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 ) 23 , b ) 43 , c ) 21 , d ) 31 , e ) 43 | d | subtract(add(multiply(40, const_2), multiply(43, const_2)), multiply(45, const_3)) | the average weight of a , b , c is 45 kg . the avgwgt of a & b be 40 kg & that of b , c be 43 kg . find the wgt of b . | sol . let a , b , c represent their individual wgts . then , a + b + c = ( 45 * 3 ) kg = 135 kg a + b = ( 40 * 2 ) kg = 80 kg & b + c = ( 43 * 2 ) kg = 86 kg b = ( a + b ) + ( b + c ) - ( a + b + c ) = ( 80 + 86 - 135 ) kg = 31 kg . answer d | a = 40 * 2
b = 43 * 2
c = a + b
d = 45 * 3
e = c - d
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a ) $ 97.75 , b ) $ 90 , c ) $ 91.56 , d ) $ 95.62 , e ) $ 93.45 | a | multiply(multiply(subtract(const_1, divide(15, const_100)), add(const_1, divide(15, const_100))), const_100) | the price of a shirt is increased by 15 % and then reduced by 15 % . the final price of the shirt is ? | let the original price be $ 100 new final price = 85 % of ( 115 % of $ 100 ) = 85 / 100 * 115 / 100 * 100 = $ 97.75 answer is a | a = 15 / 100
b = 1 - a
c = 15 / 100
d = 1 + c
e = b * d
f = e * 100
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a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28 | e | add(add(add(add(add(add(add(4, 3), add(4, const_2)), add(4, const_1)), const_4), const_3), const_2), const_1) | if two integers x , y ( x > y ) are selected from - 3 to 4 ( inclusive ) , how many cases are there ? | there are 8 integers from - 3 to 4 inclusive . 8 c 2 = 28 . the answer is e . | a = 4 + 3
b = 4 + 2
c = a + b
d = 4 + 1
e = c + d
f = e + 4
g = f + 3
h = g + 2
i = h + 1
|
a ) 10 , b ) 12 , c ) 30 , d ) 40 , e ) 20 | e | multiply(divide(100, 45), subtract(45, 36)) | in 100 m race , a covers the distance in 36 seconds and b in 45 seconds . in this race a beats b by : | dist = ( 100 / 45 * 9 ) = 20 m answer e | a = 100 / 45
b = 45 - 36
c = a * b
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['a ) 54', 'b ) 64', 'c ) 75', 'd ) 85', 'e ) 100'] | c | multiply(const_3, power(5, const_2)) | the citizens of planet nigiet are 5 fingered and have thus developed their decimal system in base 8 . a certain street in nigiet contains 1000 ( in base 5 ) buildings numbered 1 to 1000 . how many 3 s are used in numbering these buildings ? express result in terms of base 10 . | no of 3 s b / w 1 - 99 is 20,100 - 199 is 20 and so on . so leavn d range b / w 300 - 399 total no of 3 s is ( 9 * 20 = ) 180 . no of 3 s b / w 300 - 399 is ( 20 + 100 = ) 120 . total no of 3 s b / w 1 - 1000 = 120 + 180 = 300 in base 10 300 = 3 * 5 ^ 2 = 75 . answer : c | a = 5 ** 2
b = 3 * a
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a ) 80 , b ) 180 , c ) 240 , d ) 360 , e ) 480 | b | add(divide(150, 5), 150) | of the people who responded to a market survey , 150 preferred brand x and the rest preferred brand y . if the respondents indicated a preference for brand x over brand y by ratio of 5 to 1 , how many people responded to the survey ? | ratio = 5 : 1 = > 5 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 150 = > 5 x = 150 = > x = 30 hence total no . of respondents = 150 + 30 = 180 hence b is the answer . | a = 150 / 5
b = a + 150
|
a ) 276 , b ) 299 , c ) 230 , d ) 345 , e ) 395 | c | multiply(23, 10) | the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 9 and 10 . the larger of the two numbers is : | "clearly , the numbers are ( 23 x 9 ) and ( 23 x 10 ) . larger number = ( 23 x 10 ) = 230 . answer : option c" | a = 23 * 10
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['a ) 45', 'b ) 51', 'c ) 57', 'd ) 63', 'e ) 69'] | c | add(divide(circumface(11), const_2), multiply(const_2, 11)) | a semicircle has a radius of 11 . what is the approximate perimeter of the semicircle ? | the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 11 + 2 * 11 which is about 57 . the answer is c . | a = circumface / (
