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NLP Centre, Faculty of Informatics, Masaryk University 15

math_qa__MHy1Uyngmk9JiL94

If a certain number X is divided by 62, the reminder is 7. what is the reminder when X+11 is divided by 31? Choices. A) 3 B) 5 C) 18 D) 6 E) 8

<gadget id="calculator">7 + 11</gadget> <output>18</output> <result>C</result>

C

If a certain number X is divided by 62, the reminder is 7. what is the reminder when X+11 is divided by 31?

add(7, 11)

add(n1,n2)

x can be written as 62 k + 7 or x = 7 , 69,131 , etc . x + 11 = 62 k + 7 + 11 = 62 k + 18 or x + 11 = 18 , 80,142 etc . when divided by 31 , we will get the remainder 18 . c

general

math_qa__LhH5MmA3Ld9M5ibs

If 7^w is a factor of the product of the integers from 1 to 100, inclusive, what is the largest value of w? Choose one A) 12 B) 13 C) 14 D) 15 E) 16

<gadget id="calculator">100 / 7</gadget> <output>100/7 = around 14.285714</output> <gadget id="calculator">7 ** 2</gadget> <output>49</output> <gadget id="calculator">100 / 49</gadget> <output>100/49 = around 2.040816</output> <gadget id="calculator">(100/7) + (100/49)</gadget> <output>800/49 = around 16.326531</output> <gadget id="calculator">floor(800/49)</gadget> <output>16</output> <result>E</result>

E

If 7^w is a factor of the product of the integers from 1 to 100, inclusive, what is the largest value of w?

floor(add(divide(100, 7), divide(100, power(7, const_2))))

divide(n2,n0)|power(n0,const_2)|divide(n2,#1)|add(#0,#2)|floor(#3)

so the question just means that we have to find all the multiples w of 7 between 1 to 100 so there are 14 multiples of 7 ( 7 - 98 ) but 49 and 98 contain two 7 ' s as factors so we have to add 14 + 2 = 16 e

general

math_qa__y2it4fjWT7gOsdR2

A women purchased 3 towels @ Rs.100 each, 5 towels @ Rs.150 each and two towels at a certain rate which is now slipped off from his memory. But she remembers that the average price of the towels was Rs.145. Find the unknown rate of two towels? Choose the correct choice from the following options. A) 400 B) 450 C) 500 D) 550 E) 600

<gadget id="calculator">3 + 5</gadget> <output>8</output> <gadget id="calculator">8 + 2</gadget> <output>10</output> <gadget id="calculator">10 * 145</gadget> <output>1_450</output> <gadget id="calculator">5 * 150</gadget> <output>750</output> <gadget id="calculator">1_450 - 750</gadget> <output>700</output> <gadget id="calculator">3 * 100</gadget> <output>300</output> <gadget id="calculator">700 - 300</gadget> <output>400</output> <result>A</result>

A

A women purchased 3 towels @ Rs.100 each, 5 towels @ Rs.150 each and two towels at a certain rate which is now slipped off from his memory. But she remembers that the average price of the towels was Rs.145. Find the unknown rate of two towels?

subtract(subtract(multiply(add(add(3, 5), const_2), 145), multiply(5, 150)), multiply(3, 100))

add(n0,n2)|multiply(n2,n3)|multiply(n0,n1)|add(#0,const_2)|multiply(n4,#3)|subtract(#4,#1)|subtract(#5,#2)|

"10 * 145 = 1450 3 * 100 + 5 * 150 = 1050 1450 – 1050 = 400 a"

general

math_qa__KyiMRvpcb3MCx020

if 2 pipes take an hour to fill a tank, then how long should 8 pipes take to fill the same tank? Options: A) 20 min B) 10 min C) 15 min D) 25 min E) 30 min

<gadget id="calculator">2 * 60</gadget> <output>120</output> <gadget id="calculator">120 / 8</gadget> <output>15</output> <result>C</result>

C

if 2 pipes take an hour to fill a tank, then how long should 8 pipes take to fill the same tank?

divide(multiply(2, const_60), 8)

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

if 2 pipes take an hour to fill a tank , then 8 pipes will take 2 * 60 / 8 = 15 mins to dig a ditch of the same type . answer : c

physics

math_qa__0r4IPcOGrvECH9UO

There are 6 chess amateurs playing in Villa's chess club tournament. If each chess amateur plays with exactly 4 other amateurs, what is the total number of chess games possible to be played in the tournament? Choose the correct choice A) 10 B) 20 C) 40 D) 60 E) 12

<gadget id="calculator">6 * 4</gadget> <output>24</output> <gadget id="calculator">24 / 2</gadget> <output>12</output> <result>E</result>

E

There are 6 chess amateurs playing in Villa's chess club tournament. If each chess amateur plays with exactly 4 other amateurs, what is the total number of chess games possible to be played in the tournament?

divide(multiply(6, 4), const_2)

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

method 2 : each person is one participant of 4 games . so there are in all 4 * 6 = 24 instances of one participant games . but each game has 2 participants so total number of games = 24 / 2 = 12 e

general

math_qa__MIUuHzGJyGbdgVpj

Worker A takes 4 hours to do a job. Worker B takes 10 hours to do the same job. How long it take both A & B, working together but independently, to do the same job? Answers A) 20 / 9 B) 40 / 9 C) 40 / 14 D) 60 / 9 E) 80 / 9

<gadget id="calculator">1 / 4</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">1 / 10</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">(1/4) + (1/10)</gadget> <output>7/20 = around 0.35</output> <gadget id="calculator">1 / (7/20)</gadget> <output>20/7 = around 2.857143</output> <result>C</result>

C

Worker A takes 4 hours to do a job. Worker B takes 10 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?

divide(const_1, add(divide(const_1, 4), divide(const_1, 10)))

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

one day work of a = 1 / 4 one day work of b = 1 / 10 so one day work of a and b together = 1 / 4 + 1 / 10 = 14 / 40 so total days required = 40 / 14 answer : c

physics

math_qa__l06jqafFpKk5cbOW

Express a speed of 30 kmph in meters per second? Choose the correct choice from the following: A) 10 mps B) 8 mps C) 9 mps D) 7 mps E) 12 mps

<gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">(5/18) * 30</gadget> <output>25/3 = around 8.333333</output> <result>B</result>

B

Express a speed of 30 kmph in meters per second?

multiply(const_0_2778, 30)

multiply(n0,const_0_2778)|

"30 * 5 / 18 = 8 mps answer : b"

physics

math_qa__FGfffT1dsTWM9CpG

In a maths test, students were asked to find 5/16 of a certain number. One of the students by mistake found 5/6th of that number and his answer was 100 more than the correct answer. Find the number. Choose the correct answer. A) 192 B) 280 C) 384 D) 400 E) 500

<gadget id="calculator">100 * 16</gadget> <output>1_600</output> <gadget id="calculator">1_600 * 6</gadget> <output>9_600</output> <gadget id="calculator">5 * 16</gadget> <output>80</output> <gadget id="calculator">5 * 6</gadget> <output>30</output> <gadget id="calculator">80 - 30</gadget> <output>50</output> <gadget id="calculator">9_600 / 50</gadget> <output>192</output> <result>A</result>

A

In a maths test, students were asked to find 5/16 of a certain number. One of the students by mistake found 5/6th of that number and his answer was 100 more than the correct answer. Find the number.

divide(multiply(multiply(100, 16), 6), subtract(multiply(5, 16), multiply(5, 6)))

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

"explanation : let the number be x . 5 * x / 6 = 5 * x / 16 + 100 25 * x / 48 = 100 x = 192 answer a"

general

math_qa__WvziAsks9Ek26jgv

The cost price of a radio is Rs.1900 and it was sold for Rs.1330, find the loss %? Choose the correct choice from the following choices: A) 18 % B) 31 % C) 30 % D) 45 % E) 12 %

<gadget id="calculator">1_900 - 1_330</gadget> <output>570</output> <gadget id="calculator">570 / 1_900</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">(3/10) * 100</gadget> <output>30</output> <result>C</result>

C

The cost price of a radio is Rs.1900 and it was sold for Rs.1330, find the loss %?

multiply(divide(subtract(1900, 1330), 1900), const_100)

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

"1900 - - - - 570 100 - - - - ? = > 30 % answer : c"

gain

math_qa__Uw6oWuRu89usJ9TH

Someone on a skateboard is traveling 13 miles per hour. How many feet does she travel in 25 seconds? (1 mile = 5280 feet) Select the correct option. A) 476.75 ft B) 450 ft C) 480 ft D) 490 ft E) 500 ft

<gadget id="calculator">13 * 5_280</gadget> <output>68_640</output> <gadget id="calculator">68_640 / 3_600</gadget> <output>286/15 = around 19.066667</output> <gadget id="calculator">25 * (286/15)</gadget> <output>1_430/3 = around 476.666667</output> <result>A</result>

A

Someone on a skateboard is traveling 13 miles per hour. How many feet does she travel in 25 seconds? (1 mile = 5280 feet)

multiply(25, divide(multiply(13, 5280), const_3600))

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

"per second = > 13 * 5280 ft / 60 * 60 = 19.07 ft 25 seconds = > 19.07 * 25 = 476.75 ft answer : a"

physics

math_qa__PQpGPvKo4Nm8SP14

There are 4 more women than there are men on a local co-ed softball team. If there are a total of 14 players on the team, what is the ratio of men to women? Choose the most appropriate option: A) 10 / 16 B) 6 / 16 C) 4 / 16 D) 6 / 10 E) 5 / 9

<gadget id="calculator">14 - 4</gadget> <output>10</output> <gadget id="calculator">1 + 1</gadget> <output>2</output> <gadget id="calculator">10 / 2</gadget> <output>5</output> <gadget id="calculator">5 + 4</gadget> <output>9</output> <gadget id="calculator">5 / 9</gadget> <output>5/9 = around 0.555556</output> <result>E</result>

E

There are 4 more women than there are men on a local co-ed softball team. If there are a total of 14 players on the team, what is the ratio of men to women?

divide(divide(subtract(14, 4), add(const_1, const_1)), add(divide(subtract(14, 4), add(const_1, const_1)), 4))

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

"w = m + 4 w + m = 14 m + 4 + m = 14 2 m = 10 m = 5 w = 9 ratio : 5 : 9 ans : e"

general

math_qa__vlgkSJDGxP93pCDW

8900 ÷ 6 ÷ 4 = ? Choose one A) 349 B) 541.75 C) 224.37 D) 370.833 E) none of these

<gadget id="calculator">8_900 / 6</gadget> <output>4_450/3 = around 1_483.333333</output> <gadget id="calculator">(4_450/3) / 4</gadget> <output>2_225/6 = around 370.833333</output> <result>D</result>

D

8900 ÷ 6 ÷ 4 = ?

divide(divide(8900, 6), 4)

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

explanation : given exp . 8900 * 1 / 6 * 1 / 4 = 370.833 answer : d

general

math_qa__crXP1K2rw2GOSPM4

The markup on a box of apples is 10 percent of the cost. The markup is what percent of the selling price? (markup = selling price - cost) Choose the correct choice from the following answers: A) 9.09 % B) 10 % C) 12 1 / 2 % D) 15 % E) 16 2 / 3 %

<gadget id="calculator">10 / 100</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">1 + (1/10)</gadget> <output>11/10 = around 1.1</output> <gadget id="calculator">10 / (11/10)</gadget> <output>100/11 = around 9.090909</output> <result>A</result>

A

The markup on a box of apples is 10 percent of the cost. The markup is what percent of the selling price? (markup = selling price - cost)

divide(10, add(const_1, divide(10, const_100)))

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

mp = 0.1 cp sp = cp + 0.1 cp = 1.1 cp hence mp = 0.1 / 1.1 sp = 1 / 1 sp . hence mp is 9.09 % of sp answer a

general

math_qa__xnfSSnmklCISynbl

A train speeds past a pole in 15 seconds and a platform 100 m long in 40 seconds. Its length is? Choose the correct choice from the following answers A) 188 m B) 876 m C) 251 m D) 100 m E) 145 m

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

D

A train speeds past a pole in 15 seconds and a platform 100 m long in 40 seconds. Its length is?

multiply(100, subtract(const_2, const_1))

subtract(const_2,const_1)|multiply(n1,#0)|

"let the length of the train be x meters and its speed be y m / sec . they , x / y = 15 = > y = x / 15 x + 100 / 40 = x / 15 x = 100 m . answer : d"

physics

math_qa__krR0Adt0nXpjV5jW

A train running at the speed of 30 km/hr crosses a pole in 12 seconds. What is the length of the train? Choose the correct option. A) 70 B) 80 C) 90 D) 100 E) 110

<gadget id="calculator">30 * 1_000</gadget> <output>30_000</output> <gadget id="calculator">30_000 / 3_600</gadget> <output>25/3 = around 8.333333</output> <gadget id="calculator">(25/3) * 12</gadget> <output>100</output> <result>D</result>

D

A train running at the speed of 30 km/hr crosses a pole in 12 seconds. What is the length of the train?

multiply(divide(multiply(30, const_1000), const_3600), 12)

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

"speed = ( 30 x ( 5 / 18 ) m / sec = ( 25 / 3 ) m / sec . length of the train = ( speed x time ) . length of the train = ( ( 25 / 3 ) x 12 ) m = 100 m d"

physics

math_qa__Gu4gZXJKwHJsykK4

Two stations P and Q are 65 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet? Choose the correct choice from the following choices: A) 9 am B) 12 am C) 10.30 am D) 12.30 am E) 11 am

<gadget id="calculator">65 + 25</gadget> <output>90</output> <gadget id="calculator">20 + 25</gadget> <output>45</output> <gadget id="calculator">90 / 45</gadget> <output>2</output> <gadget id="calculator">2 + 7</gadget> <output>9</output> <result>A</result>

