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 |
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a ) 45 kmph , b ) 50 kmph , c ) 85 kmph , d ) 60 kmph , e ) 70 kmph | c | subtract(divide(150, multiply(6, const_0_2778)), 5) | a train 150 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train . find the speed of the train . | "explanation : let the speed of the train be x kmph . speed of the train relative to man = ( x + 5 ) kmph = ( x + 5 ) × 5 / 18 m / sec . therefore 150 / ( ( x + 5 ) × 5 / 18 ) = 6 < = > 30 ( x + 5 ) = 2700 < = > x = 85 speed of the train is 85 kmph . answer : option c" | a = 6 * const_0_2778
b = 150 / a
c = b - 5
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a ) 20,000 , b ) 21,200 , c ) 28,200 , d ) 13,500 , e ) none of these | d | divide(add(multiply(subtract(const_12, 5), 15000), multiply(multiply(const_2, multiply(const_100, const_100)), 5)), multiply(const_100, const_10)) | a , b and c start a business each investing 20,000 . after 5 months a withdrew 10000 , b withdrew 15000 and c invests 5000 more . at the end of the year , a total profit of 58000 was recorded . find the share of b . | ratio of the capitals of a , b and c = 20000 ã — 5 + 10000 ã — 7 : 20000 ã — 5 + 5000 ã — 7 : 20000 ã — 5 + 25000 ã — 7 = 170000 : 135000 : 275000 = 170 : 135 : 275 . b â € ™ s share = ( 58000 ã — 135 â „ 580 ) = 13500 answer d | a = 12 - 5
b = a * 15000
c = 100 * 100
d = 2 * c
e = d * 5
f = b + e
g = 100 * 10
h = f / g
|
a ) 420 , b ) 520 , c ) 600 , d ) 720 , e ) 820 | c | add(200, multiply(divide(200, 4), 8)) | in a college , the ratio of the number of boys to girls is 8 : 4 . if there are 200 girls , the total number of students in the college is | "explanation : let the boy are 8 x and girls are 4 x = > 4 x = 200 = > x = 50 total students = 8 x + 4 x = 12 x = 12 ( 50 ) = 600 option c" | a = 200 / 4
b = a * 8
c = 200 + b
|
a ) 0.09 , b ) 0.15 , c ) 0.54 , d ) 0.75 , e ) 0.91 | d | divide(add(add(22, 18), 5), 60) | a certain bag contains 60 balls — 22 white , 18 green , 5 yellow , 6 red , and 9 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ? | according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 22 + 18 + 5 ) / 60 = 45 / 60 = 0.75 . answer : d . | a = 22 + 18
b = a + 5
c = b / 60
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a ) 59028 , b ) 27777 , c ) 29999 , d ) 59000 , e ) 27772 | d | add(multiply(multiply(divide(divide(50000, const_2), 10), const_3), const_4), 1500) | a and b start a business , with a investing the total capital of rs . 50000 , on the condition that b pays a interest @ 10 % per annum on his half of the capital . a is a working partner and receives rs . 1500 per month from the total profit and any profit remaining is equally shared by both of them . at the end of the year , it was found that the income of a is twice that of b . find the total profit for the year ? | "interest received by a from b = 10 % of half of rs . 50000 = 10 % * 25000 = 2500 . amount received by a per annum for being a working partner = 1500 * 12 = rs . 18000 . let ' p ' be the part of the remaining profit that a receives as his share . total income of a = ( 2500 + 18000 + p ) total income of b = only his share from the remaining profit = ' p ' , as a and b share the remaining profit equally . income of a = twice the income of b ( 2500 + 18000 + p ) = 2 ( p ) p = 20500 total profit = 2 p + 18000 = 2 * 20500 + 18000 = 59000 . answer : d" | a = 50000 / 2
b = a / 10
c = b * 3
d = c * 4
e = d + 1500
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a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24 | a | add(divide(add(24000, 48000), 6000), const_3) | on a certain date , pat invested $ 6000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 24000 , in how many years total will the total value of the investment plus interest increase to $ 48000 ? | 24,000 = 6,000 ( 1 + x ) ^ 10 4 = ( 1 + x ) ^ 10 = 2 ^ 2 ( 1 + x ) ^ 10 = ( ( 1 + x ) ^ 5 ) ^ 2 = 2 ^ 2 therefore , ( 1 + x ) ^ 5 = 2 48,000 = 6000 ( 1 + x ) ^ n ( 1 + x ) ^ n = 8 ( 1 + x ) ^ n = 2 ^ 3 ( 1 + x ) ^ n = ( ( 1 + x ) ^ 5 ) ^ 3 = ( 1 + x ) ^ 15 therefore , n = 15 . the answer is a . | a = 24000 + 48000
b = a / 6000
c = b + 3
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a ) 1 / 7 , b ) 2 / 7 , c ) 1 / 3 , d ) 7 / 12 , e ) 2 / 3 | c | divide(const_2, 6) | equal amount of water were poured into two empty jars of different capacities , which made one jar 1 / 6 full and other jar 1 / 5 full . if the water in the jar with lesser capacity is then poured into the jar with greater capacity , what fraction of the larger jar will be filled with water ? | "same amount of water made bigger jar 1 / 6 full , thenthe same amount of water ( stored for a while in smaller jar ) were added to bigger jar , so bigger jar is 1 / 6 + 1 / 6 = 2 / 6 = 1 / 3 full . answer : c ." | a = 2 / 6
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a ) 6 , b ) 7 , c ) 7 10 / 29 , d ) 9 , e ) 10 | c | multiply(add(2, const_4.0), 3) | abel can complete a work in 10 days , ben in 14 days and carla in 15 days . all of them began the work together , but abel had to leave after 2 days and ben 3 days before the completion of the work . how long did the work last ? | "abel in the 2 days that he worked completed 1 / 5 of the job = 4 / 5 remains then if ben had to leave 3 days before the completion , this means that carla had to work alone for these 3 days in which she completed 1 / 5 of the job . now together , ben and carla completed the job in ( 1 / 14 + 1 / 15 ) ( t ) = 3 / 5 29 / 210 ( t ) = 3 / 5 - - - > t = 126 / 29 therefore , these 4 10 / 29 days worked plus the 3 days that carla had to work by herself add to 7 10 / 29 days answer : c" | a = 2 + 4
b = a * 3
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a ) 2 , b ) 3 , c ) 5 , d ) 7 , e ) 11 | b | add(const_3, const_4) | what is the smallest positive integer that can be multiplied by 432 to make it a perfect square ? | "432 = 2 ^ 4 * 3 ^ 2 * 3 therefore the smallest integer to multiplied to 1008 to make it a perfect square is 3 . answer b ." | a = 3 + 4
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a ) 11.73 , b ) 12.85 , c ) 13.8 , d ) 14 , e ) 15.87 | b | divide(divide(multiply(207, subtract(const_100, 15)), const_100), 14) | the price of lunch for 14 people was $ 207 including a 15 % gratuity for service . what was the average price per person , excluding the gratuity ? | "clearly b is the answer i used poe here lets consider option ( b ) 14 * 12.85 = 180 now 180 ( 115 / 100 ) = 207 = > possible answer imo b" | a = 100 - 15
b = 207 * a
c = b / 100
d = c / 14
|
a ) 0 , b ) 100 , c ) 6993 , d ) 699930 , e ) none of these | d | divide(add(69758472, const_1), const_2) | the difference between the place values of two sevens in the numeral 69758472 is | "required difference = ( 700000 - 70 ) = 699930 answer : option d" | a = 69758472 + 1
b = a / 2
