide(40, 15)))

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

avg . speed = total distance / total time total distance = 80 miles total time = 40 / 30 + 40 / 15 = 4 avg . speed = 20 . answer - b

physics

math_qa__H9rXby7TpPnj6sy1

If 25% of x is 15 less than 15% of 1500, then x is? Choose one: A) 720 B) 750 C) 820 D) 840 E) 860

<gadget id="calculator">15 / 100</gadget> <output>3/20 = around 0.15</output> <gadget id="calculator">1_500 * (3/20)</gadget> <output>225</output> <gadget id="calculator">225 - 15</gadget> <output>210</output> <gadget id="calculator">25 / 100</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">210 / (1/4)</gadget> <output>840</output> <result>D</result>

D

If 25% of x is 15 less than 15% of 1500, then x is?

divide(subtract(multiply(1500, divide(15, const_100)), 15), divide(25, const_100))

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

"25 % of x = x / 4 ; 15 % of 1500 = 15 / 100 * 1500 = 225 given that , x / 4 = 225 - 15 = > x / 4 = 210 = > x = 840 . answer : d"

general

math_qa__KxolouDV1ahB1k0m

Two good train each 250 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km / hr and 30 km /hr respectively. Find the time taken by the slower train to pass the driver of the faster one. Select: A) 12 sec B) 24 sec C) 48 sec D) 60 sec E) none

<gadget id="calculator">45 + 30</gadget> <output>75</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">75 * (5/18)</gadget> <output>125/6 = around 20.833333</output> <gadget id="calculator">1 / (125/6)</gadget> <output>6/125 = around 0.048</output> <gadget id="calculator">250 * (6/125)</gadget> <output>12</output> <gadget id="calculator">12 * 2</gadget> <output>24</output> <result>B</result>

B

Two good train each 250 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km / hr and 30 km /hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

multiply(multiply(250, inverse(multiply(add(45, 30), const_0_2778))), const_2)

add(n1,n2)|multiply(#0,const_0_2778)|inverse(#1)|multiply(n0,#2)|multiply(#3,const_2)|

"sol . relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec . distance covered = ( 250 + 250 ) m = 1000 m . required time = ( 500 x 6 / 125 ) sec = 24 sec . answer b"

physics

math_qa__dwwjRAJZGw3BtaCo

A is a working partner and B is a sleeping partner in the business. A puts in Rs.3500 and B Rs.1500, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is? Options: A) 1978 B) 2707 C) 7728 D) 7008 E) 7291

<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">9_600 * (9/10)</gadget> <output>8_640</output> <gadget id="calculator">3_500 + 1_500</gadget> <output>5_000</output> <gadget id="calculator">1_500 / 5_000</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">8_640 * (3/10)</gadget> <output>2_592</output> <gadget id="calculator">9_600 - 2_592</gadget> <output>7_008</output> <result>D</result>

D

A is a working partner and B is a sleeping partner in the business. A puts in Rs.3500 and B Rs.1500, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?

subtract(9600, multiply(multiply(9600, subtract(const_1, divide(10, const_100))), divide(1500, add(3500, 1500))))

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

"35 : 15 = > 7 : 3 9600 * 10 / 100 = 960 9600 - 960 = 8640 8640 * 7 / 10 = 6048 + 960 = 7008 answer : d"

gain

math_qa__gOhHIH65oIwXM4uc

45% of major airline companies equip their planes with wireless internet access. 70% of major airlines offer passengers free on-board snacks. What is the greatest possible percentage of major airline companies that offer both wireless internet and free on-board snacks? Choose the correct choice from the following options: A) 25 % B) 35 % C) 45 % D) 55 % E) 65 %

<gadget id="calculator">45 * 1</gadget> <output>45</output> <result>C</result>

C

45% of major airline companies equip their planes with wireless internet access. 70% of major airlines offer passengers free on-board snacks. What is the greatest possible percentage of major airline companies that offer both wireless internet and free on-board snacks?

multiply(45, const_1)

multiply(n0,const_1)|

"to maximize the percentage of companies offering both , let ' s assume that all 45 % of companies which offer wireless internet also offer snacks . the answer is c ."

general

math_qa__UUya1RFGD1wymJHh

After 10% of the inhabitants of a village disappeared, a panic set in during which 25% of the remaining inhabitants left the village. At that time, the population was reduced to 4725. What was the number of original inhabitants? Choose the correct choice from the following answers: A) 5000 B) 7000 C) 4000 D) 8000 E) 9000

