options stringlengths 37 300 | correct stringclasses 5
values | annotated_formula stringlengths 7 727 | problem stringlengths 5 967 | rationale stringlengths 1 2.74k | program stringlengths 10 646 |
|---|---|---|---|---|---|
a ) 1 / 2 , b ) 2 / 3 , c ) 1 / 4 , d ) 1 / 8 , e ) 3 / 8 | a | divide(2, power(const_2, 2)) | three coins are tossed . find the probability of at least 2 tails ? | "n ( s ) = 2 ^ 3 = 8 let e is the event of getting at least 2 tails n ( e ) = ttt , tth , htt , tht = 4 p ( e ) = n ( e ) / n ( s ) = 4 / 8 = 1 / 2 ans - a" | a = 2 ** 2
b = 2 / a
|
a ) 2387 , b ) 267 , c ) 120 , d ) 277 , e ) 271 | c | divide(multiply(subtract(multiply(12.5, const_2), const_1), multiply(12.5, const_2)), add(const_4, const_1)) | a train can travel 50 % faster than a car . both start from point a at the same time and reach point b at 75 kms away from a at the same time . on the way , however , the train lost about 12.5 minutes while stopping at the stations . the speed of the car is ? | "let speed of the car be x km / hr . then , speed of the train = 150 / 100 x = 3 / 2 x km / hr . 75 / x - 75 / ( 3 / 2 x ) = 125 / ( 10 * 60 ) 75 / x - 50 / x = 5 / 24 = 120 km / hr . answer : c" | a = 12 * 5
b = a - 1
c = 12 * 5
d = b * c
e = 4 + 1
f = d / e
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a ) 20 mph , b ) 24 mph , c ) 30 mph , d ) 40 mph , e ) 42 mph | d | divide(60, add(divide(48, subtract(60, 12)), divide(12, 24))) | tom traveled the entire 60 miles trip . if he did the first 12 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 48 miles per hour , what is the his average speed , in miles per hour ? | "avg speed = total distance / total time = ( d 1 + d 2 ) / ( t 1 + t 2 ) = ( 12 + 48 ) / ( ( 12 / 24 ) + ( 48 / 48 ) ) = 60 * 2 / 3 = 40 mph d" | a = 60 - 12
b = 48 / a
c = 12 / 24
d = b + c
e = 60 / d
|
a ) 5000 , b ) 4000 , c ) 1000 , d ) 6000 , e ) 8000 | c | subtract(multiply(add(5, const_1), 2500), add(add(add(add(2435, 2920), 2855), 3230), 2560)) | a grocer has a sale of rs . 2435 , rs . 2920 , rs . 2855 , rs . 3230 and rs . 2560 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 2500 ? | "total sale for 5 months = rs . ( 2435 + 2920 + 2855 + 3230 + 2560 ) = rs . 14000 . required sale = rs . [ ( 2500 x 6 ) - 14000 ] = rs . ( 15000 - 14000 ) = rs . 1000 answer : option c" | a = 5 + 1
b = a * 2500
c = 2435 + 2920
d = c + 2855
e = d + 3230
f = e + 2560
g = b - f
|
a ) 10 litres , b ) 20 litres , c ) 30 litres , d ) 5 litres , e ) 14 litres | a | multiply(5, const_1) | a mixture contains alcohol and water in the ratio 4 : 3 . if 5 litres of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture | "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 4 x / ( 3 x + 5 ) = 4 / 5 ο³ 20 x = 4 ( 3 x + 5 ) ο³ 8 x = 20 ο³ x = 2.5 quantity of alcohol = ( 4 x 2.5 ) litres = 10 litres . answer a 10 litres" | a = 5 * 1
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a ) 232 , b ) 242 , c ) 252 , d ) 262 , e ) 280 | e | divide(28, divide(550, 28)) | evaluate 28 % of 550 + 45 % of 280 | "explanation : = ( 28 / 100 ) * 550 + ( 45 / 100 ) * 280 = 154 + 126 = 280 answer : option e" | a = 550 / 28
b = 28 / a
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a ) 8054 , b ) 8877 , c ) 2877 , d ) 2678 , e ) 1011 | a | divide(8840, power(add(subtract(divide(9261, 8840), const_1), const_1), 2)) | what sum of money put at c . i amounts in 2 years to rs . 8840 and in 3 years to rs . 9261 ? | "8840 - - - - 421 100 - - - - ? = > 4.76 % x * 104.76 / 100 * 104.76 / 100 = 8840 x * 1.0975 = 8840 x = 8840 / 1.0975 = > 8054.54 answer : a" | a = 9261 / 8840
b = a - 1
c = b + 1
d = c ** 2
e = 8840 / d
|
a ) 1.29 , b ) 1.39 , c ) 1.49 , d ) 1.59 , e ) 1.69 | a | sqrt(divide(5, 3)) | if square - root of 15 is 3.87 . then find the value of square - root of ( 5 / 3 ) | = > root 5 / root 3 = ( root 5 / root 3 ) * ( root 3 / root 3 ) = root 15 / root 9 = 3.87 / 3 = 1.29 answer : a | a = 5 / 3
b = math.sqrt(a)
|
a ) 120 , b ) 180 , c ) 240 , d ) 280 , e ) 320 | e | multiply(divide(480, const_3), const_2) | a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 480 kilograms of pears that day , how many kilograms did he sell in the afternoon ? | "3 x = 480 x = 160 therefore , the salesman sold 160 kg in the morning and 2 β
160 = 320 kg in the afternoon . so answer is e ." | a = 480 / 3
b = a * 2
|
a ) none of these , b ) 0.02 , c ) 0.002 , d ) 0.0002 , e ) 2 | c | multiply(divide(0.004, 0.5), const_100) | 0.004 Γ 0.5 = ? | "explanation : 0.004 Γ 0.5 = 0.002 . answer : option c" | a = 0 / 4
b = a * 100
|
a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | a | subtract(add(const_4, const_3), divide(divide(add(20, 10), const_2), 3)) | on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 3 cups of tea . last week mo drank a total of 20 cups of tea and hot chocolate together . if during that week mo drank 10 more tea cups than hot chocolate cups , then how many rainy days were there last week ? | t = the number of cups of tea c = the number of cups of hot chocolate t + c = 20 t - c = 10 - > t = 15 . c = 5 . mo drinks 3 cups of tea a day then number of days that are not rainy = 15 / 3 = 5 so number of rainy days = 7 - 5 = 2 a is the answer . | a = 4 + 3
b = 20 + 10
c = b / 2
d = c / 3
e = a - d
|
a ) 52 sec , b ) 45 sec , c ) 72 sec , d ) 25 sec , e ) 39 sec | c | divide(multiply(50, const_4), multiply(10, divide(const_1000, const_3600))) | how long will a boy take to run round a square field of side 50 meters , if he runs at the rate of 10 km / hr ? | "speed = 10 km / hr = 10 * 5 / 18 = 25 / 9 m / sec distance = 50 * 4 = 200 m time taken = 200 * 9 / 25 = 72 sec answer is c" | a = 50 * 4
b = 1000 / 3600
c = 10 * b
d = a / c
|
a ) 38 . , b ) 30 . , c ) 42 . , d ) 44 . , e ) 46 . | b | subtract(multiply(sqrt(divide(675, 3)), 3), sqrt(divide(675, 3))) | the roof of an apartment building is rectangular and its length is 3 times longer than its width . if the area of the roof is 675 feet squared , what is the difference between the length and the width of the roof ? | "let the width = x x * 3 x = 675 x ^ 2 = 225 x = 15 length = 3 * 15 = 45 difference = 45 - 15 = 30 b is the answer" | a = 675 / 3
b = math.sqrt(a)
c = b * 3
d = 675 / 3
e = math.sqrt(d)
f = c - e
|
a ) 4857 , b ) 4184 , c ) 4012 , d ) 5191 , e ) 5291 | d | subtract(multiply(6500, add(5, const_1)), add(add(add(6855, add(6235, 6927)), 7230), 6562)) | a grocery shop has a sale of rs . 6235 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ? | "let the sale in the sixth month = x then ( 6235 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6235 + 6927 + 6855 + 7230 + 6562 + x = 6 Γ 6500 = > 33809 + x = 39000 = > x = 39000 β 33809 = 5191 answer : d" | a = 5 + 1
b = 6500 * a
c = 6235 + 6927
d = 6855 + c
e = d + 7230
f = e + 6562
g = b - f
|