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a ) 2 / 3 , b ) 5 / 8 , c ) 3 / 5 , d ) 3 / 8 , e ) 4 / 9 | b | divide(add(1, add(divide(const_1, const_2), add(divide(1, add(1, 3)), divide(3, add(1, 3))))), add(1, 3)) | in a bag containing 3 balls , a white ball was placed and then 1 ball was taken out at random . what is the probability that the extracted ball would turnon to be white , if all possible hypothesis concerning thecolor of theballs that initiallyin the bag were equally possible ? | since , all possible hypothesis regarding the colour of the balls are equally likely , therefore these could be 3 white balls , initially in the bag . ∴ required probability = 1 / 4 [ 1 + 3 / 4 + 1 / 2 + 1 / 4 ] = 1 / 4 [ ( 4 + 3 + 2 + 1 ) / 4 ] = 5 / 8 b | a = 1 / 2
b = 1 + 3
c = 1 / b
d = 1 + 3
e = 3 / d
f = c + e
g = a + f
h = 1 + g
i = 1 + 3
j = h / i
|
a ) 12.8 , b ) 12.6 , c ) 12.5 , d ) 12.2 , e ) 16.6 | e | divide(multiply(20, 1000), add(1000, 200)) | 1000 men have provisions for 20 days . if 200 more men join them , for how many days will the provisions last now ? | "1000 * 20 = 1200 * x x = 16.6 . answer : e" | a = 20 * 1000
b = 1000 + 200
c = a / b
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a ) 18 , b ) 20 , c ) 16 , d ) 22 , e ) 24 | c | subtract(choose(6, 3), choose(subtract(6, 2), 2)) | a meeting has to be conducted with 3 managers . find the number of ways in which the managers be selected from among 6 managers , if 2 managers will not attend the meeting together ? | "we can either choose all 3 people from 4 manager who have no problems or choose 2 from the 4 and 1 from the 2 managers who have a problem sitting together so 4 c 3 + ( 4 c 2 * 2 c 1 ) this is 4 + 12 = 16 answer : c" | a = math.comb(6, 3)
b = 6 - 2
c = math.comb(b, 2)
d = a - c
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a ) 500 , b ) 277 , c ) 266 , d ) 188 , e ) 123 | a | divide(multiply(divide(multiply(616, const_100), add(const_100, 10)), add(const_100, 10)), add(const_100, 12)) | the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 12 % , then the cost price of the article is ? | "110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 110 * 560 ) / 112 = rs . 500 answer : a" | a = 616 * 100
b = 100 + 10
c = a / b
d = 100 + 10
e = c * d
f = 100 + 12
g = e / f
|
a ) 40 , b ) 30 , c ) 25 , d ) data inadequate , e ) none of these . | e | divide(add(90, 30), const_2) | the total marks obtained by a student in mathematics and physics is 90 and his score in chemistry is 30 marks more than that in physics . find the average marks scored in mathamatics and chemistry together . | "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 90 and c - p = 30 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 90 + 30 ) / 2 = 60 . answer : e" | a = 90 + 30
b = a / 2
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a ) 33.33 % , b ) 25 % , c ) 75 % , d ) 66.66 % , e ) none of these | b | multiply(subtract(divide(const_100, subtract(const_100, 20)), const_1), const_100) | if x is less than y by 20 % then y exceed x by : | using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 20 % ) = > 20 / ( 100 - 20 ) * 100 = 25 % answer : b | a = 100 - 20
b = 100 / a
c = b - 1
d = c * 100
|
a ) 240 , b ) 65 , c ) 110 , d ) 130 , e ) 200 | b | add(divide(subtract(add(divide(subtract(200, 20), const_2), 20), 20), const_2), 20) | a picnic attracts 200 persons . there are 20 more men than women , and 20 more adults than children . how many men are at this picnic ? | adult + children = 200 let , children = y then , adult = y + 20 i . e . y + ( y + 20 ) = 200 i . e . y = 900 i . e . adult = 90 + 20 = 110 adults include only men and women i . e . men + women = 110 let women , w = x then men , m = x + 20 i . e . x + ( x + 20 ) = 2 x + 20 = 110 i . e . x = 45 i . e . men , m = 45 + 20 = 65 answer : option b | a = 200 - 20
b = a / 2
c = b + 20
d = c - 20
e = d / 2
f = e + 20
|
a ) 30 / 7 , b ) 30 / 98 , c ) 60 / 147 , d ) 50 / 294 , e ) 52 / 294 | a | divide(multiply(6, 5), 7) | the smallest fraction , which each of 6 / 7 , 5 / 14 , 10 / 21 will divide exactly is : | required fraction = l . c . m of 6 / 7 , 5 / 14 , 10 / 21 = ( l . c . m of 6 , 5 , 10 ) / ( h . c . f of 7 , 14 , 21 ) = 30 / 7 answer : a | a = 6 * 5
b = a / 7
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a ) 10 , b ) 12.5 , c ) 25 , d ) 22.5 , e ) 14.5 | d | multiply(divide(180, multiply(400, 2)), const_100) | what is rate of interest if principal . amount be 400 , simple interest 180 and time 2 year . | "s . i = ( p * r * t ) / 100 180 = 800 r / 100 r = 180 / 8 = 22.5 % answer d" | a = 400 * 2
b = 180 / a
c = b * 100
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a ) 131 , b ) 197 , c ) 207 , d ) 219 , e ) 227 | a | subtract(multiply(11, 12), add(const_10, const_1)) | find the smallest number which when divided by 11 and 12 leaves respective remainders of 2 and 3 . | "let ' n ' is the smallest number which divided by 11 and 12 leaves respective remainders of 2 and 3 . required number = ( lcm of 11 and 12 ) - ( common difference of divisors and remainders ) = ( 132 ) - ( 1 ) = 131 . answer : a" | a = 11 * 12
b = 10 + 1
c = a - b
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a ) 7 , b ) 7 2 / 3 , c ) 8 1 / 3 , d ) 9 , e ) 9 1 / 3 | a | divide(add(16, const_0_33), add(2, divide(20, const_60))) | david biked 16 1 / 3 miles in 2 hours and 20 minutes . what was his average rate of speed in miles per hour ? | d = 16 ( 1 / 3 ) = 49 / 3 t = 2 ( 1 / 3 ) = 7 / 3 s = d / t = 7 answer = a | a = 16 + const_0_33
b = 20 / const_60
c = 2 + b
d = a / c
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a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8 | d | add(divide(power(2, 2), 2), const_1) | if f ( x ) = 12 - x ^ 2 / 2 and f ( 2 k ) = 6 k , what is one possible value for k ? | "first of all , see thisgmat blog postand check the related lesson linked below for some background on function notation . we can plug anything in for x and get a result . you can find f ( 1 ) , for example , by plugging in 1 where x is , and you would get 12 - 1 / 2 = 11.5 . or we could find f ( 2 ) , which would be 12 - 4 / 2 = 10 . so the notation f ( 2 k ) means that we are going to plug a 2 k in for x everywhere in the formula for f ( x ) . that would be : f ( 2 k ) = 12 - ( 2 k ) ^ 2 / 2 = 12 - 2 k ^ 2 . remember that we have to square both the 2 and the k , to get 4 k 2 . now , this expression , the output , we will set equal to 2 k . 12 - 2 k ^ 2 = 2 k - - > k = - 3 or k = 6 . all the answers are positive , so we choose k = 2 . answer = d" | a = 2 ** 2
b = a / 2
c = b + 1