b = a + 2
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a ) 20 % , b ) 25 % , c ) 33.33 % , d ) 18 % , e ) none of these | a | multiply(divide(subtract(multiply(add(add(add(20, 5), const_10), add(divide(5, const_2), const_3)), 18), multiply(15, 18)), multiply(15, 18)), const_100) | a milk man has 15 liters of milk . if he mixes 5 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is : | "explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 20 liters of milk . therefore , profit percentage = 20 % . answer : a" | a = 20 + 5
b = a + 10
c = 5 / 2
d = c + 3
e = b + d
f = e * 18
g = 15 * 18
h = f - g
i = 15 * 18
j = h / i
k = j * 100
|
a ) 36 , b ) 2 ^ 4 * 3 , c ) 24 , d ) 38 , e ) 47 | a | subtract(37, const_1) | in a lake , there is a patch of lily pads . every day , the patch doubles in size . it takes 37 days for the patch to cover the entire lake , how many days would it take the patch to cover half of the lake ? | "working backward from the day it ' s covered : day 37 : fully covered day 36 : half covered so 36 days answer : a" | a = 37 - 1
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a ) 4 : 9 , b ) 4 : 3 , c ) 4 : 5 , d ) 5 : 8 , e ) 4 : 2 | d | divide(sqrt(25), sqrt(64)) | two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 64 hours and 25 hours respectively . the ratio of their speeds is ? | "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 25 : √ 64 = 5 : 8 answer : d" | a = math.sqrt(25)
b = math.sqrt(64)
c = a / b
|
a ) 5.7 , b ) 6.0 , c ) 10.6 , d ) 9.7 , e ) 18.0 | c | divide(add(divide(divide(80, const_3), const_3), divide(multiply(divide(80, const_3), const_2), const_3)), const_2) | the total circumference of two circles is 80 . if the first circle has a circumference that is exactly twice the circumference of the second circle , then what is the approximate sum of their two radii ? | "let r = radius of smaller circle . let r = radius of larger circle therefore : 2 π r + 2 π r = 80 where 2 r = r thus : 2 π r + 4 π r = 80 6 π r = 80 r = approx 4.2 π r + 2 r π = 80 3 π r = 80 r = approx 8.4 r + r = approx 10.6 answer is c" | a = 80 / 3
b = a / 3
c = 80 / 3
d = c * 2
e = d / 3
f = b + e
g = f / 2
|
a ) 21 , b ) 20 , c ) 26 , d ) 30 , e ) 45 | c | subtract(divide(multiply(add(divide(88, const_2), 2), 2), 2), 20) | 20 is added to a certain number , the sum is multiplied by 2 , the product is divided by 2 and 2 is subtracted from the quotient . the remainder left is half of 88 . what is the number ? | "let number is x . when 20 added to it , = ( x + 20 ) 2 multiplied to sum , = 2 * ( x + 20 ) now , = [ { 2 * ( x + 20 ) } / 2 ] and , = [ { 2 * ( x + 20 ) } / 2 ] - 2 according to question , [ { 2 * ( x + 20 ) } / 2 ] - 2 = half of 88 [ ( 2 x + 40 ) / 2 ) = 44 + 2 2 x + 40 = 46 * 2 x + 20 = 46 x = 46 - 20 x = 26 so , required number is : 26 . answer : c" | a = 88 / 2
b = a + 2
c = b * 2
d = c / 2
e = d - 20
|
a ) 1 / 4 , b ) 4 / 5 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7 | e | subtract(divide(lcm(const_2, const_3), 2.8), const_2) | on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction e of the total distance did he cover while the sun was shining on him ? | if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is e = 2 / 14 = 1 / 7 . answer : e | a = math.lcm(2, 3)
b = a / 2
c = b - 2
|
a ) $ 120 , b ) $ 100 , c ) $ 91 , d ) $ 71 , e ) $ 69 | d | multiply(100, divide(const_100, add(const_100, 40))) | a shopkeeper sold an article at $ 100 with 40 % profit . then find its cost price ? | cost price = selling price * 100 / ( 100 + profit ) c . p . = 100 * 100 / 140 = $ 71 ( approximately ) answer is d | a = 100 + 40
b = 100 / a
c = 100 * b
|