A

Two stations P and Q are 65 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?

add(divide(add(65, 25), add(20, 25)), 7)

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

assume both trains meet after x hours after 7 am distance covered by train starting from p in x hours = 20 x km distance covered by train starting from q in ( x - 1 ) hours = 25 ( x - 1 ) total distance = 65 = > 20 x + 25 ( x - 1 ) = 65 = > 45 x = 90 = > x = 2 means , they meet after 2 hours after 7 am , ie , they meet at 9 am answer is a .

physics

math_qa__wYvTcMa56hAXrnQs

A store reported total sales of $385 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase W in sales? Choose the correct choice from the following answers. A) 2 % B) 17 % C) 20 % D) 65 % E) 83 %

<gadget id="calculator">385 - 320</gadget> <output>65</output> <gadget id="calculator">65 / 320</gadget> <output>13/64 = around 0.203125</output> <gadget id="calculator">(13/64) * 100</gadget> <output>325/16 = around 20.3125</output> <result>C</result>

C

A store reported total sales of $385 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase W in sales?

multiply(divide(subtract(385, 320), 320), const_100)

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

"last year ' s sales = $ 320 million ; this year ' s sales = $ 385 million ; increase w = $ 65 million . now , 20 % of $ 320 million is $ 64 million , which is very close to actual increase of $ 65 million . answer : c ."

general

math_qa__XHKt0BOFiF6FgIWl

A man saves 10% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 5%, he is only able to save Rs. 400 per month. What is his monthly salary? Choose the correct option. A) rs . 6500 B) rs . 7500 C) rs . 7200 D) rs . 7273 E) rs . 6300

<gadget id="calculator">400 * 100</gadget> <output>40_000</output> <gadget id="calculator">100 - 10</gadget> <output>90</output> <gadget id="calculator">5 / 100</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">90 * (1/20)</gadget> <output>9/2 = around 4.5</output> <gadget id="calculator">90 + (9/2)</gadget> <output>189/2 = around 94.5</output> <gadget id="calculator">100 - (189/2)</gadget> <output>11/2 = around 5.5</output> <gadget id="calculator">40_000 / (11/2)</gadget> <output>80_000/11 = around 7_272.727273</output> <result>D</result>

D

A man saves 10% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 5%, he is only able to save Rs. 400 per month. What is his monthly salary?

divide(multiply(400, const_100), subtract(const_100, add(subtract(const_100, 10), multiply(subtract(const_100, 10), divide(5, const_100)))))

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

"income = rs . 100 expenditure = rs . 90 savings = rs . 10 present expenditure 90 + 90 * ( 5 / 100 ) = rs . 94.5 present savings = 100 – 94.5 = rs . 5.50 if savings is rs . 5.50 , salary = rs . 100 if savings is rs . 400 , salary = 100 / 5.5 * 400 = 7273 answer : d"

general

math_qa__bmc3HMatd4n7hH9f

Working individually, Emma can wrap presents for 6 hours and Troy can wrap presents in 8 hours. If Emma and Troy work together but independently at the task for 2 hours, at which point Troy leaves, how many remaining hours will it take Emma to complete the task alone? Choose the correct choice from the following answers A) 30 / 12 B) 5 / 12 C) 3 / 4 D) 2 / 12 E) 3 / 5

<gadget id="calculator">1 / 6</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">2 * (1/6)</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">1 / 8</gadget> <output>1/8 = around 0.125</output> <gadget id="calculator">2 * (1/8)</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(1/3) + (1/4)</gadget> <output>7/12 = around 0.583333</output> <gadget id="calculator">1 - (7/12)</gadget> <output>5/12 = around 0.416667</output> <gadget id="calculator">(5/12) / (1/6)</gadget> <output>5/2 = around 2.5</output> <result>A</result>

A

Working individually, Emma can wrap presents for 6 hours and Troy can wrap presents in 8 hours. If Emma and Troy work together but independently at the task for 2 hours, at which point Troy leaves, how many remaining hours will it take Emma to complete the task alone?

divide(subtract(const_1, add(multiply(2, inverse(6)), multiply(2, inverse(8)))), inverse(6))

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

in first 2 hrs troy will finish 2 / 8 = 1 / 4 of work and emma will finish 2 / 6 work so total 1 / 4 + 1 / 3 = 7 / 12 work is finished and 1 - 7 / 12 = 5 / 12 work remaining . now emma will take ( 5 / 12 ) * 6 = 30 / 12 hrs to finish it . so answer is a .

physics

math_qa__sthEFJducu3rj6R4

A certain electric-company plan offers customers reduced rates for electricity used between 8 p.m. and 8 a.m. weekdays and 24 hours a day Saturdays and Sundays. Under this plan, the reduced rates Z apply to what fraction of a week? Choose the correct answer: A) 1 / 2 B) 5 / 8 C) 9 / 14 D) 16 / 21 E) 9 / 10

<gadget id="calculator">24 / 2</gadget> <output>12</output> <gadget id="calculator">2 + 3</gadget> <output>5</output> <gadget id="calculator">12 * 5</gadget> <output>60</output> <gadget id="calculator">24 * 2</gadget> <output>48</output> <gadget id="calculator">60 + 48</gadget> <output>108</output> <gadget id="calculator">3 + 4</gadget> <output>7</output> <gadget id="calculator">24 * 7</gadget> <output>168</output> <gadget id="calculator">108 / 168</gadget> <output>9/14 = around 0.642857</output> <result>C</result>

C

A certain electric-company plan offers customers reduced rates for electricity used between 8 p.m. and 8 a.m. weekdays and 24 hours a day Saturdays and Sundays. Under this plan, the reduced rates Z apply to what fraction of a week?

divide(add(multiply(divide(24, const_2), add(const_2, const_3)), multiply(24, const_2)), multiply(24, add(const_3, const_4)))

add(const_2,const_3)|add(const_3,const_4)|divide(n2,const_2)|multiply(n2,const_2)|multiply(#0,#2)|multiply(n2,#1)|add(#4,#3)|divide(#6,#5)

number of hours between 8 pm to 8 am = 12 number of hours with reduced rates = ( 12 * 5 ) + ( 24 * 2 ) hours with reduced rates z / total number of hours in a week = ( 12 * 5 ) + ( 24 * 2 ) / ( 24 * 7 ) = 108 / ( 24 * 7 ) = 9 / 14 answer : c

physics

math_qa__iJ4YtimpFA7KfpPP

The average weight of D, E and F is 42 kg. If the average weight of D and E be 35 kg and that of E and F be 41 kg, what is the weight of E? Choose the correct choice from the following answers: A) 23 kg B) 24 kg C) 25 kg D) 26 kg E) 27 kg

<gadget id="calculator">35 * 2</gadget> <output>70</output> <gadget id="calculator">41 * 2</gadget> <output>82</output> <gadget id="calculator">70 + 82</gadget> <output>152</output> <gadget id="calculator">42 * 3</gadget> <output>126</output> <gadget id="calculator">152 - 126</gadget> <output>26</output> <result>D</result>

D

The average weight of D, E and F is 42 kg. If the average weight of D and E be 35 kg and that of E and F be 41 kg, what is the weight of E?

subtract(add(multiply(35, const_2), multiply(41, const_2)), multiply(42, const_3))

multiply(n1,const_2)|multiply(n2,const_2)|multiply(n0,const_3)|add(#0,#1)|subtract(#3,#2)

let the weight of d , e and f are a , b and c respectively . average weight of d , e and f = 42 a + b + c = 42 × 3 = 126 - - - equation ( 1 ) average weight of d and e = 35 a + b = 35 × 2 = 70 - - - equation ( 2 ) average weight of e and f = 41 b + c = 41 × 2 = 82 - - - equation ( 3 ) equation ( 2 ) + equation ( 3 ) - equation ( 1 ) = > a + b + b + c - ( a + b + c ) = 70 + 82 - 126 = > b = 152 - 126 = 26 weight of b = 26 kg answer : d

general

math_qa__lvkeEQG27qT0oF2Z

Two trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 75 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet? Choose the correct choice from the following choices. A) 7.19 B) 7.17 C) 7.2 D) 7.35 E) 7.11

<gadget id="calculator">121 + 165</gadget> <output>286</output> <gadget id="calculator">75 + 65</gadget> <output>140</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">140 * (5/18)</gadget> <output>350/9 = around 38.888889</output> <gadget id="calculator">286 / (350/9)</gadget> <output>1_287/175 = around 7.354286</output> <result>D</result>

D

Two trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 75 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?

divide(add(121, 165), multiply(add(75, 65), const_0_2778))

add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)|

"t = ( 121 + 165 ) / ( 75 + 65 ) * 18 / 5 t = 7.35 answer : d"

physics

math_qa__OG9TAF35ZKkeOUFP

A merchant marks his goods up by 20% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount? Choose the correct choice from the following answers: A) 8 % B) 10 % C) 21 % D) 15 % E) 17 %

<gadget id="calculator">20 + 100</gadget> <output>120</output> <gadget id="calculator">120 * 10</gadget> <output>1_200</output> <gadget id="calculator">1_200 / 100</gadget> <output>12</output> <gadget id="calculator">120 - 12</gadget> <output>108</output> <gadget id="calculator">108 - 100</gadget> <output>8</output> <result>A</result>

A

A merchant marks his goods up by 20% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount?

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

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

"let the price be 100 . the price becomes 120 after a 20 % markup . now a discount of 10 % on 120 . profit = 108 - 100 8 % answer a"

gain

math_qa__WB9YnpvneNJnmYfK

A batsman in his 20th innings makes a score of 90, and thereby increases his average by 2. What is his average after the 20th innings? He had never been ’not out’. Choose the correct choice A) 52 B) 37 C) 39 D) 43 E) 42

<gadget id="calculator">2 * 20</gadget> <output>40</output> <gadget id="calculator">90 - 40</gadget> <output>50</output> <gadget id="calculator">50 + 2</gadget> <output>52</output> <result>A</result>

A

A batsman in his 20th innings makes a score of 90, and thereby increases his average by 2. What is his average after the 20th innings? He had never been ’not out’.

add(subtract(90, multiply(2, 20)), 2)

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

"average score before 20 th innings = 90 - 2 × 20 = 50 average score after 20 th innings = > 50 + 2 = 52 answer : a"

general

math_qa__p4rSR7y1OAwff2dp

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

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

B

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

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

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

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

general

math_qa__qqZAVuPCitjTclAo

The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 10 and 12. The larger of the two numbers is: Choose the correct answer A) 276 B) 295 C) 322 D) 345 E) 354

<gadget id="calculator">23 * 12</gadget> <output>276</output> <result>A</result>

A

The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 10 and 12. The larger of the two numbers is:

multiply(23, 12)

multiply(n0,n2)|

"clearly , the numbers are ( 23 x 10 ) and ( 23 x 12 ) . larger number = ( 23 x 12 ) = 276 . answer : option a"

other

math_qa__Y3k5ke3YCOqJTpVl

A and B are mixed together in the ratio 9 : 11. What is the weight of mixture, if 26.1 kg of A has been consumed in it? Choose the most appropriate option: A) 56 B) 45 C) 58.2 D) 58 E) 46

<gadget id="calculator">26.1 / 9</gadget> <output>2.9</output> <gadget id="calculator">11 * 2.9</gadget> <output>31.9</output> <gadget id="calculator">31.9 + 26.1</gadget> <output>58</output> <result>D</result>

D

A and B are mixed together in the ratio 9 : 11. What is the weight of mixture, if 26.1 kg of A has been consumed in it?

add(multiply(11, divide(26.1, 9)), 26.1)

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

explanation : for 9 kg a , mixture = ( 9 + 11 ) kg . for 26.1 kg a , mixture = ( ( 20 / 9 ) x 26.1 ) kg = 58 kg . answer : d

general

math_qa__nqXd7O77ZrLVrUsj

Find the constant k so that : -x2 - (k + 12)x - 8 = -(x - 2)(x - 4) Select the correct option: A) 11 B) 12 C) 18 D) 14 E) 15

<gadget id="calculator">4 + 2</gadget> <output>6</output> <gadget id="calculator">12 + 6</gadget> <output>18</output> <result>C</result>

C

Find the constant k so that : -x2 - (k + 12)x - 8 = -(x - 2)(x - 4)

add(12, add(4, 2))

add(n0,n4)|add(n1,#0)|

"- x 2 - ( k + 12 ) x - 8 = - ( x - 2 ) ( x - 4 ) : given - x 2 - ( k + 12 ) x - 8 = - x 2 + 6 x - 8 - ( k + 12 ) = 6 : two polynomials are equal if their corresponding coefficients are equal . k = - 18 : solve the above for k correct answer c"

general

math_qa__inh2YI8Vyi7CSOjR

The duplicate ratio of 2:3 is? Select the correct option: A) 4 : 9 B) 1 : 4 C) 1 : 8 D) 1 : 18 E) 1 : 13

<gadget id="calculator">2 ** 2</gadget> <output>4</output> <gadget id="calculator">3 ** 2</gadget> <output>9</output> <gadget id="calculator">4 / 9</gadget> <output>4/9 = around 0.444444</output> <result>A</result>

A

The duplicate ratio of 2:3 is?

divide(power(2, const_2), power(3, const_2))

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

"2 ^ 2 : 3 ^ 2 = 4 : 9 answer : a"

other

math_qa__w1uYPzy8Zs1MXMAf

The water level in a rectangular swimming pool measuring 40 feet by 25 feet is to be lowered by 6 inches. How many gallons of water must be removed? (1 cu ft = 7.5 gallons) Choose the correct answer. A) 100 B) 250 C) 750 D) 3750 E) 5625