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a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) it can not be determined | b | subtract(add(60, 50), const_100) | a box contains either blue or red flags . the total number of flags in the box is an even number . a group of children are asked to pick up two flags each . if all the flags are used up in the process such that 60 % of the children have blue flags , and 50 % have red flags , what percentage of children have flags of both the colors ? | "solution : let the total number of flags be 100 ( even number ) let the total number of ' blue ' flags alone be ' a ' let the total number of ' red ' flags alone be ' b ' let the total number of ' both ' flags be ' c ' we have given , total number of blue flags = 60 % = 60 = a + c total number of red flags = 50 % = 50 = b + c total number of flags = a + b + c = 100 ( since all the flags have been utilized ) so , substituting for c in the third equation , we have , 60 - c + c + 50 - c = 100 c = 10 option b ." | a = 60 + 50
b = a - 100
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a ) rs . 2522 , b ) rs . 2512 , c ) rs . 2572 , d ) rs . 2592 , e ) none | a | subtract(multiply(power(add(const_1, divide(divide(20, const_4), const_100)), const_3), multiply(multiply(multiply(const_4, const_4), const_100), sqrt(const_100))), multiply(multiply(multiply(const_4, const_4), const_100), sqrt(const_100))) | find the compound interest on rs . 16,000 at 20 % per annum for 9 months , compounded quartely . | "solution principal = rs . 16,000 ; time = 9 months = 3 quarters ; amount = rs . [ 16000 x ( 1 + 5 / 100 ) ³ ] = [ 16000 x 21 / 20 x 21 / 20 x 21 / 20 ] = rs . 18522 . c . i = rs . ( 18522 - 16000 ) = rs . 2522 . answer a" | a = 20 / 4
b = a / 100
c = 1 + b
d = c ** 3
e = 4 * 4
f = e * 100
g = math.sqrt(100)
h = f * g
i = d * h
j = 4 * 4
k = j * 100
l = math.sqrt(100)
m = k * l
n = i - m
|
a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9 | b | subtract(power(subtract(73, multiply(add(const_3, const_4), const_10)), subtract(330, multiply(floor(divide(330, const_4)), const_4))), multiply(const_2, const_10)) | find the ones digit of 73 ^ 330 | "cyclicity of 3 is 3,9 , 7,1 after 4 multiplication again the cycle repeats . so divide 330 by 4 and we get 87 as quotient and 2 as remainder . so cycle will run for 87 times and then 2 times more . so pick up the 2 nd item from the cycle . hence answer b ." | a = 3 + 4
b = a * 10
c = 73 - b
d = 330 / 4
e = math.floor(d)
f = e * 4
g = 330 - f
h = c ** g
i = 2 * 10
j = h - i
|
a ) 36.0 , b ) 36.5 , c ) 36.1 , d ) 36.2 , e ) 36.8 | c | divide(add(multiply(36, 50), subtract(subtract(50, const_2), 23)), 50) | the mean of 50 observations was 36 . it was found later that an observation 28 was wrongly taken as 23 . the corrected new mean is : | "explanation : correct sum = ( 36 * 50 + 28 - 23 ) = 1825 . correct mean = = 1805 / 50 = 36.1 answer : c ) 36.1" | a = 36 * 50
b = 50 - 2
c = b - 23
d = a + c
e = d / 50
|
a ) 1,125 , b ) 2,000 , c ) 2,100 , d ) 2,250 , e ) 2,540 | a | divide(540, 540) | the rate of interest on a sum of money is 9 % p . a . for the first 3 years , 4 % p . a . for the next 4 years , and 5 % for the period beyond 7 years . if the s . i , occured on the sum for the total period of 8 years is rs . 540 / - , the sum is | "explanation : i 1 = ( p x 3 x 9 ) / 100 = 10 p / 37 i 2 = ( p x 4 x 4 ) / 100 = 4 p / 25 i 3 = ( p x 1 x 5 ) / 100 = p / 20 10 p / 37 + 4 p / 25 + p / 20 = 540 12 p / 25 = 540 p = 1125 answer : option a" | a = 540 / 540
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a ) 70 , b ) 52 , c ) 62 , d ) 77 , e ) 79 | d | add(add(22, 15), add(21, 19)) | in a games hour 4 different types of players came to the ground ? cricket 22 , hokey 15 , football 21 , softball 19 . how many players are present in the ground ? | "total number of players = 22 + 15 + 21 + 19 = 77 answer is d" | a = 22 + 15
b = 21 + 19
c = a + b
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a ) 15 kg , b ) 20 kg , c ) 8 kg , d ) 24 kg , e ) 32 kg | d | divide(multiply(40, 3), 5) | an alloy is to contain copper and zinc in the ratio 5 : 3 . the zinc required to be melted with 40 kg of copper is ? | let the required quantity of copper be x kg 5 : 3 : : 40 : x 5 x = 40 * 3 x = 24 kg answer is d | a = 40 * 3
b = a / 5
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a ) 289 , b ) 231 , c ) 200 , d ) 40 , e ) 111 | d | divide(subtract(350, 348), divide(5, const_100)) | if 5 % more is gained by selling an article for rs . 350 than by selling it for rs . 348 , the cost of the article is | "explanation : let c . p . be rs . x . then , 5 % of x = 350 - 348 = 2 x / 20 = 2 = > x = 40 answer : d" | a = 350 - 348
b = 5 / 100
c = a / b
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a ) 200 , b ) 300 , c ) 400 , d ) 500 , e ) 600 | a | multiply(divide(subtract(20, 10), subtract(30, 20)), 200) | solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 200 milliliters of solution x to create a solution that is 20 percent alcohol by volume ? | "20 % is an equal distance between 10 % and 30 % . thus there should be equal parts of both solutions . we should add 200 ml of solution y . the answer is a ." | a = 20 - 10
b = 30 - 20
c = a / b
d = c * 200
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a ) 12.5 % , b ) 40 % , c ) 80 % , d ) 200 % , e ) none | d | multiply(divide(6, 3), const_100) | the ratio 6 : 3 expressed as a percent equals | "solution 6 : 3 = 6 / 3 = ( 6 / 3 x 100 ) % . = 200 % . answer d" | a = 6 / 3
b = a * 100
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a ) 80 kg , b ) 85 kg , c ) 90 kg , d ) 88 kg , e ) 110 kg | d | add(multiply(8, 6), 40) | the average weight of 8 person ' s increases by 6 kg when a new person comes in place of one of them weighing 40 kg . what might be the weight of the new person ? | "total weight increased = ( 8 x 6 ) kg = 48 kg . weight of new person = ( 40 + 48 ) kg = 88 kg . answer : d" | a = 8 * 6
b = a + 40
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a ) 88 / 5 , b ) 13 , c ) 17 , d ) 21 , e ) 23 | a | divide(multiply(add(add(8, const_3), const_2), divide(8, const_2)), add(const_2, divide(const_1, const_2))) | a and b are two partially filled buckets of water . if 8 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 8 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ? | "let bucket a be a and bucket b be b scenario 1 a - 8 = 1 / 3 ( b + 8 ) - - - - > 3 a - 24 = b + 8 scenario 2 b - 8 = 1 / 2 ( a + 8 ) - - - - - > 2 b - 16 = a + 8 from scenario 1 , b = 3 a - 32 substitute b with this information in stmt 2 2 ( 3 a - 32 ) - 16 = a + 8 - - - - - - > 6 a - 64 - 16 = a + 8 - - - - - - > 6 a - a = 80 + 8 - - - > 5 a = 88 a = 88 / 5 , answer choice a" | a = 8 + 3
b = a + 2
c = 8 / 2
d = b * c
e = 1 / 2
f = 2 + e
g = d / f
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a ) 23 , b ) 27 , c ) 20 , d ) 27 , e ) 11 | c | divide(multiply(25, 16), 20) | 16 men can complete a piece of work in 25 days . in how many days can 20 men complete that piece of work ? | "16 * 25 = 20 * x = > x = 20 days answer : c" | a = 25 * 16
b = a / 20