a ) 23760 , b ) 47520 , c ) 33000 , d ) 48600 , e ) 54000 | a | multiply(divide(factorial(divide(12, 2)), const_2), divide(factorial(12), multiply(factorial(subtract(12, 2)), factorial(2)))) | a plant manager must assign 12 new workers to one of five shifts . she needs a first , second , and third shift , and two alternate shifts . each of the shifts will receive 2 new workers . how many different ways can she assign the new workers ? | "whatever : my take selecting team of 2 out of 12 to assign to the shifts = 12 c 2 = 66 ways . now 2 out of 12 means total of 6 group possible . so putting them in shifts = counting methode : first , second , third , alt , alt = 6 * 5 * 4 * 3 * 2 * 1 = 720 here alt and alt are the same : so 720 / 2 = 360 ways . total ways of selecting = ( selecting 2 out of 12 ) * arranging those teams in shifts = 66 * 360 = 23760 ans : a" | a = 12 / 2
b = math.factorial(a)
c = b / 2
d = math.factorial(12)
e = 12 - 2
f = math.factorial(e)
g = math.factorial(2)
h = f * g
i = d / h
j = c * i
|
a ) 96 % , b ) 98 % , c ) 95 % , d ) 97 % , e ) 96 % | b | subtract(const_100, multiply(divide(divide(10, 10), multiply(5, 10)), const_100)) | instead of multiplying a number by 5 , the number is divided by 10 . what is the percentage of error obtained ? | "let the number be x the right number is 5 x the wrong number is x / 10 error is ( 5 x - x / 10 ) = 49 x / 10 percentage of error is ( ( 49 x / 10 ) / 5 x ) * 100 = 98 % answer : b" | a = 10 / 10
b = 5 * 10
c = a / b
d = c * 100
e = 100 - d
|
a ) 45 , b ) 50 , c ) 53 , d ) 55 , e ) 60 | e | divide(80, divide(add(multiply(subtract(10, 9), const_60), subtract(30, 10)), const_60)) | a car going at 30 miles per hour set out on an 80 - mile trip at 9 : 00 a . m . exactly 10 minutes later , a second car left from the same place and followed the same route . how fast , in miles per hour , was the second car going if it caught up with the first car at 10 : 30 a . m . ? | let car a = car that starts at 9 am car b = car that starts at 9 : 10 am time for which car a travels at speed of 30 m per hour = 1.5 hours distance travelled by car a = 30 * 1.5 = 45 miles since car b catches up car a at 10 : 30 , time = 80 mins = 4 / 3 hour speed of car b = 45 / ( 4 / 3 ) = 60 miles per hour answer e | a = 10 - 9
b = a * const_60
c = 30 - 10
d = b + c
e = d / const_60
f = 80 / e
|
a ) 4.86 km , b ) 2.5 km , c ) 6.86 km , d ) 5.867 km , e ) 3.25 km | b | multiply(divide(divide(multiply(50, 15), subtract(60, 50)), const_60), 60) | a train moves at average speed of 60 kmph reaches its destination on time . what its average speed becomes 50 kmph , then it reaches its destination 15 late . find the length of the journey ? | "difference between timings = 15 min = 1 / 4 hr let the length of the journey be x km . then x / 50 - x / 60 = 1 / 4 x / 10 = 1 / 4 x = 2.5 km answer ( b )" | a = 50 * 15
b = 60 - 50
c = a / b
d = c / const_60
e = d * 60
|
a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5 | e | add(const_2, const_3) | if 325 / 999 = 0.125 , what is the 81 st digit to the right of the decimal point in the decimal equivalent of the fraction ? | "0 . [ u ] 325 [ / u = 0.325325325 . . . . . every 3 rd digit is 5 and every multiple of 3 will be the digit 5 . since 81 is multiple of 3 , the 81 st digit is 5 . answer e" | a = 2 + 3
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a ) 7 / 2 , b ) 300 / 13 , c ) 20 / 3 , d ) 8 , e ) 39 / 4 | b | divide(100, add(const_4, const_3)) | how many liters of pure alcohol must be added to a 100 - liter solution that is 20 percent alcohol in order to produce a solution that is 35 percent alcohol ? | "20 % alcohol solution means ; in the 100 liter solution , 20 liters of solution is alcohol and 80 liters other solvents . if we addxliters of alcohol to the solution , the solution becomes 100 + xliters and alcohol , which was 20 liters , becomes 20 + x liters . according to the statement ; 20 + x = 35 % of ( 100 + x ) or 20 + x = ( 100 + x ) 7 / 20 400 + 20 x = 700 + 7 x 13 x = 300 x = 300 / 13 ans : b" | a = 4 + 3