<gadget id="calculator">10 + 2</gadget> <output>12</output> <gadget id="calculator">6 / 12</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">40 * 25 * (1/2)</gadget> <output>500</output> <gadget id="calculator">500 * 7.5</gadget> <output>3_750</output> <result>D</result>

D

The water level in a rectangular swimming pool measuring 40 feet by 25 feet is to be lowered by 6 inches. How many gallons of water must be removed? (1 cu ft = 7.5 gallons)

multiply(volume_rectangular_prism(40, 25, divide(6, add(const_10, const_2))), 7.5)

add(const_10,const_2)|divide(n2,#0)|volume_rectangular_prism(n0,n1,#1)|multiply(n4,#2)|

"6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 40 * 25 * 1 / 2 = 500 feet ^ 3 of water must be removed , which equals to 500 * 7.5 = 3750 gallons . answer : d ."

geometry

math_qa__y2o2wuzyviAzo4Jy

3 maths classes : a , b and c take an algebra test . the average score of class a is 83 . the average score of class b is 76 . the average score of class c is 85 . the average score of class a and b is 79 and average score of class b and c is 81 . what is the average score of classes a , b , c ? Choose the correct choice from the following choices. A) 81.8 B) 81.1 C) 81.2 D) 81.5 E) 81.9

<gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">81 + (1/2)</gadget> <output>163/2 = around 81.5</output> <result>D</result>

D

3 maths classes : a , b and c take an algebra test . the average score of class a is 83 . the average score of class b is 76 . the average score of class c is 85 . the average score of class a and b is 79 and average score of class b and c is 81 . what is the average score of classes a , b , c ?

add(81, divide(const_1, const_2))

divide(const_1,const_2)|add(n5,#0)

let the number of students in classes a , b and c be p , q and r respectively . then , total score of a = 83 p , total score of b = 76 q , total score of c = 85 r . also given that , ( 83 p + 76 q ) / ( p + q ) = 79 = > 4 p = 3 q . ( 76 q + 85 r ) / ( q + r ) = 81 = > 4 r = 5 q , = > q = 4 p / 3 and r = 5 p / 3 therefore , average score of a , b , c = ( 83 p + 76 q + 85 r ) / ( p + q + r ) = 978 / 12 = 81.5 answer : d

general

math_qa__vAuj31OU3q61vz61

At a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 19 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 4 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants? Choose the correct option: A) 2 B) 3 C) 4 D) 5 E) 6

<gadget id="calculator">19 + 18</gadget> <output>37</output> <gadget id="calculator">37 + 12</gadget> <output>49</output> <gadget id="calculator">49 - 4</gadget> <output>45</output> <gadget id="calculator">45 - 39</gadget> <output>6</output> <gadget id="calculator">6 / 2</gadget> <output>3</output> <result>B</result>

B

At a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 19 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 4 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants?

divide(subtract(subtract(add(add(19, 18), 12), 4), 39), 2)

add(n4,n5)|add(n6,#0)|subtract(#1,n7)|subtract(#2,n0)|divide(#3,n8)|

"39 = 19 + 18 + 12 - 4 - 2 x 2 x = 19 + 18 + 12 - 4 - 39 = 45 - 39 = 6 x = 3 answer : b"

physics

math_qa__rpuHVGqWT7z9ejvu

The volume of a cube is 1728 cc. Find its surface. Choose the correct choice from the following answers: A) 864 B) 556 C) 255 D) 287 E) 267

<gadget id="calculator">1_728 ** (1/3)</gadget> <output>12</output> <gadget id="calculator">6 * (12 ** 2)</gadget> <output>864</output> <result>A</result>

A

The volume of a cube is 1728 cc. Find its surface.

surface_cube(cube_edge_by_volume(1728))

cube_edge_by_volume(n0)|surface_cube(#0)|

"a 3 = 1728 = > a = 12 6 a 2 = 6 * 12 * 12 = 864 answer : a"

geometry

math_qa__sGoJkThdR00sDISB

The length of rectangle is thrice its breadth and its perimeter is 40 m, find the area of the rectangle? Select the correct option: A) 432 B) 212 C) 75 D) 992 E) 212

<gadget id="calculator">3 * 2</gadget> <output>6</output> <gadget id="calculator">1 * 2</gadget> <output>2</output> <gadget id="calculator">6 + 2</gadget> <output>8</output> <gadget id="calculator">40 / 8</gadget> <output>5</output> <gadget id="calculator">5 * 3</gadget> <output>15</output> <gadget id="calculator">15 * 5</gadget> <output>75</output> <result>C</result>

C

The length of rectangle is thrice its breadth and its perimeter is 40 m, find the area of the rectangle?

multiply(multiply(divide(40, add(multiply(const_3, const_2), multiply(const_1, const_2))), const_3), divide(40, add(multiply(const_3, const_2), multiply(const_1, const_2))))

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

"2 ( 3 x + x ) = 40 l = 15 b = 5 lb = 15 * 5 = 75 answer : c"

geometry

math_qa__P6KipzJh5XVruxxX

A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is? Choose the correct choice from the following choices: A) 3.34 sq m B) 98.8 sq m C) 67.8 sq m D) 27.9 sq m E) 19.9 sq m

<gadget id="calculator">4 / 2</gadget> <output>2</output> <gadget id="calculator">25 / 100</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">2 + (1/4)</gadget> <output>9/4 = around 2.25</output> <gadget id="calculator">pi * ((9/4) ** 2)</gadget> <output>81*pi/16 = around 15.904313</output> <gadget id="calculator">pi * (2 ** 2)</gadget> <output>4*pi = around 12.566371</output> <gadget id="calculator">(81*pi/16) - (4*pi)</gadget> <output>17*pi/16 = around 3.337942</output> <result>A</result>

A

A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is?

subtract(circle_area(add(divide(4, const_2), divide(25, const_100))), circle_area(divide(4, const_2)))

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

"area of the path = area of the outer circle - area of the inner circle = ∏ { 4 / 2 + 25 / 100 } 2 - ∏ [ 4 / 2 ] 2 = ∏ [ 2.252 - 22 ] = ∏ ( 0.25 ) ( 4.25 ) { ( a 2 - b 2 = ( a - b ) ( a + b ) } = ( 3.14 ) ( 1 / 4 ) ( 17 / 4 ) = 53.38 / 16 = 3.34 sq m answer : a"

geometry

math_qa__6yXwgvVpKNS9lVER

A train is 700 meter long is running at a speed of 21 km/hour. In what time will it pass a bridge of 130 meter length? Choose the correct choice from the following: A) 142.286 B) 251.228 C) 34 D) 200 E) 150.627

<gadget id="calculator">700 + 130</gadget> <output>830</output> <gadget id="calculator">21 * 1_000</gadget> <output>21_000</output> <gadget id="calculator">21_000 / 3_600</gadget> <output>35/6 = around 5.833333</output> <gadget id="calculator">830 / (35/6)</gadget> <output>996/7 = around 142.285714</output> <result>A</result>

A

A train is 700 meter long is running at a speed of 21 km/hour. In what time will it pass a bridge of 130 meter length?

divide(add(700, 130), divide(multiply(21, const_1000), const_3600))

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

"speed = 21 km / hr = 21 * ( 5 / 18 ) m / sec = 35 / 6 m / sec total distance = 700 + 130 = 830 meter time = distance / speed = 830 * ( 6 / 35 ) = 142.286 seconds . answer : a"

physics

math_qa__fGI4DTsa9en0cMnM

A coin is tossed 4 times. What is the probability of getting exactly 3 heads? Select. A) 1 / 2 B) 1 / 4 C) 1 / 8 D) 1 / 16 E) 3 / 16

<gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">(1/2) ** 3</gadget> <output>1/8 = around 0.125</output> <gadget id="calculator">binomial(4, 3)</gadget> <output>4</output> <gadget id="calculator">4 * (1/2)</gadget> <output>2</output> <gadget id="calculator">(1/8) * 2</gadget> <output>1/4 = around 0.25</output> <result>B</result>

B

A coin is tossed 4 times. What is the probability of getting exactly 3 heads?

multiply(power(divide(const_1, const_2), 3), multiply(choose(const_4, const_3), divide(const_1, const_2)))

choose(const_4,const_3)|divide(const_1,const_2)|multiply(#0,#1)|power(#1,n1)|multiply(#2,#3)

the number of possible outcomes is 2 ^ 4 = 16 there are 4 ways to get exactly 3 heads . p ( exactly 3 heads ) = 4 / 16 = 1 / 4 the answer is b .

probability

math_qa__N4dN00CS8SJ7eplH

The ratio of pens to pencils is 5 to 6. There are 4 more pencils than pens. How many pencils are there? Choose the correct choice A) 12 B) 16 C) 20 D) 24 E) 28

<gadget id="calculator">4 * 5</gadget> <output>20</output> <gadget id="calculator">20 + 4</gadget> <output>24</output> <result>D</result>

D

The ratio of pens to pencils is 5 to 6. There are 4 more pencils than pens. How many pencils are there?

add(multiply(4, 5), 4)

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

"let the number of pens be 5 x and the number of pencils be 6 x . 6 x - 5 x = 4 x = 4 the number of pencils is 24 . the answer is d ."

other

math_qa__gSxBqap8zFZLTzpP

In what ratio mental A at Rs.68 per kg be mixed with another metal at Rs.96 per kg so that cost of alloy (mixture) is Rs.75 per kg? Choose the correct choice from the following answers: A) 5 : 8 B) 3 : 1 C) 3 : 7 D) 9 : 5 E) 9 : 8

<gadget id="calculator">96 - 75</gadget> <output>21</output> <gadget id="calculator">96 - 68</gadget> <output>28</output> <gadget id="calculator">21 / 28</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">1 - (3/4)</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(3/4) / (1/4)</gadget> <output>3</output> <result>B</result>

B

In what ratio mental A at Rs.68 per kg be mixed with another metal at Rs.96 per kg so that cost of alloy (mixture) is Rs.75 per kg?

divide(divide(subtract(96, 75), subtract(96, 68)), subtract(const_1, divide(subtract(96, 75), subtract(96, 68))))

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

"( 96 - 75 ) / ( 75 - 68 ) = 21 / 7 = 3 / 1 answer : b"

other

math_qa__wh5X1tyqIkhlNq3O

A shopkeeper fixes the marked price of an item 30% above its cost price. The percentage of discount allowed to gain 6% is Choose the correct choice from the following answers: A) 18.45 % B) 18.46 % C) 18.47 % D) 18.48 % E) none of these

<gadget id="calculator">6 + 100</gadget> <output>106</output> <gadget id="calculator">30 + 100</gadget> <output>130</output> <gadget id="calculator">106 / 130</gadget> <output>53/65 = around 0.815385</output> <gadget id="calculator">(53/65) * 100</gadget> <output>1_060/13 = around 81.538462</output> <gadget id="calculator">100 - (1_060/13)</gadget> <output>240/13 = around 18.461538</output> <result>B</result>

B

A shopkeeper fixes the marked price of an item 30% above its cost price. The percentage of discount allowed to gain 6% is

subtract(const_100, multiply(divide(add(6, const_100), add(30, const_100)), const_100))

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

"explanation : let the cost price = rs 100 then , marked price = rs 130 required gain = 6 % , so selling price = rs 106 discount = 130 - 106 = 24 discount % = ( 24 / 130 ) * 100 = 18.46 % option b"

gain

math_qa__EOqgzYkYMV8cx2av

The product of two numbers is 120 and the sum of their squares is 289. Find the sum? Choose the correct choice from the following answers A) 23 B) 20 C) 15 D) 26 E) 28

<gadget id="calculator">2 * 120</gadget> <output>240</output> <gadget id="calculator">289 - 240</gadget> <output>49</output> <gadget id="calculator">49 ** (1/2)</gadget> <output>7</output> <gadget id="calculator">7 ** 2</gadget> <output>49</output> <gadget id="calculator">4 * 120</gadget> <output>480</output> <gadget id="calculator">49 + 480</gadget> <output>529</output> <gadget id="calculator">529 ** (1/2)</gadget> <output>23</output> <result>A</result>

A

The product of two numbers is 120 and the sum of their squares is 289. Find the sum?

sqrt(add(power(sqrt(subtract(289, multiply(const_2, 120))), const_2), multiply(const_4, 120)))

multiply(n0,const_4)|multiply(n0,const_2)|subtract(n1,#1)|sqrt(#2)|power(#3,const_2)|add(#0,#4)|sqrt(#5)|

"nos a and b ab = 120 and a 2 + b 2 = 289 ( a + b ) 2 = 529 a + b = root ( 529 ) = 23 answer a"

general

math_qa__1fPcN2QCfyCaYKIW

x+(1/x) = 3 find x^2 + (1/x^2) Select: A) 2.25 B) 7 C) 4.25 D) 5.25 E) 6.25

<gadget id="calculator">3 ** 2</gadget> <output>9</output> <gadget id="calculator">9 - 2</gadget> <output>7</output> <result>B</result>

B

x+(1/x) = 3 find x^2 + (1/x^2)

subtract(power(3, 2), 2)

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

"squaring on both sides ( x + 1 / x ) ^ 2 = 3 ^ 2 x ^ 2 + 1 / x ^ 2 = 9 - 2 x ^ 2 + 1 / x ^ 2 = 7 answer : b"

general

math_qa__ovNN2iusEZ1vkJh5

A certain debt will be paid in 52 installments from January 1 to December 31 of a certain year. Each of the first 8 payments is to be $410; each of the remaining payments is to be $65 more than each of the first 8 payments. What is the average (arithmetic mean) payment that will be made on the debt for the year? Choices: A) 443 B) 450 C) 465 D) 468 E) 475