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a ) 400 km , b ) 450 km , c ) 500 km , d ) 550 km , e ) 600 km | a | divide(multiply(divide(multiply(900, const_2), const_3), const_3), add(const_2, const_3)) | a man traveled a total distance of 900 km . he traveled one - third of the whole trip by plane and the distance traveled by train is one - half of the distance traveled by bus . if he traveled by train , plane and bus , how many kilometers did he travel by bus ? | "total distance traveled = 900 km . distance traveled by plane = 300 km . distance traveled by bus = x distance traveled by train = x / 2 x + x / 2 + 300 = 900 3 x / 2 = 600 x = 400 km the answer is a ." | a = 900 * 2
b = a / 3
c = b * 3
d = 2 + 3
e = c / d
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a ) 37 % , b ) 45 % , c ) 55 % , d ) 65 % , e ) 75 % | a | add(divide(multiply(25, subtract(const_100, 40)), const_100), subtract(40, 18)) | in country z , 18 % of the people do not have a university diploma but have the job of their choice , and 25 % of the people who do not have the job of their choice have a university diploma . if 40 % of the people have the job of their choice , what percent of the people have a university diploma ? | "setting up a matrix is how i solve this one . diploma no diploma totals job of choice w / diploma job of choice w / o diploma = 18 % job of choice total = 40 % not job of choice with diploma = . 25 x not job of choice w / o diploma = . 75 x total not job of choice = x total with diploma total without diploma total citizen = 100 if 40 % of people have their job of choice , then 60 % of people do not have their job of choice . 25 % of 60 % = 15 % . we can also see that 30 % of the people have their job of choice and a diploma ( 40 % - 18 % = 22 % ) . 22 % + 15 % = 37 % . therefore 37 % of the people in country z have a diploma . ans a" | a = 100 - 40
b = 25 * a
c = b / 100
d = 40 - 18
e = c + d
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a ) 2 : 3 , b ) 3 : 4 , c ) 3 : 20 , d ) 3 : 7 , e ) 9 : 50 | e | divide(multiply(0.09, const_100), multiply(0.5, const_100)) | if 0.5 of a number is equal to 0.09 of another number , the ratio of the numbers i | sol . 0.5 a = 0.09 b â ‡ ” a / b = 0.09 / 0.50 = 9 / 50 â ˆ ´ a : b = 9 : 50 . answer e | a = 0 * 9
b = 0 * 5
c = a / b
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a ) 210 km , b ) 240 km , c ) 220 km , d ) 180 km , e ) 190 km | a | add(multiply(70, 2), 70) | two trains t 1 and t 2 start simultaneously from two stations x and y respectively towards each other . if they are 70 km apart both 3 and 6 hours after start , then find the distance between the two stations . | in first 3 hours t 1 travels r km and t 2 travels s km . after 6 hours they traveled r + s + 70 + 700 2 ( r + s ) = r + s + 140 r + s = 140 hence distance between xy is r + s + 70 = 140 + 70 = 210 answer : a | a = 70 * 2
b = a + 70
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a ) 60 , b ) 52 , c ) 5 , d ) 25 , e ) 125 | d | power(subtract(multiply(4, 15), 55), const_2) | among 7 numbers the average of first 4 numbers is 13 and the average of last 4 numbers is 15 . the sum of last 3 numbers is 55 . the square of the fourth number is equal to the last number then what is the last number ? | let the numbers be a , b , c , d , e , f , g d + e + f + g = 15 * 4 = 60 e + f + g = 55 , 60 - 55 = 5 so the fourth number is 5 . the square is 25 . the answer is option d . | a = 4 * 15
b = a - 55
c = b ** 2
|
a ) 16 , b ) 20 , c ) 24 , d ) 28 , e ) 32 | c | divide(multiply(subtract(1, divide(1, 3)), 12), subtract(1, subtract(1, divide(1, 3)))) | a driver would have reduced the time it took to drive from home to the store by 1 / 3 if the average speed had been increased by 12 miles per hour . what was the actual average speed , in miles per hour , when the driver drove from home to the store ? | "since the distance remains the same ( we ' re just changing the rate and time ) , any increase in rate or time is met with a decrease in the other term . decreasing the time by 1 / 3 would give us : d = ( r ) ( t ) = ( 2 t / 3 ) ( x * r ) x = 3 / 2 since ( 2 t / 3 ) ( 3 r / 2 ) = ( r ) ( t ) = d 3 r / 2 = r + 12 r / 2 = 12 r = 24 the answer is c ." | a = 1 / 3
b = 1 - a
c = b * 12
d = 1 / 3
e = 1 - d
f = 1 - e
g = c / f
|
a ) 450 , b ) 810 , c ) 900 , d ) 1000 , e ) 1100 | c | multiply(divide(multiply(9, add(9, 1)), 2), multiply(2, const_10)) | the sum of all the digits of the integers from 18 to 21 inclusive is 24 ( 1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24 ) . what is the sum q of all the digits of the integers from 0 to 99 inclusive ? | "we want the sum of the digits from 0 to 99 , so i approximated : 0 - 9 - > 45 - > ( 9 + 0 ) * 10 / 2 40 - 49 - > 85 ( 13 + 4 ) * 10 / 2 90 - 99 - > 135 ( 18 + 9 ) * 10 / 2 we can see at a glance that theweightgoes up as the numbers go up ( meaning the difference between 85 and 45 is 40 , while 135 - 85 is 50 , this means that the second part of this sequence carries more weight for our result ) , so we know that the final answer has to be more than 850 ( 85 * 10 ) but close to it , and that ' s just q = 900 : the answer is c ." | a = 9 + 1
b = 9 * a
c = b / 2
d = 2 * 10
e = c * d
|
a ) 115 , b ) 121 , c ) 117 , d ) 119 , e ) 121 | c | divide(subtract(multiply(500, 126), 10350), subtract(500, 50)) | a man has rs . 10350 in the form of rs . 50 notes and rs . 500 notes . the total number of notes are 126 . find the number of notes of rs . 50 denomination . | "total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 126 - x now , 50 * x + 500 * ( 126 - x ) = 10350 50 x + 63000 - 500 x = 10350 - 450 x = - 52650 x = 117 . no . of 50 rupees note = 117 . answer : option c" | a = 500 * 126
b = a - 10350
c = 500 - 50
d = b / c
|
a ) 65 % , b ) 50 % , c ) 59 % , d ) 40 % , e ) 53 % | a | subtract(multiply(33, add(const_4, const_1)), multiply(25, const_4)) | a dealer purchases 15 articles for rs . 25 and sells 12 articles for rs . 33 . find the profit percentage ? | "l . c . m of 15 and 12 = 60 cp of 60 articles = rs . 100 ( 25 * 4 ) sp of 60 articles = rs . 165 ( 33 * 5 ) profit percentage = ( 165 - 100 ) / 100 * 100 = 65 % answer : a" | a = 4 + 1
b = 33 * a
c = 25 * 4
d = b - c
|
a ) 1 / 16 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 4 | d | divide(divide(choose(42, const_1), 42), power(const_3, const_2)) | each factor of 230 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 42 ? | "210 = 2 * 3 * 5 * 7 , so the # of factors 210 has is ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 16 ( see below ) ; 42 = 2 * 3 * 7 , so out of 16 factors only two are multiples of 42 : 42 and 210 , itself ; so , the probability is 2 / 16 = 3 / 16 . answer : d" | a = math.comb(42, 1)
b = a / 42
c = 3 ** 2
d = b / c
|
a ) 30 litres , b ) 31 litres , c ) 32 litres , d ) 33 litres , e ) 34 litres | b | add(add(const_12, 3), multiply(multiply(multiply(const_2, const_2), const_2), const_2)) | 3 different containers contain 496 litres , 403 litres and 713 litres of mixtures of milk and water respectively . what biggest measure can measure all the different quantities exactly ? | 403 ) 713 ( 1 403 - - - - - - - - - 310 ) 403 ( 1 310 - - - - - - - - - - 93 ) 310 ( 3 279 - - - - - - - - 31 ) 93 ( 3 93 - - - - - - - x so answer is 31 litres . . . . . . answer : b | a = 12 + 3