a ) 86 , b ) 50 , c ) 12 , d ) 13 , e ) 67 | a | divide(divide(subtract(225, multiply(multiply(5, const_0_2778), 5)), 5), const_0_2778) | a train 225 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is : | "speed of the train relative to man = ( 225 / 10 ) m / sec = ( 45 / 2 ) m / sec . [ ( 45 / 2 ) * ( 18 / 5 ) ] km / hr = 81 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 81 = = > x = 86 km / hr . answer : option a" | a = 5 * const_0_2778
b = a * 5
c = 225 - b
d = c / 5
e = d / const_0_2778
|
a ) 450.1 , b ) 910.1 , c ) 930.1 , d ) 920.1 , e ) 950.1 | e | divide(0.0006688, 0.0000120) | 0.0006688 / 0.0000120 x 17.05 = ? | "explanation : ? = 0.0006688 / 0.0000120 x 17.05 = 950.1 answer : option e" | a = 0 / 6688
|
a ) 18 , b ) 56 , c ) 12 , d ) 15 , e ) 14 | d | subtract(45, multiply(10, 3)) | the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 45 years , was replaced by a new person . find the age of the new person ? | initial average age of the 10 persons be p . age of the new person q . sum of the ages of the initial 10 persons = 10 p new average = ( p - 3 ) 10 ( p - 3 ) = 10 p - 45 + q = > q = 15 answer : d | a = 10 * 3
b = 45 - a
|
a ) 30 , b ) 35 , c ) 25 , d ) 40 , e ) 45 | c | divide(subtract(add(50, 75), 75), subtract(divide(add(50, 75), 50), divide(75, 75))) | a car traveled 75 % of the way from town a to town b at an average speed of 75 mph . the car traveled at an average speed of v mph for the remaining part of the trip . the average speed for the entire trip was 50 mph . what is v in mph ? | "assume total distance = 100 miles time taken for 75 miles = 75 / 75 = 1 hour time taken for the rest of the 25 miles = 25 / v hours . average speed = 50 therefore the total time needed = 2 hours . 2 = 1 + 25 / v hence v = 25 mph answer : c" | a = 50 + 75
b = a - 75
c = 50 + 75
d = c / 50
e = 75 / 75
f = d - e
g = b / f
|
a ) 151.36 mtrs , b ) 378.4 mtrs , c ) 478.4 mtrs , d ) 488.4 mtrs , e ) 578.4 mtrs | a | multiply(66, divide(multiply(86, 8), multiply(20, 15))) | if 20 men can build a wall 66 metres long in 15 days , what length of a similar can be built by 86 men in 8 days ? | "if 20 men can build a wall 66 metres long in 15 days , length of a similar wall that can be built by 86 men in 8 days = ( 66 * 86 * 8 ) / ( 15 * 20 ) = 151.36 mtrs answer : a" | a = 86 * 8
b = 20 * 15
c = a / b
d = 66 * c
|
a ) $ 0.15 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45 | d | divide(multiply(add(const_1, const_1), 0.60), add(const_1, const_2)) | on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price per glass on the second day ? | "we are given that orangeade is made on day 1 with an equal amount of water and orange juice . we can set this information up into a ratio using a variable multiplier : w : oj = x : x thus , orangeade quantity = amount of water + amount of oj = x + x = 2 x we are next given that orangeade on day 2 was made by mixing the same amount of orange juice with twice the amount of water . we can set this information up into a ratio using a variable multiplier : w : oj = 2 x : x thus , orangeade quantity = amount of water + amount of oj = 2 x + x = 3 x we also know that all orangeade made was sold and that the revenue on both days was the same . we can therefore set up the following equation : day 1 revenue = day 2 revenue that is , ( quantity sold day 1 ) ( price per glass day 1 ) = ( quantity sold day 2 ) ( price per glass day 2 ) let a be the amount of orangeade a glass can hold , then quantity sold day 1 = the number of glasses of orangeade sold on day 1 = 2 x / a similarly , quantity sold day 2 = the number of glasses of orangeade sold on day 2 = 3 x / a we also know that the price per glass on day 1 = $ 0.6 but we don β t know the price per glass on day 2 , so let β s label it as variable p . we now have : ( 2 x / a ) ( 0.6 ) = ( 3 x / a ) ( p ) multiplying both sides by a , we have : ( 2 x ) ( 0.6 ) = ( 3 x ) ( p ) 1.2 x = 3 xp 1.2 = 3 p p = 0.4 thus , each glass of orangeade was sold for $ 0.40 on day 2 . answer d ." | a = 1 + 1
b = a * 0
c = 1 + 2
d = b / c
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a ) 41.4 , b ) 34.1 , c ) 13.4 , d ) 12.4 , e ) 10.8 | a | add(inverse(subtract(divide(const_1, 12.5), divide(const_1, 30))), inverse(subtract(divide(const_1, 7.5), divide(const_1, 12)))) | two consultants can type up a report in 12.5 hours and edit it in 7.5 hours . if mary needs 30 hours to type the report and jim needs 12 hours to edit it alone , how many r hours will it take if jim types the report and mary edits it immediately after he is done ? | "break down the problem into two pieces : typing and editing . mary needs 30 hours to type the report - - > mary ' s typing rate = 1 / 30 ( rate reciprocal of time ) ( point 1 in theory below ) ; mary and jim can type up a report in 12.5 and - - > 1 / 30 + 1 / x = 1 / 12.5 = 2 / 25 ( where x is the time needed for jim to type the report alone ) ( point 23 in theory below ) - - > x = 150 / 7 ; jim needs 12 hours to edit the report - - > jim ' s editing rate = 1 / 12 ; mary and jim can edit a report in 7.5 and - - > 1 / y + 1 / 12 = 1 / 7.5 = 2 / 15 ( where y is the time needed for mary to edit the report alone ) - - > y = 20 ; how many r hours will it take if jim types the report and mary edits it immediately after he is done - - > x + y = 150 / 7 + 20 = ~ 41.4 answer : a ." | a = 1 / 12
b = 1 / 30
c = a - b
d = 1/(c)
e = 1 / 7
f = 1 / 12
g = e - f
h = 1/(g)
i = d + h
|
a ) 8 , b ) 7 , c ) 4 , d ) 5 , e ) 6 | e | divide(1254, add(add(const_100, const_100), subtract(const_10, const_1))) | the number 1254 is divisible by which number ? | last 3 digit can not divisible by 8 so , reject option a 1254 is not divisible by 7 last number is not 0 or 5 , so neglect 4 is not divide 1254 divisibility rule of 6 is a number divisible both by 3 and 2 . 1254 attains both divisible . so the number is divisible by 6 option e | a = 100 + 100
b = 10 - 1
c = a + b
d = 1254 / c
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a ) s . 600 , b ) s . 630 , c ) s . 640 , d ) s . 648 , e ) s . 816 | e | multiply(multiply(24, 34), divide(40, 10)) | what is the cost of leveling the field in the form of parallelogram at the rate of rs . 40 / 10 sq . metre , whose base & perpendicular distance from the other side being 24 m & 34 m respectively ? | "area of the parallelogram = length of the base * perpendicular height = 24 * 34 = 816 m . total cost of levelling = rs . 816 e" | a = 24 * 34
b = 40 / 10
c = a * b
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a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 8 | c | subtract(subtract(subtract(35, 25), const_4), const_2) | a certain no . when divided by 35 leaves aremainder 25 , what is the remainder if the same no . be divided by 15 ? | explanation : 35 + 25 = 60 / 15 = 4 ( remainder ) c | a = 35 - 25
b = a - 4
c = b - 2