<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">25 / 100</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(9/10) * (1/4)</gadget> <output>9/40 = around 0.225</output> <gadget id="calculator">(9/10) - (9/40)</gadget> <output>27/40 = around 0.675</output> <gadget id="calculator">4_725 / (27/40)</gadget> <output>7_000</output> <result>B</result>

B

After 10% of the inhabitants of a village disappeared, a panic set in during which 25% of the remaining inhabitants left the village. At that time, the population was reduced to 4725. What was the number of original inhabitants?

divide(4725, subtract(subtract(const_1, divide(10, const_100)), multiply(subtract(const_1, divide(10, const_100)), divide(25, const_100))))

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

"let the total number of original inhabitants be x . ( 75 / 100 ) * ( 90 / 100 ) * x = 4725 ( 27 / 40 ) * x = 4725 x = 4725 * 40 / 27 = 7000 the answer is b ."

gain

math_qa__s13s8HGvt6cnxI4u

A and B invests Rs.3000 and Rs.6500 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit? Pick. A) 8 : 8 B) 9 : 8 C) 9 : 6 D) 9 : 5 E) 9 : 13

<gadget id="calculator">3_000 * 6</gadget> <output>18_000</output> <gadget id="calculator">3_000 * 2</gadget> <output>6_000</output> <gadget id="calculator">6_000 * 6</gadget> <output>36_000</output> <gadget id="calculator">18_000 + 36_000</gadget> <output>54_000</output> <gadget id="calculator">6 + 6</gadget> <output>12</output> <gadget id="calculator">6_500 * 12</gadget> <output>78_000</output> <gadget id="calculator">54_000 / 78_000</gadget> <output>9/13 = around 0.692308</output> <result>E</result>

E

A and B invests Rs.3000 and Rs.6500 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?

divide(add(multiply(3000, 6), multiply(multiply(3000, const_2), 6)), multiply(6500, add(6, 6)))

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

"( 3 * 6 + 6 * 6 ) : ( 6.5 * 12 ) 54 : 78 = > 9 : 13 answer : e"

gain

math_qa__LsLNYUBPlUmFv6aL

If a car went the first third of the distance at 10 kmh, the second third at 24 kmh, and the last third at 48 kmh, what was the average speed of the car for the entire trip? Options: A) 36 kmh B) 19 kmh C) 42 kmh D) 44 kmh E) 50 kmh

<gadget id="calculator">1 / 10</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">1 / 24</gadget> <output>1/24 = around 0.041667</output> <gadget id="calculator">(1/10) + (1/24)</gadget> <output>17/120 = around 0.141667</output> <gadget id="calculator">1 / 48</gadget> <output>1/48 = around 0.020833</output> <gadget id="calculator">(17/120) + (1/48)</gadget> <output>13/80 = around 0.1625</output> <gadget id="calculator">3 / (13/80)</gadget> <output>240/13 = around 18.461538</output> <result>B</result>

B

If a car went the first third of the distance at 10 kmh, the second third at 24 kmh, and the last third at 48 kmh, what was the average speed of the car for the entire trip?

divide(const_3, add(add(divide(const_1, 10), divide(const_1, 24)), divide(const_1, 48)))

divide(const_1,n0)|divide(const_1,n1)|divide(const_1,n2)|add(#0,#1)|add(#3,#2)|divide(const_3,#4)|

"assume d / 3 = 240 ( this number is convenient because it is divisible by 10 , 24 and 48 ) so : 240 = 10 * t 1 = 24 hrs 240 = 24 * t 2 = 10 hrs 240 = 48 * t 3 = 5 hrs t = t 1 + t 2 + t 3 = 39 hrs d = rt ( 240 * 3 ) = r * 39 r = 19 answer : b"

physics

math_qa__Rq9qmF4ITYJk34g3

If 70% of an equal to 40% of b, then ratio between a and b is? Pick one A) 4 : 7 B) 4 : 9 C) 4 : 2 D) 4 : 1 E) 4 : 5

<gadget id="calculator">40 / 70</gadget> <output>4/7 = around 0.571429</output> <result>A</result>

A

If 70% of an equal to 40% of b, then ratio between a and b is?

divide(40, 70)

divide(n1,n0)

explanation : 70 a = 40 b a : b = 4 : 7 answer : a

other