b = 2 * 2
c = b * 2
d = c * 2
e = a + d
|
a ) 10 days , b ) 9 days , c ) 8 days , d ) 7 days , e ) 6 days | b | divide(multiply(subtract(18, 6), 12), add(12, 4)) | 12 persons can complete the work in 18 days . after working for 6 days , 4 more persons added to complete the work fast . in how many more days they will complete the work ? | total work 12 * 18 = 216 units after 6 days work finished 6 * 12 = 72 units remaining work 216 - 72 = 144 units remaing days = 144 ( 12 + 4 ) = 9 days answer : b | a = 18 - 6
b = a * 12
c = 12 + 4
d = b / c
|
a ) 75 , b ) 100 , c ) 125 , d ) 175 , e ) 145 | e | divide(subtract(multiply(divide(870, const_3), const_4), 870), const_2) | there are 870 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ? | "let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 870 . hence , we have m + f = 870 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 870 / 3 = 290 solving the three equations yields the solution f = 290 , m = 580 , and d = 290 . the number of female democratic participants equals half the female participants equals 290 / 2 = 145 . answer : e" | a = 870 / 3
b = a * 4
c = b - 870
d = c / 2
|
a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 14 | e | multiply(divide(subtract(37, const_2), add(const_3, const_2)), const_2) | is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 37 , then how old is b ? | "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 37 5 x = 35 = > x = 7 hence , b ' s age = 2 x = 14 years . answer : e" | a = 37 - 2
b = 3 + 2
c = a / b
d = c * 2
|
a ) 1300,1500 , b ) 9000,12000 , c ) 7290,8000 , d ) 15000,12000 , e ) 72821,75000 | b | divide(multiply(10000, const_1), const_3) | a and b invests rs . 10000 each , a investing for 9 months and b investing for all the 12 months in the year . if the total profit at the end of the year is rs . 21000 , find their shares ? | "the ratio of their profits a : b = 9 : 12 = 3 : 4 share of a in the total profit = 3 / 7 * 21000 = rs . 9000 share of b in the total profit = 4 / 7 * 21000 = rs . 12000 answer : b" | a = 10000 * 1
b = a / 3
|
a ) 40 % , b ) 50 % , c ) 60 % , d ) 66.66 % , e ) 70 % | d | multiply(divide(subtract(150, add(multiply(5, 5), multiply(5, 5))), 150), const_100) | a batsman scored 150 runs which included 5 boundaries and 5 sixes . what percent of his total score did he make by running between the wickets . | "explanation : number of runs made by running = 150 - ( 5 x 4 + 5 x 6 ) = 150 - ( 50 ) = 100 now , we need to calculate 100 is what percent of 150 . = > 100 / 150 * 100 = 66.66 % option d" | a = 5 * 5
b = 5 * 5
c = a + b
d = 150 - c
e = d / 150
f = e * 100
|
a ) 914.2 hours , b ) 937.1 hours , c ) 915 hours , d ) 905 hours , e ) 915 hours | b | add(divide(7380, add(16, 2)), divide(7380, subtract(16, 2))) | speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph . a man rows to a place at a distance of 7380 km and comes back to the starting point . the total time taken by him is : | "explanation : speed downstream = ( 16 + 2 ) = 18 kmph speed upstream = ( 16 - 2 ) = 14 kmph total time taken = 7380 / 18 + 7380 / 14 = 410 + 527.1 = 937.1 hours answer : option b" | a = 16 + 2
b = 7380 / a
c = 16 - 2
d = 7380 / c
e = b + d
|
a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24 | a | divide(subtract(sqrt(add(multiply(multiply(220, 2), const_4), power(2, 2))), 2), const_2) | a jar of 220 marbles is divided equally among a group of marble - players today . if 2 people joined the group in the future , each person would receive 1 marble less . how many people are there in the group today ? | 220 = 20 * 11 = 22 * 10 there are 20 people in the group today . the answer is a . | a = 220 * 2
b = a * 4
c = 2 ** 2
d = b + c
e = math.sqrt(d)
f = e - 2
g = f / 2
|
a ) 100 meter , b ) 170 meter , c ) 156 meter , d ) 168 meter , e ) 154 meter | a | multiply(divide(multiply(60, const_1000), const_3600), 6) | a train running at the speed of 60 km / hr crosses a pole in 6 seconds . find the length of the train ? | "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 6 = 100 meter answer : a" | a = 60 * 1000
b = a / 3600
c = b * 6
|
a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 3 | c | divide(20, subtract(60, 20)) | a chemist mixes one liter of pure water with x liters of a 60 % salt solution , and the resulting mixture is a 20 % salt solution . what is the value of x ? | "concentration of salt in pure solution = 0 concentration of salt in salt solution = 60 % concentration of salt in the mixed solution = 20 % the pure solution and the salt solution is mixed in the ratio of - - > ( 60 - 20 ) / ( 20 - 0 ) = 2 / 1 1 / x = 2 / 1 x = 1 / 2 answer : c" | a = 60 - 20
b = 20 / a
|
a ) 36 , b ) 24 , c ) 17 , d ) 8 , e ) 5 | d | add(power(divide(subtract(4, sqrt(subtract(power(4, 2), multiply(const_4, 4)))), 2), 2), power(divide(add(4, sqrt(subtract(power(4, 2), multiply(const_4, 4)))), 2), 2)) | if a and b are the roots of the equation x 2 - 4 x + 4 = 0 , then the value of a 2 + b 2 is : | "sol . ( b ) the sum of roots = a + b = 4 product of roots = ab = 4 now , a 2 + b 2 = ( a + b ) 2 - 2 ab = 16 - 8 = 8 answer d" | a = 4 ** 2
b = 4 * 4
c = a - b
d = math.sqrt(c)
e = 4 - d
f = e / 2
g = f ** 2
h = 4 ** 2
i = 4 * 4
j = h - i
k = math.sqrt(j)
l = 4 + k
m = l / 2
n = m ** 2
o = g + n
|
a ) a . 76000 , b ) b . 77000 , c ) c . 78000 , d ) d . 79000 , e ) e . 80000 | a | multiply(multiply(multiply(5, add(const_3, const_4)), const_100), add(add(const_3, const_4), const_3)) | if a town of 75,000 people is growing at a rate of approx . 1 % per year , the population of the town in 5 years will be closest to ? | 1 % is quite small and hence the answer is a ) | a = 3 + 4
b = 5 * a
c = b * 100
d = 3 + 4
e = d + 3
f = c * e
|
a ) $ . 80 , b ) $ 1.00 , c ) $ 1.20 , d ) $ 1.50 , e ) $ 1.60 | a | multiply(divide(20, 100), 4.00) | the total cost of 100 paper plates and 200 paper cups is $ 4.00 at the same rates what is the total cost of 20 of the plates and 40 of the cups ? | "u dont need to go through all this what u have with u is 100 p + 200 c = $ 4.00 just divide the equation by 5 and you will get what u are looking for 20 p + 40 c = $ 0.80 therefore oa is a" | a = 20 / 100
b = a * 4
|
a ) 45 cm , b ) 255 cm , c ) 244 cm , d ) 55 cm , e ) 280 cm | b | floor(divide(add(multiply(15, const_100), 75), add(multiply(11, const_100), 25))) | which greatest possible length can be used to measure exactly 15 meter 75 cm , 11 meter 25 cm and 7 meter 65 cm | "explanation : convert first all terms into cm . i . e . 1575 cm , 1125 cm , 765 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 255 . option b" | a = 15 * 100
b = a + 75
c = 11 * 100
d = c + 25
e = b / d
f = math.floor(e)
|
a ) 3 , b ) 5 , c ) 6 , d ) 11 , e ) 16 | b | subtract(8, divide(24, 8)) | if ( m - 8 ) is a factor of m ^ 2 - sm - 24 , then s = | "( m - 8 ) ( m - a ) = m ^ 2 - sm - 24 a = - 3 s = 8 + a = 5 = d = b" | a = 24 / 8