<gadget id="calculator">8 * 410</gadget> <output>3_280</output> <gadget id="calculator">410 + 65</gadget> <output>475</output> <gadget id="calculator">52 - 8</gadget> <output>44</output> <gadget id="calculator">475 * 44</gadget> <output>20_900</output> <gadget id="calculator">3_280 + 20_900</gadget> <output>24_180</output> <gadget id="calculator">24_180 / 52</gadget> <output>465</output> <result>C</result>

C

A certain debt will be paid in 52 installments from January 1 to December 31 of a certain year. Each of the first 8 payments is to be $410; each of the remaining payments is to be $65 more than each of the first 8 payments. What is the average (arithmetic mean) payment that will be made on the debt for the year?

divide(add(multiply(8, 410), multiply(add(410, 65), subtract(52, 8))), 52)

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

"total number of installments = 52 payment per installment for the first 8 installments = 410 payment per installment for the remaining 32 installments = 410 + 65 = 475 average = ( 8 * 410 + 44 * 475 ) / 52 = 465 answer c"

general

math_qa__VlWN7BHAzO8SQ92s

The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 20 terms of the arithmetic progression? Choose the correct choice from the following choices: A) 300 B) 120 C) 150 D) 170 E) 200

<gadget id="calculator">20 * 20</gadget> <output>400</output> <gadget id="calculator">400 / 2</gadget> <output>200</output> <result>E</result>

E

The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 20 terms of the arithmetic progression?

divide(multiply(20, 20), const_2)

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

"n th term of a . p . is given by a + ( n - 1 ) d 4 th term = a + 3 d 12 th term = a + 11 d given a + 3 d + a + 11 d = 20 - - > 2 a + 14 d = 20 - - > a + 7 d = 10 sum of n term of a . p = n / 2 [ 2 a + ( n - 1 ) d ] subsitiuing n = 20 . . . we get 20 / 2 [ 2 a + 14 d ] = 20 [ a + 7 d ] = 20 * 10 = 200 . . . answer is e . . ."

general

math_qa__cbSKtNWOtNR49S4d

A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3100, A will get: Select A) rs . 1200 B) rs . 1500 C) rs . 1860 D) rs . 2000 E) none of these

<gadget id="calculator">15 * 2</gadget> <output>30</output> <gadget id="calculator">30 / 10</gadget> <output>3</output> <gadget id="calculator">30 / 15</gadget> <output>2</output> <gadget id="calculator">3 + 2</gadget> <output>5</output> <gadget id="calculator">3 / 5</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">(3/5) * 3_100</gadget> <output>1_860</output> <result>C</result>

C

A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3100, A will get:

multiply(divide(divide(multiply(15, const_2), 10), add(divide(multiply(15, const_2), 10), divide(multiply(15, const_2), 15))), 3100)

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

explanation : ratio of working days of a : b = 10 : 15 therefore , their wages ratio = reverse ratio = 15 : 10 therefore , a will get 15 units of ratio total ratio = 25 1 unit of ratio = 3100 / 25 = 124 so , a ’ s amount = 124 × 15 = rs . 1860 . answer : option c

physics

math_qa__hARgW6bKDdena3kj

Crazy Eddie has a key chain factory. Eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price, and thus increased the profit from the sale of each key chain from 40% of the selling price to 50% of the selling price. If the manufacturing cost is now $50, what was it before the decrease? Choose the correct choice from the following options: A) $ 20 B) $ 40 C) $ 50 D) $ 80 E) $ 60

<gadget id="calculator">50 / 100</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">50 / (1/2)</gadget> <output>100</output> <gadget id="calculator">40 / 100</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">100 * (2/5)</gadget> <output>40</output> <gadget id="calculator">100 - 40</gadget> <output>60</output> <result>E</result>

E

Crazy Eddie has a key chain factory. Eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price, and thus increased the profit from the sale of each key chain from 40% of the selling price to 50% of the selling price. If the manufacturing cost is now $50, what was it before the decrease?

subtract(divide(50, divide(50, const_100)), multiply(divide(50, divide(50, const_100)), divide(40, const_100)))

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

"deargoodyear 2013 , i ' m happy to help . this is a relatively straightforward problem , not very challenging . btw , crazy eddiewas the actually name of an electronics chain on the east coast of the usa back in the 1970 s . manufacturing now is $ 50 . they now are making a 50 % profit , so the selling price must be $ 100 . they had this same selling price , $ 100 , before they made the change , and had a profit of 40 % , so the manufacturing must have been $ 60 . answer = ( e ) ."

general

math_qa__DHubKGdlrHQGvMGf

While driving from A-ville to B-town, Harriet drove at a constant speed of 110 kilometers per hour. Upon arriving in B-town, Harriet immediately turned and drove back to A-ville at a constant speed of 140 kilometers per hour. If the entire trip took 5 hours, how many minutes did it take Harriet to drive from A-ville to B-town? Choose the correct choice A) 138 B) 148 C) 150 D) 162 E) 168

<gadget id="calculator">110 * 5</gadget> <output>550</output> <gadget id="calculator">110 + 140</gadget> <output>250</output> <gadget id="calculator">550 / 250</gadget> <output>11/5 = around 2.2</output> <gadget id="calculator">5 - (11/5)</gadget> <output>14/5 = around 2.8</output> <gadget id="calculator">(14/5) * 60</gadget> <output>168</output> <result>E</result>

E

While driving from A-ville to B-town, Harriet drove at a constant speed of 110 kilometers per hour. Upon arriving in B-town, Harriet immediately turned and drove back to A-ville at a constant speed of 140 kilometers per hour. If the entire trip took 5 hours, how many minutes did it take Harriet to drive from A-ville to B-town?

multiply(subtract(5, divide(multiply(110, 5), add(110, 140))), const_60)

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

"5 hr = 300 min . if harriet spend equal hrs on each leg she will spend 150 min on each . since speed a - b is less than speed b - a and distance on each leg is the same , time spent on a - b is more than 150 min , which mean we can eliminate ans . a , b and c . now let plug in ans . d or e and verify which one give same distance on each leg . e . t = 168 min * leg a - b - - - > d = 110.168 / 60 = 18480 / 60 * leg b - a - - - - > d = 140 * 132 / 60 = 18480 / 60 so the correct ans . ise"

physics

math_qa__AK7FypivupV4HR5v

If the average of 1, 2, 4, 5, 6, 9, 9, 10, 12 and x is 7, what is the value of x? Choose the correct choice from the following: A) 7 B) 9 C) 11 D) 12 E) 13

<gadget id="calculator">7 * 10</gadget> <output>70</output> <gadget id="calculator">1 + 2</gadget> <output>3</output> <gadget id="calculator">3 + 4</gadget> <output>7</output> <gadget id="calculator">7 + 5</gadget> <output>12</output> <gadget id="calculator">12 + 6</gadget> <output>18</output> <gadget id="calculator">18 + 9</gadget> <output>27</output> <gadget id="calculator">27 + 9</gadget> <output>36</output> <gadget id="calculator">36 + 10</gadget> <output>46</output> <gadget id="calculator">46 + 12</gadget> <output>58</output> <gadget id="calculator">70 - 58</gadget> <output>12</output> <result>D</result>

D

If the average of 1, 2, 4, 5, 6, 9, 9, 10, 12 and x is 7, what is the value of x?

subtract(multiply(7, const_10), add(add(add(add(add(add(add(add(1, 2), 4), 5), 6), 9), 9), 10), 12))

add(n0,n1)|multiply(n9,const_10)|add(n2,#0)|add(n3,#2)|add(n4,#3)|add(n5,#4)|add(n5,#5)|add(n7,#6)|add(n8,#7)|subtract(#1,#8)|

"sum of the deviations of the numbers in the set from the mean is always zero 1 , 2 , 4 , 5 , 6 , 9 , 9 , 10 , 12 mean is 7 so the list is - 6 - 5 - 3 - 2 - 1 + 2 + 2 + 3 + 5 . . . this shud total to zero but this is - 5 , hence we need a number that is 5 more than the mean to get a + 5 and make it zero hence the answer is 7 + 5 = 12 d"

general

math_qa__KBc4YcHEr99liiJP

A jogger running at 9 km/hr along side a railway track is 200 m ahead of the engine of a 200 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? Choose one: A) 89 B) 20 C) 40 D) 88 E) 34

<gadget id="calculator">200 + 200</gadget> <output>400</output> <gadget id="calculator">45 - 9</gadget> <output>36</output> <gadget id="calculator">10 / 2</gadget> <output>5</output> <gadget id="calculator">36 / 2</gadget> <output>18</output> <gadget id="calculator">5 / 18</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">36 * (5/18)</gadget> <output>10</output> <gadget id="calculator">400 / 10</gadget> <output>40</output> <result>C</result>

C

A jogger running at 9 km/hr along side a railway track is 200 m ahead of the engine of a 200 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?

divide(add(200, 200), multiply(subtract(45, 9), divide(divide(const_10, const_2), divide(subtract(45, 9), const_2))))

add(n1,n2)|divide(const_10,const_2)|subtract(n3,n0)|divide(#2,const_2)|divide(#1,#3)|multiply(#4,#2)|divide(#0,#5)|

"speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 200 + 200 = 360 m . time taken = 400 / 10 = 40 sec . answer : option c"

general

math_qa__ajeOhyLjhkdRlHhB

The dimensions of an open box are 50 cm, 40 cm and 23 cm. Its thickness is 2 cm. If 1 cubic cm of metal used in the box weighs 0.5 gms, find the weight of the box. Choose the correct answer: A) 8.04 kg B) 8.14 kg C) 8.24 kg D) 9.04 kg E) none of these

<gadget id="calculator">50 * 40</gadget> <output>2_000</output> <gadget id="calculator">2_000 * 23</gadget> <output>46_000</output> <gadget id="calculator">2 * 3</gadget> <output>6</output> <gadget id="calculator">50 - 6</gadget> <output>44</output> <gadget id="calculator">40 - 6</gadget> <output>34</output> <gadget id="calculator">44 * 34</gadget> <output>1_496</output> <gadget id="calculator">23 - 3</gadget> <output>20</output> <gadget id="calculator">1_496 * 20</gadget> <output>29_920</output> <gadget id="calculator">46_000 - 29_920</gadget> <output>16_080</output> <gadget id="calculator">16_080 * 0.5</gadget> <output>8_040</output> <gadget id="calculator">8_040 / 1_000</gadget> <output>201/25 = around 8.04</output> <result>A</result>

A

The dimensions of an open box are 50 cm, 40 cm and 23 cm. Its thickness is 2 cm. If 1 cubic cm of metal used in the box weighs 0.5 gms, find the weight of the box.

divide(multiply(subtract(multiply(multiply(50, 40), 23), multiply(multiply(subtract(50, multiply(2, const_3)), subtract(40, multiply(2, const_3))), subtract(23, const_3))), 0.5), const_1000)

multiply(n0,n1)|multiply(n3,const_3)|subtract(n2,const_3)|multiply(n2,#0)|subtract(n0,#1)|subtract(n1,#1)|multiply(#4,#5)|multiply(#6,#2)|subtract(#3,#7)|multiply(n5,#8)|divide(#9,const_1000)

explanation : volume of the metal used in the box = external volume - internal volume = [ ( 50 x 40 x 23 ) - ( 44 x 34 x 20 ) ] cm 3 = 16080 cm 3 weight of the metal = [ ( 16080 x 0.5 ) / 1000 ] kg = 8.04 kg . answer : a

physics

math_qa__ur5DpbDSM67VuhTp

Mike needs 30% to pass. If he scored 212 marks and falls short by 25 marks, what was the maximum marks he could have got? Select the correct option: A) 343 B) 677 C) 790 D) 867 E) 932

<gadget id="calculator">212 + 25</gadget> <output>237</output> <gadget id="calculator">30 / 100</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">237 / (3/10)</gadget> <output>790</output> <result>C</result>

C

Mike needs 30% to pass. If he scored 212 marks and falls short by 25 marks, what was the maximum marks he could have got?

divide(add(212, 25), divide(30, const_100))

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

"if mike had scored 25 marks more , he could have scored 30 % therefore , mike required 212 + 25 = 237 marks let the maximum marks be m . then 30 % of m = 237 ( 30 / 100 ) × m = 237 m = ( 237 × 100 ) / 30 m = 23700 / 30 m = 790 answer : c"

gain

math_qa__sCMMvBN12xRylRXF

An aeroplane covers a certain distance of 420 Kmph in 6 hours. to cover the same distance in 4 2/3 hours, it Must travel at a speed of ? Select the correct option A) 450 km B) 480 km C) 500 km D) 540 km E) 590 km

<gadget id="calculator">420 * 6</gadget> <output>2_520</output> <gadget id="calculator">3 * 4</gadget> <output>12</output> <gadget id="calculator">12 + 2</gadget> <output>14</output> <gadget id="calculator">14 / 3</gadget> <output>14/3 = around 4.666667</output> <gadget id="calculator">2_520 / (14/3)</gadget> <output>540</output> <result>D</result>

D

An aeroplane covers a certain distance of 420 Kmph in 6 hours. to cover the same distance in 4 2/3 hours, it Must travel at a speed of ?

divide(multiply(420, 6), divide(add(multiply(3, 4), 2), 3))

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

"speed of aeroplane = 420 kmph distance travelled in 6 hours = 420 * 6 = 2520 km speed of aeroplane to acver 2520 km in 14 / 3 = 2520 * 3 / 14 = 540 km answer : option ' d '"

physics

math_qa__nyihdZFGB5ODBmYJ

What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 15%? Choose one: A) 20 % B) 27.5 % C) 10 % D) 80 % E) 90 %