b = 100 / a
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a ) 2 hours , b ) 1.2 hours , c ) 3 hours , d ) 1.5 hours , e ) 2.5 hours | b | inverse(add(divide(const_1, 12), add(divide(const_1, 2), divide(const_1, 4)))) | pipe p can fill a tank in 2 hours , pipe q in 4 hours and pipe r in 12 hours . if all the pipes are open , in how many hours will the tank be filled ? | "explanation : part filled by ( p + q + r ) in 1 hour = ( 1 / 2 + 1 / 4 + 1 / 12 ) = 5 / 6 all the three pipes together will fill the tank = 6 / 5 = 1.2 hours answer b" | a = 1 / 12
b = 1 / 2
c = 1 / 4
d = b + c
e = a + d
f = 1/(e)
|
a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18 | b | divide(300, add(subtract(26, 2), const_1)) | 300 metres long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees | 26 trees have 25 gaps between them , required distance ( 300 / 25 ) = 12 b | a = 26 - 2
b = a + 1
c = 300 / b
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a ) 160 , b ) 787 , c ) 144 , d ) 128 , e ) 121 | a | multiply(add(const_1, const_4), 40) | one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill tank in 40 min , then the slower pipe alone will be able to fill the tank in ? | "let the slower pipe alone fill the tank in x min . then , faster pipe will fill it in x / 3 min . 1 / x + 3 / x = 1 / 40 4 / x = 1 / 40 = > x = 160 min . answer : a" | a = 1 + 4
b = a * 40
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a ) 1 : 3 , b ) 2 : 3 , c ) 3 : 5 , d ) 4 : 5 , e ) none of these | c | divide(subtract(6.30, 5.70), subtract(10.0, 6.30)) | find the ratio in which rice at rs . 10.0 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg ? | "solution required ratio = 60 : 100 = 3 : 5 answer c" | a = 6 - 30
b = 10 - 0
c = a / b
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a ) 10.66 seconds , b ) 25 seconds , c ) 29 seconds , d ) 21 seconds , e ) 6.25 seconds | a | divide(subtract(100, 36), 6) | in a 100 m race , sam beats john by 6 seconds . on the contrary , if sam allowed john to start 36 m ahead of sam , then sam and john reach the finishing point at the same time . how long does sam take to run the 100 m race ? | "their difference is 6 second but this difference is 0 if john allows sam to start the race from 36 m ahead . that means jhon was 36 m away from finishing line when they started together . so he will cover 36 m in 6 seconds . so his speed = 36 / 6 = 6 metre / second . so time taken = 100 / 6 = 16.66 seconds . so sam took = 10.66 seconds . correct answer = a" | a = 100 - 36
b = a / 6
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a ) 9 / 16 , b ) 7 / 18 , c ) 12 / 55 , d ) 14 / 67 , e ) 19 / 87 | c | divide(multiply(choose(4, const_2), choose(add(3, 5), const_1)), choose(add(add(3, 5), 4), 3)) | a bag contains 3 red , 5 yellow and 4 green balls . 3 balls are drawn randomly . what is the probability that balls drawn contain exactly two green balls ? | total number of balls = 3 + 5 + 4 = 12 n ( s ) = 12 c 3 = 12 * 11 * 10 / 3 * 2 = 220 n ( e ) = 4 c 2 * 8 c 1 = 6 * 8 = 48 probability = 48 / 220 = 12 / 55 answer is c | a = math.comb(4, 2)
b = 3 + 5
c = math.comb(b, 1)
d = a * c
e = 3 + 5
f = e + 4
g = math.comb(f, 3)
h = d / g