b = 8 - a
|
a ) 41 , b ) 43 , c ) 60 , d ) 68 , e ) 70 | b | add(add(add(add(add(const_2, divide(6, const_2)), add(const_2, const_3)), add(const_3, const_4)), add(add(const_3, const_4), const_4)), add(const_2, add(add(const_3, const_4), const_4))) | a dice has one of the first 4 prime number on each its 6 sides , with no two sides having the same number . the dice is rolled 10 times and the results added . the addition is most likely to be closet to | if die is rolled then avg score = ( 2 + 3 + 5 + 7 ) / 4 = 41 / 4 so , most likely sum for 10 times = 41 / 4 * 10 = 43 answer : b | a = 6 / 2
b = 2 + a
c = 2 + 3
d = b + c
e = 3 + 4
f = d + e
g = 3 + 4
h = g + 4
i = f + h
j = 3 + 4
k = j + 4
l = 2 + k
m = i + l
|
a ) 2 / 3 , b ) 5 / 6 , c ) 7 / 8 , d ) 4 / 5 , e ) 5 / 8 | a | divide(subtract(0.7, 0.5), subtract(0.8, 0.5)) | each of the products produced yesterday was checked by worker x or worker y . 0.5 % of the products checked by worker x are defective and 0.8 % of the products checked by worker y are defective . if the total defective rate of all the products checked by worker x and worker y is 0.7 % , what fraction of the products was checked by worker y ? | x : 0.5 % is 0.2 % - points from 0.7 % . y : 0.8 % is 0.1 % - points from 0.7 % . therefore the ratio of products checked by y : x is 2 : 1 . thus , worker y checked 2 / 3 of the products . the answer is a . | a = 0 - 7
b = 0 - 8
c = a / b
|
a ) 25 cm , b ) 20 cm , c ) 35 cm , d ) 50 cm , e ) none of these | b | divide(multiply(4, 40), multiply(40, 20)) | 40 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 4 m 3 , then the rise in the water level in the tank will be : | "explanation : total volume of water displaced = ( 4 x 40 ) m 3 = 160 m 3 rise in water level = 160 / 40 ã — 20 = 0.2 m = 20 cm answer : b" | a = 4 * 40
b = 40 * 20
c = a / b
|
a ) 36 , b ) 42 , c ) 24 , d ) 54 , e ) 45 | c | inverse(divide(const_3, multiply(18, const_4))) | if a is thrice as fast as b and together can do a work in 18 days . in how many days a alone can do the work ? | "a ’ s one day ’ s work = 1 / x b ’ s one day ’ s work = 1 / 3 x a + b ’ s one day ’ s work = 1 / x + 1 / 3 x = 1 / 18 = 3 + 1 / 3 x = 4 / 3 x = 1 / 18 x = 18 * 4 / 3 = 24 answer : c" | a = 18 * 4
b = 3 / a
c = 1/(b)
|
a ) a ) 44 , b ) b ) 77 , c ) c ) 79 , d ) d ) 81 , e ) e ) 82 | a | multiply(divide(divide(multiply(21, add(21, const_1)), const_2), 21), 4) | what is the average of first 21 multiples of 4 ? | "required average = 7 ( 1 + 2 + . . . . + 21 ) / 21 ( 4 / 21 ) x ( ( 21 x 22 ) / 2 ) ( because sum of first 21 natural numbers ) = 44 a" | a = 21 + 1
b = 21 * a
c = b / 2
d = c / 21
e = d * 4
|
a ) 575 toys , b ) 375 toys , c ) 680 toys , d ) 475 toys , e ) 675 toys | c | divide(3400, 5) | a factory produces 3400 toys per week . if the workers at this factory work 5 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ? | "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 5 days ) by 5 . 3400 / 5 = 680 toys correct answer c" | a = 3400 / 5
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a ) 1 , b ) 1.11 , c ) 1.01 , d ) 1.1 , e ) 1.21 | c | multiply(divide(subtract(const_100, 99), 99), const_100) | if the cost price is 99 % of selling price then what is the profit percentage . | "selling price = rs 100 : then cost price = rs 99 : profit = rs 1 . profit = { ( 1 / 99 ) * 100 } % = 1.01 % answer is c ." | a = 100 - 99
b = a / 99
c = b * 100
|
a ) 22 , b ) 24 , c ) 28 , d ) 32 , e ) 44 | b | add(multiply(divide(4, const_2), 11), const_2) | g ( a ) is defined as the product of all even integers k such that 0 < k ≤ x . for example , g ( 14 ) = 2 × 4 × 6 × 8 × 10 × 12 × 14 . if g ( y ) is divisible by 4 ^ 11 , what is the smallest possible value for a ? | g ( a ) = 4 ^ 11 = 2 ^ 22 . so we have to find a product with atleast 22 2 ' s in it . in option 1 22 the total no of 2 ' s = [ 22 / 2 ] + [ 22 / 4 ] + [ 22 / 8 ] + [ 22 / 16 ] = 11 + 5 + 2 + 1 = 19 in option 2 24 the total no of 2 ' s = [ 24 / 2 ] + [ 24 / 4 ] + [ 24 / 8 ] + [ 24 / 16 ] = 12 + 6 + 3 + 1 = 22 . hence b | a = 4 / 2
b = a * 11
c = b + 2
|
a ) 93.5 , b ) 90 , c ) 6.75 , d ) 6.25 , e ) 2 | d | divide(multiply(25, 25), const_100) | j is 25 % less than p and 20 % less than t . t is w % less than p . what is the value of w ? | "usually we can solve every question of this type by choosing appropriate value of the variable and deriving the value of other related variables . let , p = 400 then j = ( 75 / 100 ) * 400 = 300 also j = ( 80 / 100 ) * t i . e . t = 300 * 100 / 80 = 375 and t = [ 1 - ( w / 100 ) ] * p i . e . 100 - w = 100 * t / p = 100 * 375 / 400 = 93.75 i . e . w = 6.25 answer : option d" | a = 25 * 25
b = a / 100
|
a ) 1.5 , b ) 1.6 , c ) 1.7 , d ) 1.8 , e ) 1.4 | e | multiply(divide(35, const_100), 4) | how many litres of pure acid are there in 4 litres of a 35 % solution | explanation : question of this type looks a bit typical , but it is too simple , as below . . . it will be 8 * 20 / 100 = 1.4 answer : option e | a = 35 / 100
b = a * 4
|
a ) 1 / 4 , b ) 4 / 15 , c ) 1 / 3 , d ) 7 / 18 , e ) 4 / 5 | d | divide(7, add(subtract(const_12, const_1), 7)) | last year department store x had a sales total for december that was 7 times the average ( arithmetic mean ) of the monthly sales totals for january through november . the sales total for december was what fraction of the sales total for the year ? | "let avg for 11 mos . = 10 therefore , dec = 70 year total = 11 * 10 + 70 = 180 answer = 70 / 180 = 7 / 18 = d" | a = 12 - 1
b = a + 7
c = 7 / b
|
a ) 1 : 2 , b ) 2 : 5 , c ) 6 ' ' 2 , d ) 3 : 1 , e ) 4 : 7 | d | divide(add(const_1, const_2), subtract(const_2, const_1)) | a man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream . the ratio of the speed of the boat ( in still water ) and the stream is : | explanation : let speed upstream = x hen , speed downstream = 2 x speed in still water = 2 x + x / 2 speed of the stream = 2 x - x / 2 speed in still water : speed of the stream = 3 x / 2 : x / 2 = 3 : 1 answer : d | a = 1 + 2
b = 2 - 1
c = a / b
|
a ) 9 , b ) 11 , c ) 15 , d ) 12 , e ) 20 | b | subtract(multiply(15, 15), add(multiply(5, 14), multiply(9, 16))) | the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years . the age of the 15 th student is ? | "age of the 15 th student = 15 * 15 - ( 14 * 5 + 16 * 9 ) = 225 - 214 = 11 years answer is b" | a = 15 * 15
b = 5 * 14
c = 9 * 16
d = b + c
e = a - d
|
a ) $ 120 , b ) $ 100 , c ) $ 91 , d ) $ 72 , e ) $ 69 | c | multiply(100, divide(100, add(100, 10))) | a shopkeeper sold an article at $ 100 with 10 % profit . then find its cost price ? | "cost price = selling price * 100 / ( 100 + profit ) c . p . = 100 * 100 / 110 = $ 91 ( approximately ) answer is c" | a = 100 + 10
b = 100 / a
c = 100 * b
|
a ) 2 , b ) 8 , c ) 24 , d ) 25 , e ) 26 | b | divide(25, multiply(const_10, const_2)) | how many factors does 25 ^ 2 have ? | "36 ^ 2 = 6 * 6 * 6 * 6 = 2 ^ 4 * 3 ^ 4 total factors = ( 4 + 1 ) * ( 4 + 1 ) = 4 * 2 = 8 answer b ." | a = 10 * 2