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a ) 10.5 % , b ) 12.5 % , c ) 15 % , d ) 22 % , e ) 50 % | e | multiply(divide(40, subtract(const_100, 20)), const_100) | on a certain road , 40 % of the motorists exceed the posted speed limit and receive speeding tickets , but 20 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on that road exceed the posted speed limit ? | "suppose there are x motorists . 40 % of them exceeded the speed limit and received the ticket , i . e . 2 x / 5 . again , suppose total no . of motorists who exceeded the speed limit are y . 20 % of y exceeded the speed limit but did n ' t received the ticket , i . e . y / 5 . it means 4 y / 5 received the ticket . hence , 4 y / 5 = 2 x / 5 or y / x = 1 / 2 or y / x * 100 = 1 / 2 * 100 = 50 % e" | a = 100 - 20
b = 40 / a
c = b * 100
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a ) $ 280 , b ) $ 800 , c ) $ 892 , d ) $ 1,108 , e ) $ 1,200 | b | subtract(multiply(multiply(const_100, 10), const_2), divide(add(multiply(multiply(10, 8), const_2), 56), add(divide(10, const_100), divide(8, const_100)))) | if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 56 . if $ 2,000 is the total amount invested , how much is invested at 8 percent ? | "( a ) $ 280 ( b ) $ 800 ( c ) $ 892 ( d ) $ 1,108 ( e ) $ 1,200 y = 2000 - x . 1 x - . 08 ( 2000 - x ) = 56 . - 160 + . 18 x = 56 x = 1200 and y = 800 answer : b" | a = 100 * 10
b = a * 2
c = 10 * 8
d = c * 2
e = d + 56
f = 10 / 100
g = 8 / 100
h = f + g
i = e / h
j = b - i
|
a ) 3 β 7 , b ) 4 β 7 , c ) 3 β 4 , d ) 4 β 3 , e ) 7 β 4 | c | divide(divide(const_2.0, 2), divide(3, 2)) | if a mixture is 1 β 2 alcohol by volume and 3 β 2 water by volume , what is the ratio of the volume of alcohol to the volume of water in this mixture ? | "should be a sub - 600 level q . . volume = { 1 / 2 } / { 3 / 2 } = 1 / 3 c" | a = 2 / 0
b = 3 / 2
c = a / b
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a ) 7 , b ) 6 , c ) 9 , d ) 2 , e ) 3 | d | subtract(38, multiply(21, const_2)) | a number when divided by 342 gives a remainder 38 , what remainder will be obtained by dividing the same number 21 ? | "explanation : 342 + 38 = 380 / 21 = 2 ( remainder ) answer : d" | a = 21 * 2
b = 38 - a
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a ) 1 , 180000 , b ) 1 , 200000 , c ) 1 , 200300 , d ) 1 , 228500 , e ) 1 , 330,000 | d | divide(600000, const_3) | at the beginning of 1992 , maria ' s stock portfolio was worth $ 600000 . during 1992 , the portfolio ' s value increased by 95 % . during the next year , the portfolio increased its worth by only 5 % . what was maria ' s portfolio worth , in dollars , by the end of 1993 ? | by the end of 1992 , the port folio worth is 1.95 * ( $ 600 k ) by 1993 , the portfolio is 1.05 * ( 1.95 * $ 600 k ) = $ 1 , 228,500 answer : d | a = 600000 / 3
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a ) 28 days , b ) 30 days , c ) 33 days , d ) 35 days , e ) 39 days | e | add(divide(subtract(const_1, multiply(inverse(15), 3)), inverse(45)), 3) | amit and ananthu can do a work in 15 days and 45 days respectively . amit started the work and left after 3 days . ananthu took over and completed the work . in how many days was the total work completed ? | "amit β s one day β s work = 1 / 15 amit β s 3 day β s work = 1 / 15 * 3 = 1 / 5 work left = 1 - 1 / 5 = 4 / 5 ananthu β s one day β s work = 1 / 45 ananthu can do work in = 4 / 5 * 45 = 36 days so total days = 36 + 3 = 39 days answer : e" | a = 1/(15)
b = a * 3
c = 1 - b
d = 1/(45)
e = c / d
f = e + 3
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a ) 1 : 3 , b ) 20 : 25 , c ) 1 : 5 , d ) 2 : 5 , e ) 4 : 6 | b | divide(multiply(5, const_4), add(multiply(5, const_4), 5)) | a pet store holds cats and dogs . if the difference between the number of cats and the number of dogs is 5 . what could be the ratio of cats to dogs in the pet store ? | "say theratioof cats to dogs is a / b . then thenumberof cats would be ax and thenumberof dogs bx , for some positive integer x . we are told that ax - bx = 5 - - > x ( a - b ) = 5 . since 5 is a prime number it could be broken into the product of two positive multiples only in one way : x ( a - b ) = 1 * 5 . the above implies that either x = 1 and a - b = 5 or x = 5 and a - b = 1 . therefore the correct answer should have the difference between numerator and denominator equal to 1 or 13 . for the original question only option which fits is e , 4 : 5 . cats = 5 * 4 = 20 and dogs = 5 * 5 = 25 . answer : b ." | a = 5 * 4
b = 5 * 4
c = b + 5
d = a / c
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a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95 | d | add(multiply(const_2, const_3), subtract(const_100, const_10)) | a number is said to be prime saturated if the product of all the different positive prime factors of w is less than the square root of w . what is the greatest two digit prime saturated integer ? | "w 96 = 3 * 32 = 3 * 2 ^ 5 answer is d ." | a = 2 * 3
b = 100 - 10
c = a + b
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a ) 24 , b ) 30 , c ) 32 , d ) 34 , e ) 36 | d | subtract(54, divide(subtract(780, multiply(54, 10)), subtract(22, 10))) | 54 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780 . the bigger part is | "solution let the two parts be ( 54 - x ) and x . then , 10 ( 54 - x ) + 22 x = 780 = 12 x = 240 βΉ = βΊ x = 20 . therefore bigger part = ( 54 - x ) = 34 . answer d" | a = 54 * 10
b = 780 - a
c = 22 - 10
d = b / c
e = 54 - d
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a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26 | b | divide(multiply(multiply(3, const_2), 10), subtract(9, multiply(3, const_2))) | a work which could be finished in 9 days was finished 3 days earlier after 10 more men joined . the number of men employed was ? | "explanation : x - - - - - - - 9 ( x + 10 ) - - - - 6 x * 9 = ( x + 10 ) 6 x = 20 answer : b" | a = 3 * 2
b = a * 10
c = 3 * 2
d = 9 - c
e = b / d
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a ) rs . 880 , b ) rs . 890 , c ) rs . 1800 , d ) rs . 900 , e ) none | c | divide(multiply(multiply(multiply(multiply(const_3.0, const_100), 10), 10), 6), const_100) | if the compound interest on a certain sum of money for 6 years at 10 % per annum be rs . 993 , what would be the simple interest ? | "let p = principal a - amount we have a = p ( 1 + r / 100 ) 3 and ci = a - p atq 993 = p ( 1 + r / 100 ) 3 - p ? p = 3000 / - now si @ 10 % on 3000 / - for 6 yrs = ( 3000 x 10 x 6 ) / 100 = 1800 / - answer : c ." | a = 3 * 0
b = a * 10
c = b * 10
d = c * 6
e = d / 100
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a ) 246 , b ) 448 , c ) 1408 , d ) 482 , e ) 223 | d | divide(multiply(const_1000, 1), multiply(add(const_3, divide(add(multiply(const_3, const_4), const_2), power(add(multiply(const_4, const_2), const_2), const_2))), 0.66)) | a bicycle wheel has a diameter of 0.66 m . how many complete revolutions does it make in 1 km ? | "1 revolution = 3.14 * diameter . number of revolutions in 1 km = 1000 m / ( 3.14 * 0.66 m ) = 482.5 . hence 482 complete revolutions . answer d" | a = 1000 * 1
b = 3 * 4
c = b + 2
d = 4 * 2
e = d + 2
f = e ** 2
g = c / f
h = 3 + g
i = h * 0
j = a / i