<gadget id="calculator">100 - 15</gadget> <output>85</output> <gadget id="calculator">2 / 3</gadget> <output>2/3 = around 0.666667</output> <gadget id="calculator">85 / (2/3)</gadget> <output>255/2 = around 127.5</output> <gadget id="calculator">(255/2) - 100</gadget> <output>55/2 = around 27.5</output> <result>B</result>

B

What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 15%?

subtract(divide(subtract(const_100, 15), divide(2, 3)), const_100)

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

"sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 85 2 / 3 sp 1 = 85 sp 1 = 127.5 100 - - - 27.5 = > 27.5 % answer : b"

gain

math_qa__DWIeWbMVdtfwi2Gn

Machine P and Machine Q are each used to manufacture 880 sprockets. It takes Machine P 10 hours longer to produce 880 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce? Select the correct option. A) 2 B) 4 C) 6 D) 8 E) 10

<gadget id="calculator">10 / 100</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">(1/10) + 1</gadget> <output>11/10 = around 1.1</output> <gadget id="calculator">880 / (11/10)</gadget> <output>800</output> <gadget id="calculator">880 - 800</gadget> <output>80</output> <gadget id="calculator">80 / 10</gadget> <output>8</output> <result>D</result>

D

Machine P and Machine Q are each used to manufacture 880 sprockets. It takes Machine P 10 hours longer to produce 880 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce?

divide(subtract(880, divide(880, add(divide(10, const_100), const_1))), 10)

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

"p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 880 / x = 880 / 1.1 x + 10 1.1 ( 880 ) = 880 + 11 x 11 x = 88 x = 8 the answer is d ."

gain

math_qa__uzAUpS23maOz3kC2

In an examination 35% of the students passed and 351 failed. How many students appeared for the examination? Answers. A) 540 B) 400 C) 700 D) 650 E) 840

<gadget id="calculator">351 * 100</gadget> <output>35_100</output> <gadget id="calculator">100 - 35</gadget> <output>65</output> <gadget id="calculator">35_100 / 65</gadget> <output>540</output> <result>A</result>

A

In an examination 35% of the students passed and 351 failed. How many students appeared for the examination?

divide(multiply(351, const_100), subtract(const_100, 35))

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

let the number of students appeared be x then , 65 % of x = 351 65 x / 100 = 351 x = 351 * 100 / 65 = 540 answer is a

gain

math_qa__vKIMGkOlIu5Q7sEN

What is the average of 1200, 1300, 1400, 1510, 1520, 1530, and 1200? Answers A) 1360.47 B) 1355.8 C) 1380 D) 1350 E) 1333

<gadget id="calculator">1_200 + 1_300</gadget> <output>2_500</output> <gadget id="calculator">2_500 + 1_400</gadget> <output>3_900</output> <gadget id="calculator">3_900 + 1_510</gadget> <output>5_410</output> <gadget id="calculator">5_410 + 1_520</gadget> <output>6_930</output> <gadget id="calculator">6_930 + 1_530</gadget> <output>8_460</output> <gadget id="calculator">8_460 + 1_200</gadget> <output>9_660</output> <gadget id="calculator">3 + 4</gadget> <output>7</output> <gadget id="calculator">9_660 / 7</gadget> <output>1_380</output> <result>C</result>

C

What is the average of 1200, 1300, 1400, 1510, 1520, 1530, and 1200?

divide(add(add(add(add(add(add(1200, 1300), 1400), 1510), 1520), 1530), 1200), add(const_3, const_4))

add(n0,n1)|add(const_3,const_4)|add(n2,#0)|add(n3,#2)|add(n4,#3)|add(n5,#4)|add(n0,#5)|divide(#6,#1)

add 1200 , 1300 , 1400 , 1510 , 1520 , 1530 , and 1200 grouping numbers together may quicken the addition sum = 9660 9660 / 7 = 1380 c

general

math_qa__1T4M5zChqdg7tS76

If w is 40 percent less than q, q is 40 percent less than y, and z is 46 percent less than y, then z is greater than w by what percent of w? Pick one. A) 4 % B) 18 % C) 36 % D) 40 % E) 50 %

<gadget id="calculator">100 - 46</gadget> <output>54</output> <gadget id="calculator">100 - 40</gadget> <output>60</output> <gadget id="calculator">40 * 60</gadget> <output>2_400</output> <gadget id="calculator">2_400 / 100</gadget> <output>24</output> <gadget id="calculator">60 - 24</gadget> <output>36</output> <gadget id="calculator">54 - 36</gadget> <output>18</output> <gadget id="calculator">18 / 36</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">(1/2) * 100</gadget> <output>50</output> <result>E</result>

E

If w is 40 percent less than q, q is 40 percent less than y, and z is 46 percent less than y, then z is greater than w by what percent of w?

multiply(divide(subtract(subtract(const_100, 46), subtract(subtract(const_100, 40), divide(multiply(40, subtract(const_100, 40)), const_100))), subtract(subtract(const_100, 40), divide(multiply(40, subtract(const_100, 40)), const_100))), const_100)

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

given w = 0.6 q , q = 0.6 y , z = 0.54 y , substituting , w = 2 / 3 z - - - - > z = 1.5 w and thus z is 50 % greater than w . e is the correct answer .

gain

math_qa__Kx6Tm5onYS3WwKJc

A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 12%. What was its profit on the items sold in February? Select the correct option A) 27.5 % B) 32 % C) 35 % D) 37.5 % E) 40 %

<gadget id="calculator">100 - 12</gadget> <output>88</output> <gadget id="calculator">88 / 100</gadget> <output>22/25 = around 0.88</output> <gadget id="calculator">100 + 20</gadget> <output>120</output> <gadget id="calculator">100 + 25</gadget> <output>125</output> <gadget id="calculator">125 / 100</gadget> <output>5/4 = around 1.25</output> <gadget id="calculator">120 * (5/4)</gadget> <output>150</output> <gadget id="calculator">(22/25) * 150</gadget> <output>132</output> <gadget id="calculator">132 - 100</gadget> <output>32</output> <result>B</result>

B

A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 12%. What was its profit on the items sold in February?

subtract(multiply(divide(subtract(const_100, 12), const_100), multiply(add(const_100, 20), divide(add(const_100, 25), const_100))), const_100)

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

"assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.88 * 150 x = 132 x hence total profit = 32 % option b"

gain

math_qa__b6TSSezzWhELuHyT

A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18600. A's share is? Choose the correct choice A) 8876 B) 2765 C) 6000 D) 6200 E) 1261

<gadget id="calculator">1 * 12</gadget> <output>12</output> <gadget id="calculator">12 - 6</gadget> <output>6</output> <gadget id="calculator">6 * 2</gadget> <output>12</output> <gadget id="calculator">12 + 12</gadget> <output>24</output> <gadget id="calculator">12 - 8</gadget> <output>4</output> <gadget id="calculator">4 * 3</gadget> <output>12</output> <gadget id="calculator">24 + 12</gadget> <output>36</output> <gadget id="calculator">18_600 / 36</gadget> <output>1_550/3 = around 516.666667</output> <gadget id="calculator">12 * (1_550/3)</gadget> <output>6_200</output> <result>D</result>

D

A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18600. A's share is?

multiply(multiply(const_1, const_12), divide(18600, add(add(multiply(const_1, const_12), multiply(subtract(const_12, 6), const_2)), multiply(subtract(const_12, 8), const_3))))

multiply(const_1,const_12)|subtract(const_12,n0)|subtract(const_12,n1)|multiply(#1,const_2)|multiply(#2,const_3)|add(#0,#3)|add(#5,#4)|divide(n2,#6)|multiply(#7,#0)|

"x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 18600 = 6200 answer : d"

gain

math_qa__GrNSuViG09e5XrmV

a student took 5 papers in an examination , where the full marks were the same for each paper . his marks in these papers were in the proportion of 5 : 6 : 7 : 8 : 9 . in all papers together , the candidate obtained 60 % of the total marks . then the number of papers in which he got more than 50 % marks is Choose one. A) 2 B) 3 C) 4 D) 5 E) 1

<gadget id="calculator">1 + 4</gadget> <output>5</output> <result>D</result>

D

a student took 5 papers in an examination , where the full marks were the same for each paper . his marks in these papers were in the proportion of 5 : 6 : 7 : 8 : 9 . in all papers together , the candidate obtained 60 % of the total marks . then the number of papers in which he got more than 50 % marks is

add(const_1, const_4)

add(const_1,const_4)

here we can assume that one subject is of 100 marks so total there are 5 subjects = > 100 * 5 = 500 . now according to the question he secured 60 % of those which is 60 % of 500 = 300 marks in total . the ratio between the marks is given as 5 : 6 : 7 : 8 : 9 , so now we can distribute 300 marks according to the ratio . total ratio = 35 for 6 : ( 300 / 35 ) * 6 = 51.4 similarly , we will get for others as 60 , 68.57 , 77.14 hence , there are 5 subject where he secured more that 50 % . the answer is 5 . d

general

math_qa__zczljkVmy2yofhx0

If x ¤ y = (x + y)^2 - (x - y)^2. Then √6 ¤ √6 = Choose the correct choice from the following. A) 0 B) 5 C) 10 D) 24 E) 20

<gadget id="calculator">6 ** (1/2)</gadget> <output>sqrt(6) = around 2.44949</output> <gadget id="calculator">(sqrt(6)) + (sqrt(6))</gadget> <output>2*sqrt(6) = around 4.898979</output> <gadget id="calculator">(2*sqrt(6)) ** 2</gadget> <output>24</output> <result>D</result>

D

If x ¤ y = (x + y)^2 - (x - y)^2. Then √6 ¤ √6 =

power(add(sqrt(6), sqrt(6)), 2)

sqrt(n2)|add(#0,#0)|power(#1,n0)|

"x = √ 6 and y also = √ 6 applying the function ( √ 6 + √ 6 ) ^ 2 - ( √ 6 - √ 6 ) ^ 2 = ( 2 √ 6 ) ^ 2 - 0 = 4 x 6 = 24 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = √ 6 and y = √ 6 you get the answer 24 . answer d"

general

math_qa__tzwMJHi9yv1ALG3T

An investment yields an interest payment of $240 each month. If the simple annual interest rate is 9%, what is the amount of the investment? Choose the correct choice. A) $ 28,300 B) $ 30,400 C) $ 31,300 D) $ 32,500 E) $ 32,000

<gadget id="calculator">3 * 4</gadget> <output>12</output> <gadget id="calculator">9 / 12</gadget> <output>3/4 = around 0.75</output> <gadget id="calculator">240 / (3/4)</gadget> <output>320</output> <gadget id="calculator">320 * 100</gadget> <output>32_000</output> <result>E</result>

E

An investment yields an interest payment of $240 each month. If the simple annual interest rate is 9%, what is the amount of the investment?

multiply(divide(240, divide(9, multiply(const_3, const_4))), const_100)

multiply(const_3,const_4)|divide(n1,#0)|divide(n0,#1)|multiply(#2,const_100)|

"let the principal amount = p simple annual interest = 9 % simple monthly interest = ( 9 / 12 ) = ( 3 / 4 ) % ( 3 / 4 ) * ( p / 100 ) = 240 = > p = ( 240 * 4 * 10 ^ 2 ) / 3 = 80 * 4 * 10 ^ 2 = 320 * 10 ^ 2 = 32000 answer e"

gain

math_qa__W9Cw5IJJK9lXflCC

The inner circumference of a circular race track, 14 m wide, is 440 m. Find radius of the outer circle? Choose one: A) 22 B) 37 C) 87 D) 84 E) 82

<gadget id="calculator">440 / pi</gadget> <output>440/pi = around 140.05635</output> <gadget id="calculator">(440/pi) / 2</gadget> <output>220/pi = around 70.028175</output> <gadget id="calculator">14 + (220/pi)</gadget> <output>14 + 220/pi = around 84.028175</output> <result>D</result>

D

The inner circumference of a circular race track, 14 m wide, is 440 m. Find radius of the outer circle?

add(14, divide(divide(440, const_pi), const_2))

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

"let inner radius be r metres . then , 2 r = 440 ; r = = 70 m . radius of outer circle = ( 70 + 14 ) m = 84 m . answer : d"

physics

math_qa__eaVPMXQeS74VdQNs

The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 25hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor? Choose the correct answer. A) 400 km B) 500 km C) 331.2 km D) 550 km E) 600 km

<gadget id="calculator">4 / 5</gadget> <output>4/5 = around 0.8</output> <gadget id="calculator">1 + (4/5)</gadget> <output>9/5 = around 1.8</output> <gadget id="calculator">575 / 25</gadget> <output>23</output> <gadget id="calculator">2 * 23</gadget> <output>46</output> <gadget id="calculator">(9/5) * 46</gadget> <output>414/5 = around 82.8</output> <gadget id="calculator">(414/5) * 4</gadget> <output>1_656/5 = around 331.2</output> <result>C</result>

C

The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 25hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor?

multiply(multiply(add(1, divide(4, 5)), multiply(const_2, divide(575, 25))), 4)

divide(n1,n2)|divide(n3,n4)|add(n0,#0)|multiply(#1,const_2)|multiply(#2,#3)|multiply(n5,#4)|

"sol . average speed of a tractor = 23 km / h the speed of a bus in an hour = 23 × 2 = 46 km the speed of a car in an hour = 9 / 5 * 46 = 82.8 km so , the distance covered by car in 4 h is 82.8 × 4 = 331.2 km ans . ( c )"

general

math_qa__AU3Th2qK1RLxbIr8

There are 56 lights which are functional and each is controlled by a separate On/Off switch. Two children X and Y start playing with the switches. X starts by pressing every third switch till he reaches the end. Y, thereafter, presses every fifth switch till he too reaches the end. If all switches were in Off position at the beggining, How many lights are switched On by the end of this operation? Choose the correct answer A) 18 B) 19 C) 17 D) 15 E) 16