b = 25 / a
|
a ) 5.002 % , b ) 5.5 % , c ) 0.5 % , d ) 5 % , e ) 20 % | b | multiply(divide(multiply(0.03, 22), 12), const_100) | a glass was filled with 12 ounces of water , and 0.03 ounce of the water evaporated each day during a 22 - day period . what percent of the original amount of water evaporated during this period ? | "in 22 days 22 * 0.03 = 0.66 ounces of water evaporated , which is 0.66 / 12 â ˆ — 100 = 5.5 of the original amount of water . answer : b ." | a = 0 * 3
b = a / 12
c = b * 100
|
a ) 212 , b ) 256 , c ) 304 , d ) 372 , e ) 460 | c | divide(multiply(38, 32), 4) | dan ’ s car gets 32 miles per gallon . if gas costs $ 4 / gallon , then how many miles can dan ’ s car go on $ 38 of gas ? | "38 / 4 = 9.5 gallons 9.5 * 32 = 304 miles the answer is c ." | a = 38 * 32
b = a / 4
|
a ) 15 , b ) 20 , c ) 25 , d ) 13 , e ) 42 | a | divide(add(20, 10), const_2) | if x + y = 20 , x - y = 10 , for integers of x and y , x = ? | "x + y = 20 x - y = 10 2 x = 30 x = 15 answer is a" | a = 20 + 10
b = a / 2
|
a ) 8 , b ) 9 , c ) 10 , d ) 12 , e ) 14 | d | subtract(18, 6) | molly ' s age in 18 years will be 5 times her age 6 years ago . what is molly ' s present age ? | let x be molly ' s present age . x + 18 = 5 ( x - 6 ) x = 12 the answer is d . | a = 18 - 6
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a ) 72 , b ) 192 , c ) 456 , d ) 256 , e ) 264 | c | add(multiply(subtract(3200, 64), divide(1, 8)), 64) | in a circuit board factory , all circuit boards that pass a verification process are certified . every board that fails the verification process is indeed faulty , but 1 / 8 of those that pass are also faulty . approximately how many faulty circuit boards exist in a group of 3200 circuit boards where 64 fail inspection ? | total of 3,200 boards . all that fail verification are indeed faulty . so the 64 are indeed faulty . 1 / 8 those that pass are also faulty . from the 3,200 we know 64 fail . so 3,136 must pass . of these 1 / 8 are faulty . 3,136 divided by 8 gives you 392 . what one must do now is to add to the 392 which were not detected the actually detected faulty ones , namely the 64 . total faulty : 456 . answer : c | a = 3200 - 64
b = 1 / 8
c = a * b
d = c + 64
|
a ) 50 , b ) 60 , c ) 80 , d ) 90 , e ) 120 | d | divide(90, multiply(subtract(const_1, divide(20, const_100)), add(divide(20, const_100), const_1))) | the prices of tea and coffee per kg were the same in june . in july the price of coffee shot up by 20 % and that of tea dropped by 20 % . if in july , a mixture containing equal quantities of tea and coffee costs 90 / kg . how much did a kg of coffee cost in june ? | "let the price of tea and coffee be x per kg in june . price of tea in july = 1.2 x price of coffee in july = 0.8 x . in july the price of 1 / 2 kg ( 900 gm ) of tea and 1 / 2 kg ( 900 gm ) of coffee ( equal quantities ) = 90 1.2 x ( 1 / 2 ) + 0.8 x ( 1 / 2 ) = 90 = > x = 90 thus proved . . . option d ." | a = 20 / 100
b = 1 - a
c = 20 / 100
d = c + 1
e = b * d
f = 90 / e
|
a ) 108 % , b ) 300 % , c ) 100 % , d ) 180 % , e ) 200 % | c | subtract(multiply(divide(divide(3, 4), divide(50, const_100)), const_100), 50) | a dealer purchased an article at 3 / 4 of its list price and sold 50 % more than the list price . find his gain percent ? | mp = 100 cp = 75 sp = 150 - - - - - - 75 - - - - 75 100 - - - - ? = > 100 % answer : c | a = 3 / 4
b = 50 / 100
c = a / b
d = c * 100
e = d - 50
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a ) 670 , b ) 750 , c ) 945 , d ) 375 , e ) 315 | c | divide(divide(24, subtract(multiply(divide(4, 15), divide(5, 7)), multiply(divide(2, 5), divide(4, 9)))), 2) | 4 / 15 of 5 / 7 of a number is greater than 4 / 9 of 2 / 5 of the same number by 24 . what is half of that number ? | "let no . be x 4 / 15 * 5 / 7 * x - 4 / 9 * 2 / 5 * x = 8 by further solving 20 x / 105 - 8 x / 45 = 8 4 x / 315 = 24 x = 1890 we have to find x / 2 = 1890 / 2 = 945 answer : c" | a = 4 / 15
b = 5 / 7
c = a * b
d = 2 / 5
e = 4 / 9
f = d * e
g = c - f
h = 24 / g
i = h / 2
|
a ) 1.5 , b ) 2 , c ) 2.4 , d ) 2.7 , e ) 3 | e | divide(multiply(54, 5), subtract(const_100, 10)) | a driver just filled the car ' s gas tank with 54 liters of gasohol , a mixture consisting of 5 % ethanol and 95 % gasoline . if the car runs best on a mixture consisting of 10 % ethanol and 90 % gasoline , how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance ? | "let x be the number of liters of ethanol added to the gas tank . 0.05 ( 54 ) + x = 0.1 ( 54 + x ) 0.9 x = 5.4 - 2.7 = 2.7 x = 3 liters the answer is e ." | a = 54 * 5
b = 100 - 10
c = a / b
|
a ) $ 14,755 , b ) $ 15,325 , c ) $ 11,129 , d ) $ 16,225 , e ) $ 17,155 | c | multiply(divide(const_3, const_4), const_1000) | a store owner estimates that the average price of type a products will increase by 30 % next year and that the price of type b products will increase by 20 % next year . this year , the total amount paid for type a products was $ 3200 and the total price paid for type b products was $ 5800 . according to the store owner ' s estimate , and assuming the number of products purchased next year remains the same as that of this year , how much will be spent for both products next year ? | "cost of type a products next year = 1.3 * 3200 = 4160 cost of type b products next year = 1.2 * 5800 = 6960 total 4169 + 6960 = 11129 answer : c" | a = 3 / 4
b = a * 1000
|
a ) 25 , b ) 30 , c ) 50 , d ) 55 , e ) 60 | c | multiply(divide(20, 40), const_100) | 20 % of employees are women with fair hair . 40 % of fair - haired employees are women . what percent of employees have fair hair ? | 20 % of employees are women with fair hair . 40 % of fair - haired employees are women . so , 20 % * employees = 40 % * fair haired employees ( because both are equal to the number of fair haired women employees ) ( 1 / 2 ) * employees = fair haired employees answer ( c ) | a = 20 / 40
b = a * 100
|
a ) 60 % , b ) 50 % , c ) 55 % , d ) 40 % , e ) 33.3 % | d | multiply(divide(subtract(multiply(multiply(const_12, multiply(const_4, const_4)), const_1000), multiply(multiply(const_12, const_1000), const_10)), multiply(multiply(const_12, const_1000), const_10)), const_100) | the cost of a one - family home was $ 120,000 in 1980 . in 1988 , the price had increased to $ 168,000 . what was the percent increase in the cost of the home ? | "increase = 168000 - 120000 = 48000 % increase = 48000 * 100 / 120000 = 40 % answer : option d" | a = 4 * 4
b = 12 * a
c = b * 1000
d = 12 * 1000
e = d * 10
f = c - e
g = 12 * 1000
h = g * 10
i = f / h
j = i * 100
|
a ) 10 , b ) 24 , c ) 60 , d ) 70 , e ) 85 | b | divide(250, const_10) | marginal cost is the cost of increasing the quantity produced ( or purchased ) by one unit . if the fixed cost for n products is $ 10,000 and the marginal cost is $ 250 , and the total cost is $ 16,000 , what is the value of n ? | "total cost for n products = fixed cost for n products + n * marginal cost - - > $ 16,000 = $ 10,000 + n * $ 250 - - > n = 24 . answer : b ." | a = 250 / 10