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a ) 12.05 % , b ) 5 % , c ) 13.05 % , d ) 22.05 % , e ) 18.05 % | a | multiply(divide(subtract(12015, 9800), subtract(multiply(9800, 8), multiply(5, 12015))), const_100) | a sum of money amounts to rs . 9800 after 5 years and rs . 12015 after 8 years at the same rate of simple interest . the rate of interest per annum is ? | s . i . for 3 years = ( 12015 - 9800 ) = rs . 2215 s . i . for 5 years = rs . 2215 / 3 * 5 = rs . 3691 . principal = ( 9800 - 3675 ) = rs . 6108 hence , rate = ( 100 * 3691 ) / ( 6125 * 5 ) = 12.05 % answer : a | a = 12015 - 9800
b = 9800 * 8
c = 5 * 12015
d = b - c
e = a / d
f = e * 100
|
a ) 6 , b ) 3 , c ) 2 , d ) 1 , e ) 0 | e | divide(34, 51) | how many different pairs of positive integers ( a , b ) satisfy the equation 1 / a + 1 / b = 34 / 51 ? | a + b / ab = 2 / 3 3 = 1 * 3 or 3 * 1 a + b in both case = 4 correct 0 answer : e | a = 34 / 51
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a ) 20 , b ) 22 , c ) 24 , d ) 27 , e ) 30 | d | subtract(power(3, 3), const_1) | a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 8 , which can be repeated . if the product of the digits in the area code must be even , how many different codes can be created ? | "total # of codes possible is 3 * 3 * 3 = 27 . oit of those 27 codes answer : d ." | a = 3 ** 3
b = a - 1
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a ) 50 , b ) 52 , c ) 49 , d ) 32 , e ) 35 | c | subtract(multiply(add(32, const_1), add(16, const_1)), multiply(32, 16)) | the average age of one class strength 32 students is 16 yrs . if the staff ' s age is also included , the average increases by one year . find the age of the staff | total age of students = > 32 Γ 16 = 512 yrs total age inclusive staff = 33 Γ ( 16 + 1 ) = 561 = > staff ' s age 561 - 512 = 49 yrs answer c | a = 32 + 1
b = 16 + 1
c = a * b
d = 32 * 16
e = c - d
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a ) 14 m , b ) 20 m , c ) 18 m , d ) 12 m , e ) 15 m | b | sqrt(divide(460, subtract(const_1, divide(15, const_100)))) | the area of a rectangular plot is 460 square metres . if the length is 15 % more than the breadth , what is the breadth of the plot ? | "lb = 460 m 2 let breath = b l = b * ( 100 + 15 ) / 100 = 115 b / 100 from these 115 b / 100 * b = 460 b 2 = 46000 / 115 = 400 b = root of 400 = 20 m answer b" | a = 15 / 100
b = 1 - a
c = 460 / b
d = math.sqrt(c)
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a ) a ) 250 , b ) b ) 350 , c ) c ) 450 , d ) d ) 470 , e ) e ) 500 | a | subtract(multiply(const_10, 150), add(multiply(5, 100), multiply(5, 150))) | a man purchased 5 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ? | "explanation : 10 * 150 = 1500 5 * 100 + 5 * 150 = 1250 1500 β 1250 = 250 a" | a = 10 * 150
b = 5 * 100
c = 5 * 150
d = b + c
e = a - d
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a ) 30 , b ) 18 , c ) 16 , d ) 12 , e ) 8 | a | multiply(multiply(5, 3), divide(8, 4)) | working simultaneously and independently at an identical constant rate , 5 machines of a certain type can produce a total of x units of product p in 8 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 3 x units of product p in 4 days ? | 5 machines do x units in 8 days we have x / 8 = > rate of the 5 machines we know that we need to have 3 x units in 4 days therefore , we need to get to 3 x / 4 rate of the machines . rate of one machine is x / 8 * 1 / 5 = x / 40 . now , we need to know how many machines need to work simultaneously , to get 3 x done in 4 days . 3 x / 4 work needs to be done by machines that work at x / 40 rate . let ' s assign a constant y for the number of machines : ( x / 40 ) * y = 3 x / 4 y = 3 x / 4 * 40 / x cancel 4 with 40 , and x with x and get - > 30 . answer choice a | a = 5 * 3
b = 8 / 4
c = a * b
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a ) 18 . , b ) 28 . , c ) 35 . , d ) 49 . , e ) 52 . | a | add(const_3, const_2) | in a rectangular axis system , what is the area of a parallelogram with the coordinates : ( 2,2 ) , ( 8,2 ) , ( 3,5 ) , ( 9,5 ) ? | "delta x will give us the dimension of one side of the parallelogram = 8 - 2 = 6 unit delta y will give us the dimension of the other side of parallelogram = 5 - 2 = 3 unit area of parallelogram = 6 * 3 = 18 answer is a" | a = 3 + 2
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a ) $ 600 , b ) $ 800 , c ) $ 1,000 , d ) $ 1,600 , e ) $ 2,000 | e | divide(multiply(10, subtract(60, 40)), divide(10, const_100)) | on a saturday night , each of the rooms at a certain motel was rented for either $ 40 or $ 60 . if 10 of the rooms that were rented for $ 60 had instead been rented for $ 40 , then the total rent the motel charged for that night would have been reduced by 10 percent . what was the total rent the motel actually charged for that night ? | "let total rent the motel charge for all rooms = x if 10 rooms that were rented for 60 $ had instead been rented for 40 $ , then total difference in prices = 20 $ * 10 = 200 $ total rent the motel charged would have been reduced by 10 % . 10 x = 200 = > x = 2000 answer e" | a = 60 - 40
b = 10 * a
c = 10 / 100
d = b / c
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a ) 40.8 , b ) 19.75 , c ) 20.75 , d ) 21.75 , e ) 22.75 | a | subtract(multiply(divide(const_100, 50), divide(multiply(60, 84), const_100)), 60) | there is 60 lit of milk and water in which milk forms 84 % . howmuch water must be added to this solution to make it solution in which milk forms 50 % | "60 * 84 / 100 = 50.40 lit milk that is 9.60 lit water let x lit water will be added then ( 60 + x ) * 50 / 100 = 50.40 so x = 40.8 answer : a" | a = 100 / 50
b = 60 * 84
c = b / 100
d = a * c
e = d - 60
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a ) $ 10079.44 , b ) q = $ 10815.83 , c ) $ 12652.61 , d ) $ 14232.14 , e ) $ 20598.11 | b | multiply(10000, power(add(const_1, divide(divide(3.96, const_100), const_2)), const_4)) | jill invests $ 10000 in an account that pays an annual rate of 3.96 % , compounding semi - annually . approximately how much q does she have in her account after two years ? | "ps . i guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8 % hence b the answer" | a = 3 / 96
b = a / 2
c = 1 + b
d = c ** 4
e = 10000 * d
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a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10 | b | divide(subtract(440, divide(440, add(divide(10, const_100), const_1))), 10) | machine p and machine q are each used to manufacture 440 sprockets . it takes machine p 10 hours longer to produce 440 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ? | "p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 440 / x = 440 / 1.1 x + 10 1.1 ( 440 ) = 440 + 11 x 11 x = 44 x = 4 the answer is b ." | a = 10 / 100
b = a + 1
c = 440 / b
d = 440 - c
e = d / 10
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a ) 110 , b ) 175 , c ) 212 , d ) 218 , e ) 220 | b | multiply(const_100, divide(subtract(subtract(1, divide(1, const_100)), divide(36, 100)), divide(36, 100))) | a retailer buys 100 pens at the market price of 36 pens from a wholesaler , if he sells these pens giving a discount of 1 % , what is the profit % ? | "let the market price of each pen be $ 1 then , cost price of 100 pens = $ 36 selling price of 100 pens = 99 % of $ 100 = $ 99 profit % = ( ( 63 * 100 ) / 36 ) % = 175 % answer b" | a = 1 / 100