<gadget id="calculator">4 * 10</gadget> <output>40</output> <gadget id="calculator">56 - 40</gadget> <output>16</output> <gadget id="calculator">16 + 1</gadget> <output>17</output> <result>C</result>

C

There are 56 lights which are functional and each is controlled by a separate On/Off switch. Two children X and Y start playing with the switches. X starts by pressing every third switch till he reaches the end. Y, thereafter, presses every fifth switch till he too reaches the end. If all switches were in Off position at the beggining, How many lights are switched On by the end of this operation?

add(subtract(56, multiply(const_4, const_10)), const_1)

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

editing my solution : number of switches = 56 number of switches turned on by x : 3 , 6 , . . . 54 = 18 number of switches turned on by y : 5 , 10 , . . . . 55 = 11 few switches are turned on by x and later turned off by y : lcm ( 35 ) = 15 x = 15 , 30 , . . . . 90 = 6 . subtract the above 6 switches from both x and y as they are turned off . number of switches that are turned on = ( 18 - 6 ) + ( 11 - 6 ) = 17 answer : c

general

math_qa__xoGJr6YUf9VhT5TH

The difference between the local value and face value of 7 in the numeral 657903 is: Select. A) 0 B) 7896 C) 6993 D) 903 E) 803

<gadget id="calculator">7 * 1_000</gadget> <output>7_000</output> <gadget id="calculator">7_000 - 7</gadget> <output>6_993</output> <result>C</result>

C

The difference between the local value and face value of 7 in the numeral 657903 is:

subtract(multiply(7, const_1000), 7)

multiply(n0,const_1000)|subtract(#0,n0)

( local value ) - ( face value ) = ( 7000 - 7 ) = 6993 . answer : c

general

math_qa__gvhugnkpynFDHPB1

Find the value of b from (15)^2 x 9^2 ÷ 356 = b. Choices: A) 53.2 B) 52.2 C) 51.2 D) 8.2 E) 54.2

<gadget id="calculator">15 ** 2</gadget> <output>225</output> <gadget id="calculator">9 ** 2</gadget> <output>81</output> <gadget id="calculator">225 * 81</gadget> <output>18_225</output> <gadget id="calculator">18_225 / 356</gadget> <output>18_225/356 = around 51.19382</output> <result>C</result>

C

Find the value of b from (15)^2 x 9^2 ÷ 356 = b.

divide(multiply(power(15, 2), power(9, 2)), 356)

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

given exp . = ( 15 ) ^ 2 x 9 ^ 2 ã · 356 = b = 225 x 81 ã · 356 = 51.2 c

general

math_qa__oeCtgKAJkrzrq74G

An order was placed for a carpet whose length and width were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and width were in the ratio 1 : 1 but were was no change in its perimeter. What is the ratio of the areas of the carpets? Pick: A) 4 : 5 B) 9 : 10 C) 14 : 15 D) 19 : 20 E) 24 : 25

<gadget id="calculator">3 * 2</gadget> <output>6</output> <gadget id="calculator">2 * (3 + 2)</gadget> <output>10</output> <gadget id="calculator">10 / 2</gadget> <output>5</output> <gadget id="calculator">1 + 1</gadget> <output>2</output> <gadget id="calculator">5 / 2</gadget> <output>5/2 = around 2.5</output> <gadget id="calculator">(5/2) * 1</gadget> <output>5/2 = around 2.5</output> <gadget id="calculator">(5/2) * (5/2)</gadget> <output>25/4 = around 6.25</output> <gadget id="calculator">6 / (25/4)</gadget> <output>24/25 = around 0.96</output> <result>E</result>

E

An order was placed for a carpet whose length and width were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and width were in the ratio 1 : 1 but were was no change in its perimeter. What is the ratio of the areas of the carpets?

divide(rectangle_area(3, 2), rectangle_area(divide(divide(rectangle_perimeter(3, 2), 2), add(1, 1)), multiply(divide(divide(rectangle_perimeter(3, 2), 2), add(1, 1)), 1)))

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

"let the length and width of one carpet be 3 x and 2 x . let the length and width of the other carpet be y and y . 2 ( 3 x + 2 x ) = 2 ( y + y ) 5 x = 2 y ( 5 / 2 ) * x = y the ratio of the areas of the carpet in both cases : = 3 x * 2 x : y * y = 6 x ^ 2 : y ^ 2 = 6 x ^ 2 : ( 25 / 4 ) * x ^ 2 = 24 : 25 the answer is e ."

geometry

math_qa__zb5EHOLgyqOjg4m6

How many cuboids of length 5 m, width 2 m and height 3 m can be farmed from a cuboid of 18 m length, 15 m width and 2 m height. Choose the correct choice from the following choices A) 10 B) 12 C) 15 D) 16 E) 18

<gadget id="calculator">18 * 15</gadget> <output>270</output> <gadget id="calculator">270 * 2</gadget> <output>540</output> <gadget id="calculator">5 * 2</gadget> <output>10</output> <gadget id="calculator">10 * 3</gadget> <output>30</output> <gadget id="calculator">540 / 30</gadget> <output>18</output> <result>E</result>

E

How many cuboids of length 5 m, width 2 m and height 3 m can be farmed from a cuboid of 18 m length, 15 m width and 2 m height.

divide(multiply(multiply(18, 15), 2), multiply(multiply(5, 2), 3))

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

"( 18 ã — 15 ã — 12 ) / ( 5 ã — 3 ã — 2 ) = 18 answer is e ."

physics

math_qa__5w1PVepb4dJLgJ9c

An engineer undertakes a project to build a road 10 km long in 60 days and employs 30 men for the purpose. After 20 days, he finds only 2 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time. Choices: A) 20 B) 15 C) 30 D) 45 E) 60

<gadget id="calculator">10 - 2</gadget> <output>8</output> <gadget id="calculator">30 * 8</gadget> <output>240</output> <gadget id="calculator">240 * 20</gadget> <output>4_800</output> <gadget id="calculator">60 - 20</gadget> <output>40</output> <gadget id="calculator">2 * 40</gadget> <output>80</output> <gadget id="calculator">4_800 / 80</gadget> <output>60</output> <gadget id="calculator">60 - 30</gadget> <output>30</output> <result>C</result>

C

An engineer undertakes a project to build a road 10 km long in 60 days and employs 30 men for the purpose. After 20 days, he finds only 2 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time.

subtract(divide(multiply(multiply(30, subtract(10, 2)), 20), multiply(2, subtract(60, 20))), 30)

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

"30 workers working already let x be the total men required to finish the task in next 40 days 2 km done hence remaining is 8 km also , work has to be completed in next 40 days ( 60 - 20 = 40 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 30 * 8 * 20 ) / ( 2 * 40 ) thus , x = 60 thus , more men needed to finish the task = 60 - 30 = 30 answer : c"

physics

math_qa__ueUQl3lC2jHsUsBi

A retailer bought a machine at a wholesale price of $81 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price of the machine? Choices: A) 81 B) 108 C) 120 D) 135 E) 160

<gadget id="calculator">81 * 20</gadget> <output>1_620</output> <gadget id="calculator">1_620 / 100</gadget> <output>81/5 = around 16.2</output> <gadget id="calculator">81 + (81/5)</gadget> <output>486/5 = around 97.2</output> <gadget id="calculator">(486/5) * 100</gadget> <output>9_720</output> <gadget id="calculator">3 * 3</gadget> <output>9</output> <gadget id="calculator">9 * 10</gadget> <output>90</output> <gadget id="calculator">9_720 / 90</gadget> <output>108</output> <result>B</result>

B

A retailer bought a machine at a wholesale price of $81 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price of the machine?

divide(multiply(add(81, divide(multiply(81, 20), const_100)), const_100), multiply(multiply(const_3, const_3), 10))

multiply(n0,n2)|multiply(const_3,const_3)|divide(#0,const_100)|multiply(n1,#1)|add(n0,#2)|multiply(#4,const_100)|divide(#5,#3)|

"my solution : wholesale price = 81 retail price , be = x he provides 10 % discount on retail price = x - 10 x / 100 this retail price = 20 % profit on wholesale price x - 10 x / 100 = 81 + 1 / 5 ( 81 ) x = 108 ; answer : b"

gain

math_qa__3Eclb53lK3DlLoAg

At steel factory, each employee working the second shift produced 2/3 as many widgets as each employee working the first shift. If the first shift has 3/4 as many employees, what fraction of the total widgets did the second shift produce? Choose the correct choice A) 8 / 17 B) 1 / 2 C) 8 / 9 D) 9 / 8 E) 17 / 8

<gadget id="calculator">2 / 3</gadget> <output>2/3 = around 0.666667</output> <gadget id="calculator">(2/3) * 4</gadget> <output>8/3 = around 2.666667</output> <gadget id="calculator">3 + (8/3)</gadget> <output>17/3 = around 5.666667</output> <gadget id="calculator">(8/3) / (17/3)</gadget> <output>8/17 = around 0.470588</output> <result>A</result>

A

At steel factory, each employee working the second shift produced 2/3 as many widgets as each employee working the first shift. If the first shift has 3/4 as many employees, what fraction of the total widgets did the second shift produce?

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

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

at steel factory , let the first shift have 3 employee and each produce 3 widgets , so the total number of widgets produced by the first shift is 3 * 3 = 9 ; then the second shift would have 4 employees and each second shift employee would produce 3 * 2 / 3 = 2 widgets , so the total number of widgets produced by the second shift employees would be 4 * 2 = 8 ; the ratio of the second shift production to the total is 8 / ( 9 + 8 ) = 8 / 17 . answer : a .

physics

math_qa__ZL8m6zV5DSzWw4sJ

A circular swimming pool is surrounded by a concrete wall 4ft wide. If the area of the concrete wall surrounding the pool is 11/25 that of the pool, then the radius of the pool is? Choose the correct choice from the following: A) 22 B) 20 C) 88 D) 387 E) 19

<gadget id="calculator">2 * 4</gadget> <output>8</output> <gadget id="calculator">8 ** 2</gadget> <output>64</output> <gadget id="calculator">11 / 25</gadget> <output>11/25 = around 0.44</output> <gadget id="calculator">(11/25) * 4</gadget> <output>44/25 = around 1.76</output> <gadget id="calculator">4 ** 2</gadget> <output>16</output> <gadget id="calculator">(44/25) * 16</gadget> <output>704/25 = around 28.16</output> <gadget id="calculator">64 + (704/25)</gadget> <output>2_304/25 = around 92.16</output> <gadget id="calculator">(2_304/25) ** (1/2)</gadget> <output>48/5 = around 9.6</output> <gadget id="calculator">8 + (48/5)</gadget> <output>88/5 = around 17.6</output> <gadget id="calculator">(88/5) / (11/25)</gadget> <output>40</output> <gadget id="calculator">40 / 2</gadget> <output>20</output> <result>B</result>

B

A circular swimming pool is surrounded by a concrete wall 4ft wide. If the area of the concrete wall surrounding the pool is 11/25 that of the pool, then the radius of the pool is?

divide(divide(add(multiply(const_2, 4), sqrt(add(power(multiply(const_2, 4), const_2), multiply(multiply(divide(11, 25), 4), power(4, const_2))))), divide(11, 25)), const_2)

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

"let the radius of the pool be rft radius of the pool including the wall = ( r + 4 ) ft area of the concrete wall = { \ color { black } \ pi \ left [ ( r + 4 ) ^ { 2 } - r ^ { 2 } \ right ] } = { \ color { black } \ pi \ left [ ( r + 4 + r ) ( r + 4 - r ) \ right ] = 8 \ pi ( r + 2 ) } sq feet { \ color { black } \ rightarrow 8 \ pi ( r + 2 ) = \ frac { 11 } { 25 } \ pi r ^ { 2 } \ rightarrow 11 r ^ { 2 } = 200 ( r + 2 ) } radius of the pool r = 20 ft answer : b ) 20 ft"

geometry

math_qa__WC72OcATRCpy8kiE

36 men can complete a piece of work in 18 days. In how many days will 81 men complete the same work ? Choose the correct choice from the following answers: A) 8 B) 77 C) 88 D) 29 E) 21

<gadget id="calculator">18 * 36</gadget> <output>648</output> <gadget id="calculator">648 / 81</gadget> <output>8</output> <result>A</result>

A

36 men can complete a piece of work in 18 days. In how many days will 81 men complete the same work ?

divide(multiply(18, 36), 81)

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

"explanation : less men , means more days { indirect proportion } let the number of days be x then , 81 : 36 : : 18 : x x = 8 answer : a ) 8 days"

physics

math_qa__0swx8K5uTdjzMkF7

Simplify: 0.2*0.4+0.6*0.8 Choose the correct choice from the following options A) 0.52 B) 0.42 C) 0.48 D) 0.64 E) 0.56

<gadget id="calculator">0.2 * 0.4</gadget> <output>0.08</output> <gadget id="calculator">0.6 * 0.8</gadget> <output>0.48</output> <gadget id="calculator">0.08 + 0.48</gadget> <output>0.56</output> <result>E</result>

E

Simplify: 0.2*0.4+0.6*0.8

add(multiply(0.2, 0.4), multiply(0.6, 0.8))

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

"given exp . = 0.2 * 0.4 + ( 0.6 * 0.8 ) = 0.08 + 0.48 = 0.56 answer is e ."

general

math_qa__v0lQX38uteLS6MHG

What is 0.05 percent of 12,356? Choose the correct option. A) 0.6178 B) 61.78 C) 6.178 D) 0.06178 E) 0.006178