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a ) 135 , b ) 105 , c ) 95 , d ) 75 , e ) 45 | d | multiply(subtract(divide(multiply(divide(subtract(const_100, 20), const_100), multiply(divide(45, const_60), 40)), 12), divide(45, const_60)), const_60) | debanshu normally drives to work in 45 minutes at an average speed of 40 miles per hour . this week , however , she plans to bike to work along a route that decreases the total distance she usually travels when driving by 20 % . if debanshu averages between 12 and 16 miles per hour when biking , how many minutes earlier will she need to leave in the morning in order to ensure she arrives at work at the same time as when she drives ? | debanshu normally drives to work in 45 minutes at an average speed of 40 miles per hour . use formula d = rt car : t 1 : 45 min r 1 : 40 mph d 1 : [ ( 40 * 45 ) / 60 ] = 30 miles bike : t 1 : ? r 2 : 12 - 16 mph d 2 : 08 * d 1 = 24 miles t 1 : [ ( 24 * 60 ) / 12 ] = 120 min ( only 12 mph speed yields an answer given in the choices ) therefore , deb has to leave 120 min - 45 min = 75 min early answer : d | a = 100 - 20
b = a / 100
c = 45 / const_60
d = c * 40
e = b * d
f = e / 12
g = 45 / const_60
h = f - g
i = h * const_60
|
a ) 2 d , b ) d , c ) 2 d + 2 , d ) 8 d , e ) 2 d + 4 | b | sqrt(divide(multiply(power(2, 2), const_3), const_3)) | if d is the standard deviation a , b , and c , what is the standard deviation of a + 2 , b + 2 , c + 2 ? | concept : standard deviation is defined as average deviation of terms in the set from the mean value of the set . i . e . 1 ) it depends on the separation between the successive terms of the set 2 ) if a constant value is added / subtracted in every terms of set then the separation between successive terms does not change hence s . d . remains constant e . g . { 1 , 2 , 3 , 4 , 5 } will have same standard deviation as { 1 + 10 , 2 + 10 , 3 + 10 , 4 + 10 , 5 + 10 } 3 ) if a constant value is multiplied in every terms then the separation between succesive terms gets multiplied by the constant hence s . d . remains gets multiplied by same number e . g . { 0.7 , 1.4 , 2.1 , 2.8 , 3.5 } will have standard deviation = 0.7 * standard deviation of set { 1 , 2 , 3 , 4 , 5 } when 2 is added in each term of set { a , b , c } then the new set { a + 2 , b + 2 , c + 2 } will remain same as the previous standard deviation i . e . d answer : b | a = 2 ** 2
b = a * 3
c = b / 3
d = math.sqrt(c)
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a ) 412.16 , b ) 150 , c ) 400 , d ) 416.67 , e ) 420.34 | d | divide(multiply(75, 2), divide(36, const_100)) | at the end of year x , automobile installment credit accounted for 36 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 75 billion of credit , or 1 / 2 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at that time ? | "system of equations a = ( 36 / 100 ) c ( 1 / 2 ) a = 75 - - > a = 150 substitution 150 = ( 36 / 100 ) c c = ( 100 / 36 ) 150 calculate 150 / 36 * 100 the correct answer is d - the correct answer will be slightly smaller than 513 . therefore , the correct answer is 475 ." | a = 75 * 2
b = 36 / 100
c = a / b
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a ) 18 square inches , b ) 20 square inches , c ) 24 square inches , d ) 28 square inches , e ) 30 square inches | b | divide(subtract(subtract(204, 24), multiply(175, divide(80, const_100))), const_2) | three table runners have a combined area of 204 square inches . by overlapping the runners to cover 80 % of a table of area 175 square inches , the area that is covered by exactly two layers of runner is 24 square inches . what is the area of the table that is covered with three layers of runner ? | "total = a + b + c - ( sum of exactly 2 - group overlaps ) - 2 * ( all three ) + neither 80 % * 175 = 204 - 24 - 2 * ( all three ) + 0 2 * ( all three ) = 204 - 24 - 140 all three = 20 answer : b" | a = 204 - 24
b = 80 / 100
c = 175 * b
d = a - c
e = d / 2
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a ) a ) 2 , b ) b ) 4 , c ) c ) 6 , d ) d ) 8 , e ) e ) 18 | d | multiply(8, const_1) | nr books bought nr of people 6 3 7 1 8 5 9 2 what is the median of books bought per person ? | 6 , 6,6 , 7,8 , 8,8 , 8,8 , 9,9 so you will observer that the median of the list is 8 . ans d | a = 8 * 1