b = 1 - a
c = 36 / 100
d = b - c
e = 36 / 100
f = d / e
g = 100 * f
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a ) 30 % , b ) 33 % , c ) 35 % , d ) 40 % , e ) 45 % | b | multiply(divide(divide(multiply(11, 42), const_100), add(3, 11)), const_100) | 3 litre of water is added to 11 litre of a solution containing 42 % of alcohol in the water . the percentage of alcohol in the new mixture is ? | we have a 11 litre solution containing 42 % of alcohol in the water . = > quantity of alcohol in the solution = 11 Γ 42 100 = 11 Γ 42100 now 3 litre of water is added to the solution . = > total quantity of the new solution = 11 + 3 = 14 percentage of alcohol in the new solution = 11 Γ 42 100 14 Γ 100 = 11 Γ 4210014 Γ 100 = 11 Γ 3 100 = 33 % b ) | a = 11 * 42
b = a / 100
c = 3 + 11
d = b / c
e = d * 100
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a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 26 , d ) 1 / 13 , e ) 5 / 13 | a | divide(multiply(const_4, const_3), 52) | from a pack of 52 cards , 1 card is drawn at random . what is the probability that a red card is drawn ? | "the total number of cards is 52 . the number of red cards is 26 . p ( red card ) = 26 / 52 = 1 / 2 the answer is a ." | a = 4 * 3
b = a / 52
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a ) 26 , b ) 95 , c ) 90 , d ) 42 , e ) 22 | b | subtract(divide(8925, 85), 10) | a trader sells 85 meters of cloth for rs . 8925 at the profit of rs . 10 per metre of cloth . what is the cost price of one metre of cloth ? | "sp of 1 m of cloth = 8925 / 85 = rs . 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 105 - rs . 10 = rs . 95 answer : b" | a = 8925 / 85
b = a - 10
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a ) 1250 , b ) 625 , c ) 600 , d ) 7500 , e ) 375 | c | multiply(5, 120) | a trailer carries 3 , 4 and 5 crates on a trip . each crate weighs no less than 120 kg . what is the maximum weight of the crates on a single trip ? | max no . of crates = 5 . max weight = 120 kg max . weight carried = 5 * 120 = 600 kg = c | a = 5 * 120
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a ) 7 : 8 , b ) 6 : 7 , c ) 5 : 6 , d ) 4 : 5 , e ) 3 : 4 | e | divide(const_3, const_4) | a student completes a 3 part exam as follows . the student completes sections a in 24 minutes and takes an equal time to complete the two remaining sections . what is the ratio of time spent on section c to section a if the total duration is 1 hour ? | the time spent on section b and section c is 18 minutes each . the ratio of c to a is 18 : 24 = 3 : 4 the answer is e . | a = 3 / 4
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a ) 10 , b ) 20 , c ) 30 , d ) 27.7 , e ) 50 | d | divide(add(add(add(20, const_3), add(add(add(20, const_3), const_4), const_2)), add(add(add(add(20, const_3), const_4), const_2), const_2)), 3) | the average of first 3 prime numbers greater than 20 is ? | 23 + 29 + 31 = 83 / 3 = 27.7 answer : d | a = 20 + 3
b = 20 + 3
c = b + 4
d = c + 2
e = a + d
f = 20 + 3
g = f + 4
h = g + 2
i = h + 2
j = e + i
k = j / 3
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a ) 2.3 , b ) 8.3 , c ) 7.3 , d ) 3.3 , e ) 1.3 | d | multiply(const_12, divide(multiply(44, divide(44, const_100)), 64)) | a reduction of 44 % in the price of bananas would enable a man to obtain 64 more for rs . 40 , what is reduced price per dozen ? | "explanation : 40 * ( 44 / 100 ) = 17.6 - - - 64 ? - - - 12 = > rs . 3.30 answer : d" | a = 44 / 100
b = 44 * a
c = b / 64
d = 12 * c
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a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8 | e | subtract(24, 16) | if x and y are integers , what is the least positive number of 24 x + 16 y ? | "24 x + 16 y = 8 ( 3 x + 2 y ) which will be a minimum positive number when 3 x + 2 y = 1 . 3 ( 1 ) + 2 ( - 1 ) = 1 then 8 ( 3 x + 2 y ) can have a minimum positive value of 8 . the answer is e ." | a = 24 - 16
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a ) 2003 , b ) 2004 , c ) 2005 , d ) 2006 , e ) 2007 | d | add(1987, divide(subtract(70, 32), const_2)) | a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee ' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1987 on her 32 nd birthday first be eligible to retire under this provision ? | "she must gain at least 70 points , now she has 32 and every year gives her two more points : one for age and one for additional year of employment , so 32 + 2 * ( # of years ) = 70 - - > ( # of years ) = 19 - - > 1987 + 19 = 2006 . answer : d ." | a = 70 - 32
b = a / 2
c = 1987 + b
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a ) 11 , b ) 12 , c ) 29 , d ) 28 , e ) 29 | d | divide(const_1, subtract(divide(const_1, add(3, divide(1, 2))), divide(1, const_4))) | a cistern is filled by a tap in 3 1 / 2 hours . due to leak in the bottom of the cistern , it takes half an hour longer to fill the cistern . if the cistern is full how long will it take the leak to empty it ? | 2 / 7 - 1 / x = 1 / 4 x = 28 answer : d | a = 1 / 2
b = 3 + a
c = 1 / b
d = 1 / 4
e = c - d
f = 1 / e
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a ) 4.5 , b ) 7 , c ) 8 , d ) 19 / 3 , e ) 12 | d | multiply(multiply(10, 3), divide(1, 3)) | in the coordinate plane , points ( x , 1 ) and ( 10 , y ) are on line k . if line k passes through the origin and has slope 1 / 3 , then x + y = | "line k passes through the origin and has slope 1 / 3 means that its equation is y = 1 / 3 * x . thus : ( x , 1 ) = ( 3 , 1 ) and ( 10 , y ) = ( 10,10 / 3 ) - - > x + y = 3 + 10 / 3 = 19 / 3 . answer : d ." | a = 10 * 3
b = 1 / 3
c = a * b
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a ) 810 , b ) 12 , c ) 13 , d ) 14 , e ) 16 | a | divide(multiply(40, subtract(10, 8)), 8) | a 40 gallon solution of salt and water is 10 % salt . how many gallons of water must be added to the solution in order to decrease the salt to 8 % of the volume ? | "amount of salt = 4.0 assume x gallons of water are added . 4.0 / 40 + x = 8 / 100 400 = 8 x + 320 8 x = 80 x = 10 correct option : a" | a = 10 - 8
b = 40 * a
c = b / 8
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a ) 41 , b ) 42 , c ) 43 , d ) 44 , e ) 45 | e | divide(factorial(10), multiply(factorial(subtract(10, const_2)), factorial(const_2))) | if 10 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes | n ( n - 1 ) / 2 = 10 * 9 / 2 = 45 answer : e | a = math.factorial(10)
b = 10 - 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e
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a ) 10 , b ) 12 , c ) 13 , d ) 14 , e ) 15 | a | multiply(5, const_2) | 6 x β 5 y + 3 z = 22 4 x + 8 y β 11 z = 7 5 x β 6 y + 2 z = 12 given the equations above , x + y + z = ? | ( 6 x β 5 y + 3 z ) - ( 5 x β 6 y + 2 z ) = 22 - 12 or , x + y + z = 10 option a is the ans | a = 5 * 2