<gadget id="calculator">3 + 2</gadget> <output>5</output> <gadget id="calculator">5 * 2</gadget> <output>10</output> <gadget id="calculator">3 * 4</gadget> <output>12</output> <gadget id="calculator">12 * 100</gadget> <output>1_200</output> <gadget id="calculator">10 * 1_200</gadget> <output>12_000</output> <gadget id="calculator">3 + 4</gadget> <output>7</output> <gadget id="calculator">7 * 5</gadget> <output>35</output> <gadget id="calculator">35 * 10</gadget> <output>350</output> <gadget id="calculator">12_000 + 350</gadget> <output>12_350</output> <gadget id="calculator">3 + 3</gadget> <output>6</output> <gadget id="calculator">12_350 + 6</gadget> <output>12_356</output> <gadget id="calculator">0.05 * 12_356</gadget> <output>617.8</output> <gadget id="calculator">617.8 / 100</gadget> <output>6.178</output> <result>C</result>

C

What is 0.05 percent of 12,356?

divide(multiply(0.05, add(add(multiply(multiply(add(const_3, const_2), const_2), multiply(multiply(const_3, const_4), const_100)), multiply(multiply(add(const_3, const_4), add(const_3, const_2)), multiply(add(const_3, const_2), const_2))), add(const_3, const_3))), const_100)

add(const_2,const_3)|add(const_3,const_4)|add(const_3,const_3)|multiply(const_3,const_4)|multiply(#0,const_2)|multiply(#3,const_100)|multiply(#1,#0)|multiply(#4,#5)|multiply(#6,#4)|add(#7,#8)|add(#9,#2)|multiply(n0,#10)|divide(#11,const_100)

since , percent = 1 / 100 , what = something ( s ) , and is : = . we can write the question as s = 0.05 ( 1 / 100 ) 12,356 . the answer is 6.178 . hence , the correct answer is c .

gain

math_qa__M3FxVVlOPJbOXhkm

15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container S? Choose the correct answer: A) a : 45 B) b : 25 C) c : 37.5 D) d : 36 E) e : 42

<gadget id="calculator">9 + 16</gadget> <output>25</output> <gadget id="calculator">9 / 25</gadget> <output>9/25 = around 0.36</output> <gadget id="calculator">(9/25) ** (1/2)</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">1 - (3/5)</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">15 / (2/5)</gadget> <output>75/2 = around 37.5</output> <result>C</result>

C

15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container S?

divide(15, subtract(const_1, sqrt(divide(9, add(9, 16)))))

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

"if you have a 37.5 liter capacity , you start with 37.5 l of a and 0 l of b . 1 st replacement after the first replacement you have 37.5 - 15 = 22.5 l of a and 15 l of b . the key is figuring out how many liters of a and b , respectively , are contained in the next 15 liters of mixture to be removed . the current ratio of a to total mixture is 22.5 / 37.5 ; expressed as a fraction this becomes ( 45 / 2 ) / ( 75 / 2 ) , or 45 / 2 * 2 / 75 . canceling the 2 s and factoring out a 5 leaves the ratio as 9 / 15 . note , no need to reduce further as we ' re trying to figure out the amount of a and b in 15 l of solution . 9 / 15 of a means there must be 6 / 15 of b . multiply each respective ratio by 15 to get 9 l of a and 6 l of b in the next 15 l removal . final replacement the next 15 l removal means 9 liters of a and 6 liters of b are removed and replaced with 15 liters of b . 22.5 - 9 = 13.5 liters of a . 15 liters of b - 6 liters + 15 more liters = 24 liters of b . test to the see if the final ratio = 9 / 16 ; 13.5 / 24 = ( 27 / 2 ) * ( 1 / 24 ) = 9 / 16 . choice c is correct ."

general

math_qa__7U9ZVRK5ghdZRewd

A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio E of milk and water in the resultant mixture? Choose the correct choice from the following options A) 17 : 3 B) 9 : 1 C) 3 : 17 D) 5 : 3 E) 11 : 2

<gadget id="calculator">3 + 2</gadget> <output>5</output> <gadget id="calculator">3 / 5</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">20 - 10</gadget> <output>10</output> <gadget id="calculator">(3/5) * 10</gadget> <output>6</output> <gadget id="calculator">6 + 10</gadget> <output>16</output> <gadget id="calculator">16 / 20</gadget> <output>4/5 = around 0.8</output> <gadget id="calculator">(4/5) * 10</gadget> <output>8</output> <gadget id="calculator">8 + 10</gadget> <output>18</output> <gadget id="calculator">2 / 5</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">(2/5) * 10</gadget> <output>4</output> <gadget id="calculator">4 / 20</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(1/5) * 10</gadget> <output>2</output> <gadget id="calculator">18 / 2</gadget> <output>9</output> <result>B</result>

B

A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio E of milk and water in the resultant mixture?

divide(add(multiply(divide(add(multiply(divide(3, add(3, 2)), subtract(20, 10)), 10), 20), subtract(20, 10)), 10), multiply(divide(multiply(divide(2, add(3, 2)), subtract(20, 10)), 20), subtract(20, 10)))

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

"he 20 litre mixture contains milk and water in the ratio of 3 : 2 . therefore , there will be 12 litres of milk in the mixture and 8 litres of water in the mixture . step 1 . when 10 litres of the mixture is removed , 6 litres of milk is removed and 4 litres of water is removed . therefore , there will be 6 litres of milk and 4 litres of water left in the container . it is then replaced with pure milk of 10 litres . now the container will have 16 litres of milk and 4 litres of water . step 2 . when 10 litres of the new mixture is removed , 8 litres of milk and 2 litres of water is removed . the container will have 8 litres of milk and 2 litres of water in it . now 10 litres of pure milk is added . therefore , the container will have 18 litres of milk and 2 litres of water in it at the end of the second step . therefore , the ratio of milk and water is 18 : 2 or 9 : 1 . shortcut . we are essentially replacing water in the mixture with pure milk . let w _ o be the amount of water in the mixture originally = 8 litres . let w _ r be the amount of water in the mixture after the replacements have taken place . then , { w _ r } / { w _ o } = ( 1 - r / m ) ^ n where r is the amount of the mixture replaced by milk in each of the steps , m is the total volume of the mixture and n is the number of times the cycle is repeated . hence , { w _ r } / { w _ o }   = ( 1 / 2 ) ^ 2   = 1 / 4 therefore e , w _ r   = { w _ o } / 4 = 8 / 4   = 2 litres . b"

general

math_qa__qAI3gaVLh5QjMpfk

When Greenville State University decided to move its fine arts collection to a new library, it had to package the collection in 20-inch by 20-inch by 15-inch boxes. If the university pays $0.50 for every box, and if the university needs 3.06 million cubic inches to package the collection, what is the minimum amount the university must spend on boxes? Choose the correct choice from the following answers: A) $ 255 B) $ 275 C) $ 510 D) $ 1,250 E) $ 2,550

<gadget id="calculator">1_000 * 1_000</gadget> <output>1_000_000</output> <gadget id="calculator">3.06 * 1_000_000</gadget> <output>3_060_000</output> <gadget id="calculator">20 * 20</gadget> <output>400</output> <gadget id="calculator">400 * 15</gadget> <output>6_000</output> <gadget id="calculator">3_060_000 / 6_000</gadget> <output>510</output> <gadget id="calculator">510 * 0.5</gadget> <output>255</output> <result>A</result>

A

When Greenville State University decided to move its fine arts collection to a new library, it had to package the collection in 20-inch by 20-inch by 15-inch boxes. If the university pays $0.50 for every box, and if the university needs 3.06 million cubic inches to package the collection, what is the minimum amount the university must spend on boxes?

multiply(divide(multiply(3.06, multiply(const_1000, const_1000)), multiply(multiply(20, 20), 15)), 0.50)

multiply(const_1000,const_1000)|multiply(n0,n0)|multiply(n4,#0)|multiply(n2,#1)|divide(#2,#3)|multiply(n3,#4)|

"total no . of boxes = 3060000 / ( 20 × 20 × 15 ) = 510 total cost = 510 × $ 0.5 = $ 255 answer a"

general

math_qa__HIG3nYTOo7IbnobI

Diana works 10 hours per day on Monday, Wednesday and Friday, and 15 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $1800 per week. How much does she earn in dollars per hour? Choose the most appropriate option. A) 20 B) 22 C) 30 D) 24 E) 25

<gadget id="calculator">2 * 15</gadget> <output>30</output> <gadget id="calculator">10 * 3</gadget> <output>30</output> <gadget id="calculator">30 + 30</gadget> <output>60</output> <gadget id="calculator">1_800 / 60</gadget> <output>30</output> <result>C</result>

C

Diana works 10 hours per day on Monday, Wednesday and Friday, and 15 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $1800 per week. How much does she earn in dollars per hour?

divide(1800, add(multiply(const_2, 15), multiply(10, const_3)))

multiply(n1,const_2)|multiply(n0,const_3)|add(#0,#1)|divide(n2,#2)

so , she works 30 hours in 3 days so , she works 30 hours in 2 days so in a week she works 60 hours ( 30 + 30 ) and earns $ 1800 so , hourly wage is 1800 / 60 = > 30 hence answer will be ( c ) 30

physics

math_qa__ni6SOi56zoTtsBty

A car travels at a speed of 65 miles per hour. How far will it travel in 8 hours? Choose the correct choice. A) 125 miles B) 225 miles C) 520 miles D) 425 miles E) 525 miles

<gadget id="calculator">65 * 8</gadget> <output>520</output> <result>C</result>

C

A car travels at a speed of 65 miles per hour. How far will it travel in 8 hours?

multiply(65, 8)

multiply(n0,n1)|

"during each hour , the car travels 65 miles . for 8 hours it will travel 65 + 65 + 65 + 65 + 65 + 65 + 65 + 65 = 8 × 65 = 520 miles correct answer is c ) 520 miles"

physics

math_qa__gVzp8kQxUVMP6RR9

The mean of 50 observations was 36. It was found later that an observation 30 was wrongly taken as 23. The corrected new mean is : Choose the correct choice from the following answers: A) 36.02 B) 36.14 C) 36.12 D) 36.11 E) 36.8

<gadget id="calculator">36 * 50</gadget> <output>1_800</output> <gadget id="calculator">50 - 2</gadget> <output>48</output> <gadget id="calculator">48 - 23</gadget> <output>25</output> <gadget id="calculator">1_800 + 25</gadget> <output>1_825</output> <gadget id="calculator">1_825 / 50</gadget> <output>73/2 = around 36.5</output> <result>B</result>

B

The mean of 50 observations was 36. It was found later that an observation 30 was wrongly taken as 23. The corrected new mean is :

divide(add(multiply(36, 50), subtract(subtract(50, const_2), 23)), 50)

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

explanation : correct sum = ( 36 * 50 + 30 - 23 ) = 1825 . correct mean = = 1807 / 50 = 36.14 answer : b ) 36.14

general

math_qa__pF1d51rm921Bbn0U

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. 200 more than A : Answers: A) 2348 B) 7250 C) 2767 D) 1998 E) 5800

<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">200 / 2</gadget> <output>100</output> <gadget id="calculator">58 * 100</gadget> <output>5_800</output> <result>E</result>

E

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. 200 more than A :

multiply(add(add(multiply(3, 6), multiply(4, 5)), multiply(5, 4)), divide(200, 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 } = 200 total earning = \ inline \ frac { 58 xy } { 100 } = 5800 answer : e ) rs . 5800

general

math_qa__Lz2ULWRJoo9ylZrg

The average of first 14 even numbers is? Choices A) 10 B) 11 C) 12 D) 13 E) 15

<gadget id="calculator">14 + 1</gadget> <output>15</output> <result>E</result>

E

The average of first 14 even numbers is?

add(14, const_1)

add(n0,const_1)|

"sum of 14 even numbers = 14 * 15 = 210 average = 210 / 14 = 15 answer : e"

general

math_qa__SuV8FIzCk19SRlbp

A certain rectangular crate measures 12 feet by 16 feet by 18 feet. A cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces. What should the radius of the tank be if it is to be of the largest possible volume? Choose the correct choice. A) 4 B) 5 C) 6 D) 8 E) 10

<gadget id="calculator">16 / 2</gadget> <output>8</output> <gadget id="calculator">pi * (8 ** 2) * 12</gadget> <output>768*pi = around 2_412.743158</output> <gadget id="calculator">pi * 12</gadget> <output>12*pi = around 37.699112</output> <gadget id="calculator">(768*pi) / (12*pi)</gadget> <output>64</output> <gadget id="calculator">64 ** (1/2)</gadget> <output>8</output> <result>D</result>

D

A certain rectangular crate measures 12 feet by 16 feet by 18 feet. A cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces. What should the radius of the tank be if it is to be of the largest possible volume?

sqrt(divide(volume_cylinder(divide(16, const_2), 12), multiply(const_pi, 12)))

divide(n1,const_2)|multiply(n0,const_pi)|volume_cylinder(#0,n0)|divide(#2,#1)|sqrt(#3)

for max volume of cylinder ( pi * r ^ 2 * h ) we need to max out r ^ 2 * h . we do n ' t know what the dimensions of the crate refer to . . therefore for max vol base should be 18 x 16 i . e . of radius 16 / 2 = 8 d

geometry

math_qa__yKz4LgYOBXR0Hofi

For what values of k will the pair of equations 4(3x + 4y) = 48 and kx + 12y = 30 does not have a unique solution? Choose the correct choice from the following choices A) 12 B) 9 C) 3 D) 7.5 E) 2.5

<gadget id="calculator">12 * 3</gadget> <output>36</output> <gadget id="calculator">36 / 4</gadget> <output>9</output> <result>B</result>