|
a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8 | e | subtract(add(add(17, 19), 2), 30) | in a sports club with 30 members , 17 play badminton and 19 play tennis and 2 do not play either . how many members play both badminton and tennis ? | "17 + 19 = 36 but where as total number is 30 - 2 = 28 therefore answer is 36 - 28 = 8 hence answer is e" | a = 17 + 19
b = a + 2
c = b - 30
|
['a ) 2150', 'b ) 2250', 'c ) 2350', 'd ) 2850', 'e ) 3250'] | b | subtract(divide(multiply(multiply(5, 6), 7), divide(4, const_100)), divide(multiply(multiply(subtract(5, const_1), subtract(6, const_1)), subtract(7, const_1)), divide(4, const_100))) | a boy want to make a cuboid of dimension 5 m , 6 m , 7 m from small cubes of . 04 m 3 . later he realized he can make same cuboid by making it hollow . then it takes some cubes less . what is the no . of these cubes ? | volume of cuboid = 5 * 6 * 7 = 210 m 3 volume of inner cuboid = ( 5 - 1 ) * ( 6 - 1 ) * ( 7 - 1 ) = 120 m 3 therefore , volume of hollow cuboid = 210 - 120 = 90 m 3 no of cubes required = 90 / . 04 = 2250 cubes answer : b | a = 5 * 6
b = a * 7
c = 4 / 100
d = b / c
e = 5 - 1
f = 6 - 1
g = e * f
h = 7 - 1
i = g * h
j = 4 / 100
k = i / j
l = d - k
|
a ) 1 min , b ) 4 min , c ) 6 min , d ) 10 min , e ) 25 min | d | divide(10, 1) | a fill pipe can fill 1 / 2 of cistern in 10 minutes . in how many minutes , it can fill 1 / 2 of the cistern ? | "required time = 10 * 2 * 1 / 2 = 10 minutes answer is d" | a = 10 / 1
|
a ) 1 / 20 , b ) 3 / 40 , c ) 13 / 40 , d ) 3 / 20 , e ) 13 / 22 | d | multiply(divide(3, 8), subtract(const_1, divide(3, 3))) | wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 3 / 8 probability that task 1 will be completed on time , and a 3 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability that task 1 will be completed on time , but task 2 will not ? | "p ( 1 and not 2 ) = 3 / 8 * ( 1 - 3 / 5 ) = 14 / 40 = 3 / 20 . answer : d ." | a = 3 / 8
b = 3 / 3
c = 1 - b
d = a * c
|
a ) 100 kg , b ) 102.5 kg , c ) 85 kg , d ) data inadequate , e ) none of these | a | add(multiply(10, 3.5), 65) | the average weight of 10 person ' s increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ? | "explanation : total weight increased = ( 10 x 3.5 ) kg = 35 kg . weight of new person = ( 65 + 35 ) kg = 100 kg . answer : a" | a = 10 * 3
b = a + 65
|
a ) a ) 78 , b ) b ) 82 , c ) c ) 92 , d ) d ) 91 , e ) e ) 85 | c | divide(add(subtract(multiply(100, 10), 90), 10), 10) | the average marks of 10 students in a class is 100 . but a student mark is wrongly noted as 90 instead of 10 then find the correct average marks ? | "correct avg marks = 100 + ( 10 - 90 ) / 10 avg = 100 - 8 = 92 answer is c" | a = 100 * 10
b = a - 90
c = b + 10
d = c / 10
|
a ) 65 , b ) 66 , c ) 67 , d ) 71 , e ) 72 | b | add(67, power(subtract(67, 68), 67)) | what will be remainder when ( 67 ^ 67 + 67 ) is divided by 68 ? | ( xn + 1 ) will be divisible by ( x + 1 ) only when n is odd . ( 67 ^ 67 + 1 ) will be divisible by ( 67 + 1 ) ( 67 ^ 67 + 1 ) + 66 , when divided by 68 will give 66 as remainder . b ) | a = 67 - 68
b = a ** 67
c = 67 + b
|
a ) s . 50 , b ) s . 46 , c ) s . 49 , d ) s . 41 , e ) s . 42 | a | divide(divide(multiply(1000, 25), const_100), 5) | a reduction of 25 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 1000 , what is the reduced price for kg ? | "1000 * ( 25 / 100 ) = 250 - - - - 5 ? - - - - 1 = > rs . 50 answer : a" | a = 1000 * 25
b = a / 100
c = b / 5
|
['a ) 5 , 500,000', 'b ) 2 , 400,000', 'c ) 55,000', 'd ) 28,000', 'e ) 280'] | b | subtract(add(multiply(multiply(divide(volume_cube(const_100), const_10), const_4), const_4), multiply(multiply(divide(volume_cube(const_100), const_10), multiply(const_2, const_3)), const_3)), volume_cube(const_100)) | a specialized type of sand consists of 40 % mineral x by volume and 60 % mineral y by volume . if mineral x weighs 4 grams per cubic centimeter and mineral y weighs 3 grams per cubic centimeter , how many grams does a cubic meter of specialized sand combination weigh ? ( 1 meter = 100 centimeters ) | let the volume be 1 m ^ 3 = 1 m * 1 m * 1 m = 100 cm * 100 cm * 100 cm = 1 , 000,000 cm ^ 3 by volume 40 % is x = 400,000 cm ^ 3 60 % is y = 600,000 cm ^ 3 by weight , in 1 cm ^ 3 , x is 4 gms in 400,000 cm ^ 3 , x = 4 * 400,000 = 1 , 600,000 grams in 1 cm ^ 3 , y is 3 gms in 600,000 cm ^ 3 , y = 3 * 600,000 = 1 , 800,000 gms total gms in 1 m ^ 3 = 1 , 600,000 + 1 , 800,000 = 2 , 400,000 answer : b | a = volume_cube / (
b = a * 10
c = b * 4
d = c + 4
e = volume_cube / (
f = e * 10
g = 2 * 3
h = f * g
i = d - h
|
a ) 1 hour , b ) 1 hour 10 minutes , c ) 2 hours 30 minutes , d ) 1 hour 20 minutes , e ) 2 hours 10 minutes | d | add(multiply(sqrt(divide(20, 90)), 90), 20) | two cars a and b start from boston and new york respectively simultaneously and travel towards each other at constant speeds along the same route . after meeting at a point between boston and new york the two cars a and b proceed to their respective destinations of new york and boston . car a reaches new york 20 minutes after the two cars have met and car b reaches boston 90 minutes after they have met . how long did car a take to cover the distance between boston and new york ? | "both cars leave at the same time both cars travel at constant speed stealing a useful piece of information from paragkan : if two objects a and b start from opposite points and , after having met en route , reach their respective destinations in a and b mins ( or any other measure of time ) respectively , then the ratio of their speeds ratio of speed : ( a / b ) = sq . rt ( b / a ) sq . rt ( b / a ) sq . rt ( 90 / 20 ) sq . rt ( 3 / 2 ) so , for every three units of distance a travels , b travels two . because we know the ratio of speed and the time it took b to travel the distance a has n ' t yet covered , we can find the time it took a to cover the distance b did in 90 minutes . 90 * ( 2 / 3 ) where 2 / 3 represents the lesser amount of time it took a to travel the distance b did in 90 minutes . = 60 minutes . therefore , a took 20 minutes to travel the first portion then 60 minutes to travel the distance b did in 90 minutes . a spent ( 20 + 60 ) = 80 minutes on the road . d . 1 hour 20 minutes" | a = 20 / 90
b = math.sqrt(a)
c = b * 90
d = c + 20
|
a ) 10 % , b ) 15 % , c ) 20 % , d ) 60 % , e ) 30 % | d | multiply(divide(300, 500), const_100) | the price of a coat in a certain store is $ 500 . if the price of the coat is to be reduced by $ 300 , by what percent is the price to be reduced ? | price of a coat in a certain store = $ 500 the price of the coat is to be reduced by $ 300 % change = ( final value - initial value ) * 100 / initial value % reduction = ( reduction in price ) * 100 / initial value i . e . % reduction = ( 300 ) * 100 / 500 = 60 % answer : option d | a = 300 / 500
b = a * 100
|
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