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a ) 20 % , b ) 24 % , c ) 30 % , d ) 43 % , e ) 79 % | d | multiply(divide(subtract(multiply(divide(add(const_100, 10), const_100), divide(add(const_100, 60), const_100)), const_1), multiply(divide(add(const_100, 10), const_100), divide(add(const_100, 60), const_100))), const_100) | the output of a factory is increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output is increased by 60 % . by approximately what percent would the output of the factory now have to be decreased in order to restore the original output ? | "take it as original output = 100 . to meet demand increase by 10 % , then output = 110 . to meet holiday demand , new output increase by 60 % then output equals 176 to restore new holidy demand output to original 100 . final - initial / final * 100 = 76 / 176 * 100 = 8 / 33 * 100 = 43 % approxiamately . option d is correct ." | a = 100 + 10
b = a / 100
c = 100 + 60
d = c / 100
e = b * d
f = e - 1
g = 100 + 10
h = g / 100
i = 100 + 60
j = i / 100
k = h * j
l = f / k
m = l * 100
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a ) 405 , b ) 420 , c ) 440 , d ) 447 , e ) 490 | e | multiply(35, divide(multiply(divide(72, const_60), 35), subtract(38, 35))) | car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 38 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ? | "car y began travelling after 72 minutes or 1.2 hours . let t be the time for which car y travelled before it stopped . both cars stop when they have travelled the same distance . so , 35 ( t + 1.2 ) = 38 t t = 14 distance traveled by car x from the time car y began traveling until both cars stopped is 35 x 14 = 490 miles answer : - e" | a = 72 / const_60
b = a * 35
c = 38 - 35
d = b / c
e = 35 * d
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a ) $ 18,400 , b ) $ 19,500 , c ) $ 20,200 , d ) $ 20,400 , e ) $ 21,200 | e | multiply(const_2, const_10) | a certain car ' s price decreased by 2.5 % ( from the original price ) each year from 1996 to 2002 , during that time the owner of the car invested in a new carburetor and a new audio system for the car , which increased car ' s price by $ 2,500 . if the price of the car in 1996 was $ 22,000 , what is the car ' s price in 2002 ? | "price in 96 = 22000 price decrease each year = 2.5 / 100 * 22000 = 550 price in 97 = 22000 - 550 price in 98 = 22000 - 2 * 550 price in 99 = 22000 - 3 * 550 price in 00 = 22000 - 4 * 550 price in 01 = 22000 - 5 * 550 price in 02 = 22000 - 6 * 550 = 18700 investment in the car = 2500 net price of the car in 02 = 18700 + 2500 = $ 21200 correct option : e" | a = 2 * 10
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a ) 35 , b ) 42.5 , c ) 44 , d ) 50 , e ) 52.5 | a | divide(add(8, 20), add(add(divide(8, 40), divide(15, const_60)), divide(20, 60))) | jerry travels 8 miles at an average speed of 40 miles per hour , stops for 15 minutes , and then travels another 20 miles at an average speed of 60 miles per hour . what is jerry β s average speed , in miles per hour , for this trip ? | total time taken by jerry = ( 8 / 40 ) * 60 minutes + 15 minutes + ( 20 / 60 ) * 60 minutes = 47 minutes average speed = total distance / total time = ( 8 + 20 ) miles / ( 47 / 60 ) hours = 28 * 60 / 47 = 35 miles per hour answer : option a | a = 8 + 20
b = 8 / 40
c = 15 / const_60
d = b + c
e = 20 / 60
f = d + e
g = a / f
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a ) 16 % , b ) 16.66 % , c ) 18 % , d ) 21 % , e ) 50 % | e | multiply(divide(subtract(60, 40), 40), const_100) | john makes $ 40 a week from his job . he earns a raise and now makes $ 60 a week . what is the % increase ? | "increase = ( 20 / 40 ) * 100 = 50 % . e" | a = 60 - 40
b = a / 40
c = b * 100
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a ) 2736 , b ) 2309 , c ) - 2801 , d ) - 2241 , e ) none of these | d | add(multiply(negate(69), 39), 450) | - 69 * 39 + 450 = ? | "= > - 69 * ( 40 - 1 ) + 450 ; = > - ( 69 * 40 ) + 69 + 450 ; = > - 2760 + 519 = - 2241 . correct option : d" | a = negate * (
b = a + 39
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a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | b | subtract(4, reminder(3, 8)) | when n is divided by 24 , the remainder is 4 . what is the remainder when 3 n is divided by 8 ? | "let n = 4 ( leaves a remainder of 4 when divided by 24 ) 3 n = 3 ( 4 ) = 12 , which leaves a remainder of 4 when divided by 8 . answer b" | a = 4 - reminder
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a ) 90 min , b ) 100 min , c ) 72 min , d ) 75 min , e ) 130 min | c | inverse(subtract(add(inverse(45), inverse(60)), inverse(40))) | two pipes a and b can separately fill a cistern in 45 minutes and 60 minutes respectively . there is a third pipe in the bottom of the cistern to empty it . if all the three pipes are simultaneously opened , then the cistern is full in 40 minutes . in how much time , the third pipe alone can empty the cistern ? | "1 / 40 - ( 1 / 45 + 1 / 60 ) = - 1 / 72 third pipe can empty in 72 minutes answer : c" | a = 1/(45)
b = 1/(60)
c = a + b
d = 1/(40)
e = c - d
f = 1/(e)
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a ) 60 , b ) 50 , c ) 40 , d ) 70 , e ) 65 | b | divide(450, divide(multiply(6, 3), 2)) | a car takes 6 hours to cover a distance of 450 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ? | "time = 6 distance = 450 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 450 / 9 = 50 kmph answer b ." | a = 6 * 3
b = a / 2
c = 450 / b
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a ) 216 , b ) 243 , c ) 215 , d ) 729 , e ) 728 | c | subtract(multiply(multiply(6, 6), 6), const_1) | a letter lock consists of 3 rings each marked with 6 different letters . the number of distinct unsuccessful attempts to open the lock is at the most - . | since each ring consists of six different letters , the total number of attempts possible with the three rings is = 6 * 6 * 6 = 216 . of these attempts , one of them is a successful attempt . maximum number of unsuccessful attempts = 216 - 1 = 215 . answer : c | a = 6 * 6
b = a * 6
c = b - 1
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a ) 800 , b ) 900 , c ) 1000 , d ) 1100 , e ) 1250 | e | divide(multiply(subtract(850, 800), 4), divide(16, const_100)) | average of money that group of 4 friends pay for rent each month is $ 800 . after one persons rent is increased by 16 % the new mean is $ 850 . what was original rent of friend whose rent is increased ? | "0.16 x = 4 ( 850 - 800 ) 0.16 x = 200 x = 1250 answer e" | a = 850 - 800
b = a * 4
c = 16 / 100
d = b / c
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a ) 4 hours , b ) 2 hours , c ) 3 hours , d ) 6 hours , e ) 5 hours | a | divide(multiply(120, const_2), 60) | a person started from point a to point b and returned back to a with a speed of 60 kmh . if the distance between a and b is 120 km , calculate the time he travelled | time = distance / speed total distance = ( from a - > b and from b - > a ) = 120 + 120 = 240 km speed = 60 kmh 240 / 60 = 4 answer : a | a = 120 * 2