B

For what values of k will the pair of equations 4(3x + 4y) = 48 and kx + 12y = 30 does not have a unique solution?

divide(multiply(12, 3), 4)

multiply(n1,n4)|divide(#0,n0)

we have 2 equations 1 . 4 ( 3 x + 4 y ) = 48 - - > 3 x + 4 y = 12 - - > 9 x + 12 y = 36 2 . kx + 12 y = 30 substract 1 - 2 , we get ( 9 - k ) x = 6 i . e . x = 6 / ( 9 - k ) then , by looking at options , we get some value of x except for b . when we put k = 9 , x becomes 6 / 0 and hence answer is b

general

math_qa__76S4lDAsBw6UCV7g

How many different positive integers are factors of 40? Choose the most appropriate option. A) 3 B) 2 C) 1 D) 6 E) 4

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

D

How many different positive integers are factors of 40?

add(power(const_2, const_2), const_2)

power(const_2,const_2)|add(#0,const_2)

2 * 20 4 * 10 8 * 5 answer : d

other

math_qa__x5bCH0FMdZhLQB4A

A couple married in 1980 had two children, one in 1982 and the other in 1984. Their combined ages will equal the years of the marriage in? Select A) 1986 B) 1985 C) 1987 D) 1988 E) 1989

<gadget id="calculator">1_982 - 1_980</gadget> <output>2</output> <gadget id="calculator">1_984 - 1_980</gadget> <output>4</output> <gadget id="calculator">2 + 4</gadget> <output>6</output> <gadget id="calculator">1_980 + 6</gadget> <output>1_986</output> <result>A</result>

A

A couple married in 1980 had two children, one in 1982 and the other in 1984. Their combined ages will equal the years of the marriage in?

add(1980, add(subtract(1982, 1980), subtract(1984, 1980)))

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

sum of year = 1 + 9 + 8 + 0 = ( 18 ) 1 + 8 = 9 1 + 9 + 8 + 2 = ( 20 ) 2 + 0 = 2 1 + 9 + 8 + 4 = ( 13 ) 1 + 3 = 4 now 9 + 2 + 4 = ( 15 ) 1 + 5 = 6 nd option a 1 + 9 + 8 + 6 = 24 ( 2 + 4 ) = 6 answer : a

general

math_qa__feH4i9KTra0gkSZ6

Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.19 per cubic meter? Choose the most appropriate option A) 2998 B) 1881 C) 2890 D) 1485 E) 2780

<gadget id="calculator">3 / 2</gadget> <output>3/2 = around 1.5</output> <gadget id="calculator">pi * ((3/2) ** 2) * 14</gadget> <output>63*pi/2 = around 98.960169</output> <gadget id="calculator">(63*pi/2) * 19</gadget> <output>1197*pi/2 = around 1_880.243203</output> <result>B</result>

B

Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.19 per cubic meter?

multiply(volume_cylinder(divide(3, const_2), 14), 19)

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

"22 / 7 * 14 * 3 / 2 * 3 / 2 = 99 m 2 99 * 19 = 1881 answer : b"

physics

math_qa__bBNd1kWPPn4DVsIb

At an election 2 candidates are participated and a candidate got 45% of votes and defeated by 9000. and 83 votes are invalid. Find the total polled votes? Choose the correct option: A) 84512 B) 78452 C) 65893 D) 90083 E) 74502

<gadget id="calculator">9_000 + 83</gadget> <output>9_083</output> <gadget id="calculator">45 * 2</gadget> <output>90</output> <gadget id="calculator">90 / 100</gadget> <output>9/10 = around 0.9</output> <gadget id="calculator">1 - (9/10)</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">9_083 / (1/10)</gadget> <output>90_830</output> <result>D</result>

D

At an election 2 candidates are participated and a candidate got 45% of votes and defeated by 9000. and 83 votes are invalid. Find the total polled votes?

divide(add(9000, 83), subtract(const_1, divide(multiply(45, 2), const_100)))

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

winner votes = 100 - 45 = 55 polled votes = [ ( 100 * 9000 ) / 2 * 55 - 100 ] + 83 = 90083 answer is d

gain

math_qa__Jj7qkMPcA3wIwTDG

After working for 6 days, David was joined by Moore. Together they completed the remaining job in 3 days. How many days will it take both of them to complete the entire job, given that it would have taken David 12 days to complete the job alone? Select the correct option A) 7 B) 4 C) 6 D) 2 E) 7

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

C

After working for 6 days, David was joined by Moore. Together they completed the remaining job in 3 days. How many days will it take both of them to complete the entire job, given that it would have taken David 12 days to complete the job alone?

multiply(divide(12, 6), 3)

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

explanation : david and moore complete half work in 3 days = > they can complete whole work in 6 days answer : option c

physics

math_qa__rHkS1pXIXDJA7EAl

How long does a train 110 m long running at the speed of 54 km/hr takes to cross a bridge 132 m length? Choose the correct choice from the following answers: A) 12.9 sec B) 12.1 sec C) 17.9 sec D) 16.13 sec E) 14.9 sec

<gadget id="calculator">110 + 132</gadget> <output>242</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">54 * (5/18)</gadget> <output>15</output> <gadget id="calculator">242 / 15</gadget> <output>242/15 = around 16.133333</output> <result>D</result>

D

How long does a train 110 m long running at the speed of 54 km/hr takes to cross a bridge 132 m length?

divide(add(110, 132), multiply(54, const_0_2778))

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

"speed = 54 * 5 / 18 = 15 m / sec total distance covered = 110 + 132 = 242 m . required time = 242 / 15 = 16.13 sec . answer : d"

physics

math_qa__Dp7bXeFpxXb8zo1M

By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 35%? Choose one: A) 228 B) 480 C) 267 D) 416 E) 276

<gadget id="calculator">800 * 100</gadget> <output>80_000</output> <gadget id="calculator">25 + 100</gadget> <output>125</output> <gadget id="calculator">80_000 / 125</gadget> <output>640</output> <gadget id="calculator">640 * 35</gadget> <output>22_400</output> <gadget id="calculator">22_400 / 100</gadget> <output>224</output> <gadget id="calculator">640 - 224</gadget> <output>416</output> <result>D</result>

D

By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 35%?

subtract(divide(multiply(800, const_100), add(25, const_100)), divide(multiply(divide(multiply(800, const_100), add(25, const_100)), 35), const_100))

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

"sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 25 % = 25 % of 640 = rs . 224 sp = cp - loss = 640 - 224 = rs . 416 answer : d"

gain

math_qa__hhXERqeaRtzlv7Vc

The average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 55 kg. What is the weight of the new person? Select: A) 75 kg B) 85 kg C) 95 kg D) 65 kg E) 55 kg

<gadget id="calculator">2.5 * 8</gadget> <output>20</output> <gadget id="calculator">20 + 55</gadget> <output>75</output> <result>A</result>

A

The average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 55 kg. What is the weight of the new person?

add(multiply(2.5, 8), 55)

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

"the total weight increase = ( 8 x 2.5 ) kg = 20 kg weight of new person = ( 55 + 20 ) kg = 75 kg the answer is a ."

general

math_qa__3NRLJwOih3M7WK3f

The length of a rectangular plot is 10mtr more than its width. The cost of fencing the plot along its perimeter at the rate of Rs. 6.5mtr is Rs.910. The perimeter of the plot is? Pick: A) 126 B) 156 C) 190 D) 140 E) 260

<gadget id="calculator">910 / 6.5</gadget> <output>140</output> <gadget id="calculator">140 / 2</gadget> <output>70</output> <gadget id="calculator">70 - 10</gadget> <output>60</output> <gadget id="calculator">60 / 2</gadget> <output>30</output> <gadget id="calculator">30 + 10</gadget> <output>40</output> <gadget id="calculator">30 + 40</gadget> <output>70</output> <gadget id="calculator">70 * 2</gadget> <output>140</output> <result>D</result>

D

The length of a rectangular plot is 10mtr more than its width. The cost of fencing the plot along its perimeter at the rate of Rs. 6.5mtr is Rs.910. The perimeter of the plot is?

multiply(add(divide(subtract(divide(divide(910, 6.5), const_2), 10), const_2), add(divide(subtract(divide(divide(910, 6.5), const_2), 10), const_2), 10)), const_2)

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

"sol . let width = x , length = ( 10 + x ) perimeter = 2 ( x + ( 10 + x ) ) = 2 ( 2 x = 10 ) & 2 ( 2 x + 10 ) * 6.5 = 910 x = 30 required perimeter = 2 ( 30 + 40 ) = 140 d"

geometry

math_qa__3j1hAW1jhwFvkBxj

What is the least number which should be added to 5432 so that the sum is exactly divisible by 5, 6, 4, and 3? Options: A) 16 B) 22 C) 28 D) 34 E) 40

<gadget id="calculator">5 * 2</gadget> <output>10</output> <gadget id="calculator">5 + 10</gadget> <output>15</output> <gadget id="calculator">6 + 15</gadget> <output>21</output> <gadget id="calculator">4 + 21</gadget> <output>25</output> <gadget id="calculator">3 + 25</gadget> <output>28</output> <result>C</result>

C

What is the least number which should be added to 5432 so that the sum is exactly divisible by 5, 6, 4, and 3?

add(3, add(4, add(6, add(5, multiply(5, const_2)))))

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

l . c . m . of 5 , 6 , 4 and 3 = 60 . when dividing 5432 by 60 , the remainder is 32 . the number to be added = 60 - 32 = 28 . the answer is c .

general

math_qa__vzTaCQfdJVI47kuN

Two airplanes take off from one airfield at noon. One flies due east at 203 miles per hour while the other flies directly northeast at 283 miles per hour. Approximately how many miles apart are the airplanes at 2 p.m.? Select the correct option. A) 166 B) 332 C) 406 D) 483 E) 566

<gadget id="calculator">283 * 2</gadget> <output>566</output> <gadget id="calculator">566 ** 2</gadget> <output>320_356</output> <gadget id="calculator">203 * 2</gadget> <output>406</output> <gadget id="calculator">406 ** 2</gadget> <output>164_836</output> <gadget id="calculator">320_356 - 164_836</gadget> <output>155_520</output> <gadget id="calculator">155_520 ** (1/2)</gadget> <output>72*sqrt(30) = around 394.360241</output> <result>C</result>

C

Two airplanes take off from one airfield at noon. One flies due east at 203 miles per hour while the other flies directly northeast at 283 miles per hour. Approximately how many miles apart are the airplanes at 2 p.m.?

sqrt(subtract(power(multiply(283, 2), 2), power(multiply(203, 2), 2)))

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

"c in two hours : the plane flying east will be 406 miles away from airport . the other plane will be 566 miles away from airport . 566 / 406 = ~ 1.4 = ~ sqrt ( 2 ) this means that planes formed a right isocheles triangle = > sides of such triangles relate as 1 : 1 : sqrt ( 2 ) = > the planes are 406 miles apart . c"

physics

math_qa__7mHPEw0hXvcNRuGG

A man can swim in still water at 6 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? Choose the correct choice from the following A) 3 B) 7.5 C) 2.25 D) 2 E) 4

<gadget id="calculator">6 / 3</gadget> <output>2</output> <result>D</result>

D

A man can swim in still water at 6 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?

divide(6, const_3)

divide(n0,const_3)|

"m = 6 s = x ds = 6 + x us = 6 - x 6 + x = ( 6 - x ) 2 6 + x = 12 - 2 x 3 x = 6 x = 2 answer : d"

general

math_qa__mPXclz2o1JK0noJd

A certain roller coaster has 4 cars, and a passenger is equally likely to ride in any 1 of the 4 cars each time that passenger rides the roller coaster. If a certain passenger is to ride the roller coaster 4 times, what is the probability that the passenger will ride in each of the 4 cars? Choose one: A) 0 B) 1 / 9 C) 2 / 9 D) 3 / 32 E) 1

<gadget id="calculator">factorial(4)</gadget> <output>24</output> <gadget id="calculator">1 / 4</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(1/4) ** 4</gadget> <output>1/256 = around 0.003906</output> <gadget id="calculator">24 * (1/256)</gadget> <output>3/32 = around 0.09375</output> <result>D</result>

D

A certain roller coaster has 4 cars, and a passenger is equally likely to ride in any 1 of the 4 cars each time that passenger rides the roller coaster. If a certain passenger is to ride the roller coaster 4 times, what is the probability that the passenger will ride in each of the 4 cars?

multiply(factorial(4), power(divide(1, 4), 4))

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

"if he is to ride 4 times and since he can choose any of the 4 cars each time , total number of ways is = 4 * 4 * 4 * 4 = 256 now the number of ways if he is to choose a different car each time is = 4 * 3 * 2 * 1 = 24 so the probability is = 24 / 256 = 6 / 64 = 3 / 32 = 3 / 32 answer : d"

general

math_qa__Dgrwdlvbwgn1kryq

What will be the ratio between the area of a rectangle and the area of a triangle with one of the sides of rectangle as base and a vertex on the opposite side of rectangle. Choose the correct choice from the following answers: A) 1 : 2 B) 2 : 1 C) 3 : 1 D) data inadequate E) none of these

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

B

What will be the ratio between the area of a rectangle and the area of a triangle with one of the sides of rectangle as base and a vertex on the opposite side of rectangle.

divide(rectangle_area(const_1, const_1), triangle_area(rectangle_area(const_1, const_1), rectangle_area(const_1, const_1)))

rectangle_area(const_1,const_1)|triangle_area(#0,#0)|divide(#0,#1)|

"area of δ ebc = 1 ⁄ 2 × bc × ef = 1 ⁄ 2 × bc × ab [ since , ef = ab ] area of δ ebc = 1 ⁄ 2 × area of δ abcd \ required ratio = 2 : 1 . answer b"

geometry