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a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28 | b | multiply(55, divide(18, 45)) | a flagpole 18 meters high casts a shadow of length 45 meters . if a building under similar conditions casts a shadow of length 55 meters , what is the height of the building ( in meters ) ? | "the height : length ratio will be equal in both cases . 18 / 45 = x / 55 x = 22 the answer is b ." | a = 18 / 45
b = 55 * a
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a ) 2 , b ) 7 , c ) 13 , d ) 17 , e ) 19 | d | subtract(divide(34, 2), const_1) | for every even positive integer m , f ( m ) represents the product of all even integers from 2 to m , inclusive . for example , f ( 12 ) = 2 x 4 x 6 x 8 x 10 x 12 . what is the greatest prime factor of f ( 34 ) ? | "f ( 34 ) = 2 * 4 * 6 * 8 * 10 * 12 * 14 * 16 * 18 * 20 * 22 * 24 * 26 * 28 * 30 * 32 * 34 the greatest prime factor in this list is 17 . the answer is d ." | a = 34 / 2
b = a - 1
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['a ) 10 years', 'b ) 38 years', 'c ) 39 years', 'd ) 64 years', 'e ) 44 years'] | b | divide(const_3, const_3) | nitin ' s age was equal to square of some number last year and the following year it would be cube of a number . if again nitin ' s age has to be equal to the cube of some number , then for how long he will have to wait ? | current age = 26 years because nitin ' s age was equal to square of some number ( 25 = 5 ^ 2 ) last year and the following year it would be cube of a number ( 27 = 3 ^ 3 ) . next cube age will be 64 = 4 ^ 3 which will come after 64 - 26 = 38 years . answer : b | a = 3 / 3
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a ) $ 1,000 , b ) $ 1,200 , c ) $ 1,400 , d ) $ 1,500 , e ) $ 1,700 | e | subtract(1,000, 900) | a family pays $ 900 per year for an insurance plan that pays 60 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total how much ? | "assuming the medical expenses are $ 1000 or more , the family pays $ 900 + $ 400 = $ 1300 . the total amount paid by insurance plan for the first $ 1000 of expenses is $ 600 . the insurance will pay another $ 700 when the medical expenses are $ 1700 . the answer is e ." | a = 1 - 0
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a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 3 | a | subtract(multiply(divide(3, 2), add(13, 7)), add(floor(multiply(divide(3, 4), multiply(divide(3, 2), add(13, 7)))), const_1)) | a certain basketball team that has played 2 / 3 of its games has a record of 13 wins and 7 losses . what is the greatest number of the remaining games that the team can lose and still win at least 3 / 4 of all of its games ? | 13 wins , 7 losses - total 20 games played . the team has played 2 / 3 rd of all games so total number of games = 30 3 / 4 th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games . it has already lost 7 games so it can lose another 0 at most . answer ( a ) | a = 3 / 2
b = 13 + 7
c = a * b
d = 3 / 4
e = 3 / 2
f = 13 + 7
g = e * f
h = d * g
i = math.floor(h)
j = i + 1
k = c - j
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a ) 2 : 3 , b ) 4 : 3 , c ) 6 : 7 , d ) 7 : 2 , e ) none of these | d | divide(sqrt(49), sqrt(4)) | two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 4 hours and 49 hours respectively . the ratio of their speeds is : | "let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 49 : â ˆ š 4 = 7 : 2 . answer d" | a = math.sqrt(49)
b = math.sqrt(4)
c = a / b
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a ) 412 , b ) 502 , c ) 512 , d ) 522 , e ) none | c | divide(62976, 123) | find 62976 ÷ ? = 123 | "answer let 62976 / n = 123 then n = 62976 / 123 = 512 . option : c" | a = 62976 / 123