b = a / 60
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a ) 6 , b ) 8 , c ) 10 , d ) 11 , e ) 15 | d | subtract(choose(7, 5), choose(subtract(7, 2), 2)) | a meeting has to be conducted with 5 managers . find the number of ways in which the managers may be selected from among 7 managers , if there are 2 managers who refuse to attend the meeting together . | "the total number of ways to choose 5 managers is 7 c 5 = 21 we need to subtract the number of groups which include the two managers , which is 5 c 3 = 10 . 21 - 10 = 11 the answer is d ." | a = math.comb(7, 5)
b = 7 - 2
c = math.comb(b, 2)
d = a - c
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a ) 1 : 3 , b ) 2 : 3 , c ) 3 : 2 , d ) 3 : 1 , e ) 3 : 4 | c | divide(multiply(multiply(multiply(multiply(const_4, const_3), multiply(10, const_2)), const_100), const_4.0), multiply(8000, 10)) | ravi and sunil are partners in a business . ravi invests rs . 15,000 for 8 months and sunil invested rs . 8000 for 10 months then after one year ratio of their profits will be | "= ( 15000 * 8 ) : ( 8000 * 10 ) = 120000 : 80000 = 3 : 2 answer : c" | a = 4 * 3
b = 10 * 2
c = a * b
d = c * 100
e = d * 4
f = 8000 * 10
g = e / f
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a ) $ 400 , b ) $ 800 , c ) $ 1,000 , d ) $ 1,600 , e ) $ 2,400 | a | divide(multiply(10, subtract(60, 50)), divide(25, const_100)) | on a saturday night , each of the rooms at a certain motel was rented for either $ 50 or $ 60 . if 10 of the rooms that were rented for $ 60 had instead been rented for $ 50 , then the total rent the motel charged for that night would have been reduced by 25 percent . what was the total rent the motel actually charged for that night ? | let total rent the motel charge for all rooms = x if 10 rooms that were rented for 60 $ had instead been rented for 50 $ , then total difference in prices = 10 $ * 10 = 100 $ total rent the motel charged would have been reduced by 25 % . 25 x = 100 = > x = 400 answer a | a = 60 - 50
b = 10 * a
c = 25 / 100
d = b / c
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a ) 44 , b ) 45 , c ) 46 , d ) 67 , e ) 48 | d | multiply(subtract(multiply(divide(subtract(const_100, 10), const_100), divide(add(const_100, 85), const_100)), const_1), const_100) | if price of t . v set is reduced by 10 % , then its sale increases by 85 % , find net effect on sale value | - a + b + ( ( - a ) ( b ) / 100 ) = - 10 + 85 + ( - 10 * 85 ) / 100 = - 10 + 85 - 8.5 = 67 answer : d | a = 100 - 10
b = a / 100
c = 100 + 85
d = c / 100
e = b * d
f = e - 1
g = f * 100
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a ) 22.4 % , b ) 50 % , c ) 25 % , d ) 52 % , e ) none of these | a | subtract(multiply(divide(300, add(225, 20)), const_100), const_100) | a retailer buys a radio for rs 225 . his overhead expenses are rs 20 . he sellis the radio for rs 300 . the profit percent of the retailer is | "explanation : cost price = ( 225 + 20 ) = 245 sell price = 300 gain = ( 55 / 245 ) * 100 = 22.4 % . answer : a" | a = 225 + 20
b = 300 / a
c = b * 100
d = c - 100
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a ) 27 , b ) 36 , c ) 54 , d ) 72 , e ) 90 | c | sqrt(multiply(162, 18)) | which number should replace both the asterisks in ( * / 18 ) x ( * / 162 ) = 1 ? | let ( y / 18 ) x ( y / 162 ) = 1 y ^ 2 = 18 x 162 = 18 x 18 x 9 y = ( 18 x 3 ) = 54 the answer is c . | a = 162 * 18
b = math.sqrt(a)
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a ) 22 , b ) 36 , c ) 39 , d ) 21 , e ) 11 | a | add(add(5, 6), 11) | anne bought doughnuts for a class breakfast party . she bought 5 chocolate doughnuts , 6 coconut doughnuts , and 11 jam - filled doughnuts . how many doughnuts did anne buy in all ? | "add the numbers of doughnuts . 5 + 6 + 11 = 22 . answer is a ." | a = 5 + 6
b = a + 11
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a ) 3 / 16,000 , b ) 1 / 8,000 , c ) 3 / 1,600 , d ) 1 / 90 , e ) 2 / 45 | b | multiply(divide(120, 800), divide(const_1, 600)) | a certain music store stocks 800 cellos and 600 violas . of these instruments , there are 120 cello - viola pairs , such that a cello and a viola were both made with wood from the same tree ( each tree can make at most one viola and one cello , so there are no pairs other than these 90 ) . if one viola and one cello are chosen at random , what is the probability that the two instruments are made with wood from the same tree ? | "solution provided by stanford 2012 is correct : 120 / 800 choosing one of the cellos which has a pair viola , 1 / 600 choosing the viola which is the pair of chosen cello - - > p = 120 / 800 * 1 / 600 = 1 / 8,000 . answer : b ." | a = 120 / 800
b = 1 / 600
c = a * b
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a ) 1000 meters , b ) 1050 meters , c ) 1200 meters , d ) 1250 meters , e ) 2500 meters | e | multiply(multiply(10, divide(15, const_60)), const_1000) | a man is walking at the rate of 10 km / hr crosses a bridge in 15 minutes . the length of the bridge is | "explanation : we need to get the answer in meters . so we will first of change distance from km / hour to meter / sec by multiplying it with 5 / 18 and also change 15 minutes to seconds by multiplying it with 60 . speed = 10 Γ’ Λ β 5 / 18 = 25 / 9 m / sec time = 15 Γ’ Λ β 60 seconds = 900 seconds distance = time Γ’ Λ β speed / distance = 25 / 9 Γ’ Λ β 900 = 2500 meter option e" | a = 15 / const_60
b = 10 * a
c = b * 1000
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a ) 8248402936 , b ) 8268413076 , c ) 8268413071 , d ) 8064329671 , e ) 8244563371 | b | multiply(divide(826924, 9999), const_100) | 826924 Γ 9999 = ? | "b 8268413076 826924 Γ 9999 = 826924 Γ ( 10000 - 1 ) = 826924 Γ 10000 - 826924 Γ 1 = 8269240000 - 826924 = 8268413076" | a = 826924 / 9999
b = a * 100
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a ) 20 % , b ) 25 % , c ) 30 % , d ) 40 % , e ) 72 % | d | multiply(divide(144, divide(const_3600, const_10)), const_100) | the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 144 Β° of the circle , what percentage of megatek employees are in manufacturing ? | answer : d 144 Β° divided by 360 Β° equals 0.4 , therefore the sector is equal to 40 % of the total | a = 3600 / 10
b = 144 / a
c = b * 100
|
a ) 100 m , b ) 125 m , c ) 130 m , d ) 150 m , e ) none | d | multiply(100, subtract(const_2, const_1)) | a train speeds past a pole in 15 seconds and a platfrom 100 m long in 25 seconds . its length is : | "sol . let the length of the train be x metres and its speed be y m / sec . they , x / y = 15 β y = x / 15 β΄ x + 100 / 25 = x / 15 β x = 150 m . answer d" | a = 2 - 1
b = 100 * a
|
a ) 27 , b ) 36 , c ) 29 , d ) 50 , e ) 11 | d | subtract(multiply(divide(subtract(90, 55), subtract(const_12, 9)), const_12), 90) | gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 55 and the turban . find the price of the turban . | let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 55 . thus , 3434 ( 90 + x ) = 55 + x or 270 + 3 x = 220 + 4 x or x = 50 answer : d | a = 90 - 55
b = 12 - 9
c = a / b
d = c * 12
e = d - 90
|
a ) 72 , b ) 85 , c ) 100 , d ) 51 , e ) 80 | c | add(50, divide(50, const_2)) | in a ratio which is equal to 2 : 4 , if the antecedent is 50 , then the consequent is ? | "we have 2 / 4 = 50 / x 2 x = 50 * 4 x = 100 consequent = 100 answer is c" | a = 50 / 2
b = 50 + a
|
a ) 1 / 3 , b ) 1 / 18 , c ) 1 / 10 , d ) 2 , e ) 30 | b | divide(const_1, multiply(divide(1.5, 5), 60)) | before leaving home for the town of madison , pete checks a map which shows that madison is 5 inches from his current location , gardensquare . pete arrives in madison 1.5 hours later and drove at an average speed of 60 miles per hour . at what scale , in inches per mile , is the map drawn ? | "pete covered 1.5 * 60 = 90 miles which correspond to 5 inches on the map - - > scale in inches per mile is 5 / 90 = 1 / 18 . answer : b ." | a = 1 / 5
b = a * 60
c = 1 / b
|
a ) 38.5 , b ) 37.5 , c ) 37.0 , d ) 36.5 , e ) none of these | b | divide(subtract(subtract(multiply(50, 38), 45), 55), subtract(50, const_2)) | the average of 50 numbers is 38 . if two numbers 45 and 55 are discarded , the average of the remaining set of numbers is | average of the remaining set of numbers [ 50 x 38 - ( 45 + 55 ) ] / ( 50 - 2 ) = ( 1900 - 100 ) / 48 = 37.5 answer : b | a = 50 * 38
b = a - 45
c = b - 55
d = 50 - 2
e = c / d
|
a ) 197 , b ) 245 , c ) 189 , d ) 278 , e ) 268 | b | divide(multiply(420, add(const_100, 19)), add(subtract(const_100, 15), add(const_100, 19))) | i bought two books ; for rs . 420 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ? | "x * ( 85 / 100 ) = ( 420 - x ) 119 / 100 x = 245 answer : b" | a = 100 + 19
b = 420 * a
c = 100 - 15
d = 100 + 19
e = c + d
f = b / e
|
a ) 2 : 3 , b ) 7 : 11 , c ) 5 : 4 , d ) 4 : 5 , e ) 11 : 9 | e | divide(add(multiply(4, divide(28, add(4, 3))), 6), add(multiply(3, divide(28, add(4, 3))), 6)) | the ratio of the ages of mini and minakshi is 4 : 3 . the sum of their ages is 28 years . the ratio of their ages after 6 years will be | "let mini β s age = 4 x and minakshi β s age = 3 x then 4 x + 3 x = 28 x = 4 mini β s age = 16 years and minakshi β s age = 12 years ratio of their ages after 8 years = ( 16 + 6 ) : ( 12 + 6 ) = 22 : 18 = 11 : 9 answer : e" | a = 4 + 3
b = 28 / a
c = 4 * b
d = c + 6
e = 4 + 3
f = 28 / e
g = 3 * f
h = g + 6
i = d / h
|
a ) 31.25 cm , b ) 25 cm , c ) 35 cm , d ) 50 cm , e ) none of these | a | divide(multiply(5, 50), multiply(40, 20)) | 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day . if the average displacement of water by a man is 5 m 3 , then the rise in the water level in the tank will be : | "explanation : total volume of water displaced = ( 5 x 50 ) m 3 = 250 m 3 rise in water level = 250 / 40 Γ£ β 20 = 0.3125 m = 31.25 cm answer : a" | a = 5 * 50
b = 40 * 20
c = a / b
|
a ) 16.7 % , b ) 20 % , c ) 24.67 % , d ) 33.33 % , e ) none of these | a | multiply(subtract(const_1, divide(const_100, add(const_100, 20))), const_100) | if the price of petrol increases by 20 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ? | "explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 20 ) i . e 120 . now , his consumption should be reduced to : - = ( 120 β 100 ) / 120 β 100 . hence , the consumption should be reduced to 16.7 % . answer : a" | a = 100 + 20
b = 100 / a
c = 1 - b
d = c * 100
|
a ) 35 % , b ) 45 % , c ) 55 % , d ) 65 % , e ) 75 % | c | multiply(divide(subtract(subtract(const_100, 60), multiply(divide(multiply(const_10, const_3), const_100), subtract(const_100, 40))), 40), const_100) | thirty percent of the women in a college class are science majors , and the non - science majors make up 60 % of the class . what percentage of the men are science majors if 40 % of the class are men ? | science majors make up 0.4 of the class . 60 % of the class are women and 0.3 * 0.6 = 0.18 of the class are female science majors . then 0.22 of the class are male science majors . 0.4 x = 0.22 x = 0.55 = 55 % the answer is c . | a = 100 - 60
b = 10 * 3
c = b / 100
d = 100 - 40
e = c * d
f = a - e
g = f / 40
h = g * 100
|
a ) 2 , b ) 3 , c ) 4 , d ) 25 , e ) 20 , 870,080 | a | add(const_1, const_1) | a cargo ship carrying 4 kinds of items , doohickies , geegaws , widgets , and yamyams , arrives at the port . each item weighs 2 , 11 , 5 , and 7 pounds , respectively , and each item is weighed as it is unloaded . if , in the middle of the unloading process , the product of the individual weights of the unloaded items equals 104 , 350400 pounds , how many widgets have been unloaded ? | we need to know the number of widgets ( which weigh 5 pounds each ) . the number of times that 5 divides the number is related to the number of times that 10 divides the number . when we divide 104 , 350,400 by 100 , we get 104 , 350,400 = 1 , 043,504 * 5 ^ 2 * 2 ^ 2 . 1 , 043,504 is not divisible by 5 , thus there are 2 widgets . the answer is a . | a = 1 + 1
|
a ) 228 , b ) 112 , c ) 80 , d ) 96 , e ) 100 | b | add(add(add(add(add(add(const_12, const_2), const_1), add(add(const_12, const_2), add(add(add(add(add(const_2, const_4), const_4), subtract(const_10, const_1)), add(add(const_2, const_4), const_4)), add(const_10, const_2)))), add(add(add(const_12, const_2), const_1), const_1)), 18), add(const_2, const_4)) | what is the sum of all the composite numbers up to 18 ? | explanation : 4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 = 112 answer : b | a = 12 + 2
b = a + 1
c = 12 + 2
d = 2 + 4
e = d + 4
f = 10 - 1
g = e + f
h = 2 + 4
i = h + 4
j = g + i
k = 10 + 2
l = j + k
m = c + l
n = b + m
o = 12 + 2
p = o + 1
q = p + 1
r = n + q
s = r + 18
t = 2 + 4
u = s + t
|
a ) 100 , b ) 10,000 , c ) 100,000 , d ) 0.01 , e ) 0.0001 | a | multiply(divide(1, multiply(const_100, const_100)), multiply(const_100, const_100)) | if 10,000 microns = 1 decimeter , and 1 , 000,000 angstroms = 1 decimeter , how many angstroms equal 1 micron ? | "10,000 microns = 1 decimeter , and 1 , 000,000 angstroms = 1 decimeter 10,000 microns = 1 , 000,000 angstroms 1 micron = 100 answer : a" | a = 100 * 100
b = 1 / a
c = 100 * 100
d = b * c
|
a ) 98.5 % , b ) 100.0 % , c ) 102.8 % , d ) 104.5 % , e ) 105.0 % | c | divide(multiply(add(const_100, multiply(const_100, 10)), add(subtract(const_100, 5), const_4)), multiply(const_100, 10)) | this year , mbb consulting fired 5 % of its employees and left remaining employee salaries unchanged . sally , a first - year post - mba consultant , noticed that that the average ( arithmetic mean ) of employee salaries at mbb was 10 % more after the employee headcount reduction than before . the total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction ? | "100 employees , each earning 1 $ . after the cut , 95 are left , each earning 1.1 $ . 1.1 * 95 = 104.5 100 * 1 = 100 this gives you the answer . answer : c" | a = 100 * 10
b = 100 + a
c = 100 - 5
d = c + 4
e = b * d
f = 100 * 10
g = e / f
|
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