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a ) rs . 360 , b ) rs . 120 , c ) rs . 240 , d ) rs . 300 , e ) none | b | multiply(divide(subtract(subtract(divide(const_1, 5), divide(const_1, 10)), divide(const_1, 15)), divide(const_1, 5)), 720) | x alone can do a piece of work in 15 days and y alone can do it in 10 days . x and y undertook to do it for rs . 720 . with the help of z they finished it in 5 days . how much is paid to z ? | solution : in one day x can finish 1 / 15 th of the work . in one day y can finish 1 / 10 th of the work . let us say that in one day z can finish 1 / zth of the work . when all the three work together in one day they can finish 1 / 15 + 1 / 10 + 1 / z = 1 / 5 th of the work . therefore , 1 / z = 1 / 30 . ratio of their efficiencies = 1 / 15 : 1 / 10 : 1 / 30 = 2 : 3 : 1 . therefore z receives 1 / 6 th of the total money . according to their efficiencies money is divided as 240 : 360 : 120 . hence , the share of z = rs . 120 . answer b | a = 1 / 5
b = 1 / 10
c = a - b
d = 1 / 15
e = c - d
f = 1 / 5
g = e / f
h = g * 720
|
a ) 149 , b ) 169 , c ) 189 , d ) 209 , e ) 121 | e | multiply(divide(4, 25,49), const_100) | 4 , 25,49 , | "11 ^ 2 = 121 because follow sequence of square of the prime numbers answer : e" | a = 4 / 25
b = a * 100
|
a ) 3.64 , b ) 1.75 , c ) 3.52 , d ) 2.72 , e ) none of these | a | divide(divide(multiply(4, add(multiply(3, 950), multiply(2, 850))), add(3, 2)), const_1000) | the weights of one liter vegetable ghee packet of two brands ‘ a ’ and ‘ b ’ are 950 gm and 850 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters , what is the weight ( in kg ) of the mixture ? | "here ' s how i did it . my notes from reading the problem were : 1 l a = 950 gm 1 l b = 850 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 4 l , so 5 x = 4 - - - > x = 4 / 5 . each part is 4 / 5 of a liter . so if we have 3 parts a , we have 950 * 3 * ( 4 / 5 ) = 2280 if we have 2 parts b , we have 850 * 2 * ( 4 / 5 ) = 1360 2280 + 1360 = 3640 solving for units gives us 3.64 so the answer is a" | a = 3 * 950
b = 2 * 850
c = a + b
d = 4 * c
e = 3 + 2
f = d / e
g = f / 1000
|
a ) 2 , b ) 4 / 5 , c ) 7 / 9 , d ) 10 , e ) 24 / 7 | e | divide(const_1, add(add(divide(const_1, 24), divide(const_1, add(const_4, const_2))), divide(const_1, multiply(const_2, add(const_4, const_2))))) | a , b , c can complete a piece of work in 24 , 6,12 days . working together , they complete the same work in how many days ? | "a + b + c 1 day work = 1 / 24 + 1 / 6 + 1 / 12 = 7 / 24 a , b , c together will complete the job in 24 / 7 days answer is e" | a = 1 / 24
b = 4 + 2
c = 1 / b
d = a + c
e = 4 + 2
f = 2 * e
g = 1 / f
h = d + g
i = 1 / h
|
a ) 9000 , b ) 8000 , c ) 7000 , d ) 6000 , e ) 5000 | c | subtract(multiply(multiply(const_12, const_100), 25), add(multiply(400, 10), multiply(subtract(subtract(25, 10), const_1), 1,000))) | company c sells a line of 25 products with an average retail price of $ 1,000 . if none of these products sells for less than $ 400 , and exactly 10 of the products sell for less than $ 1,000 , what is the greatest possible selling price of the most expensive product ? | "the average price of 25 products is $ 1,000 means that the total price of 25 products is 25 * 1,000 = $ 25,000 . next , since exactly 10 of the products sell for less than $ 1,000 , then let ' s make these 10 items to be at $ 400 each ( min possible ) . now , the remaining 14 items can not be priced less than $ 1,000 , thus the minimum possible price of each of these 14 items is $ 1,000 . thus the minimum possible value of 24 products is 10 * 400 + 14 * 1,000 = $ 18,000 . therefore , the greatest possible selling price of the most expensive product is $ 25,000 - $ 18,200 = $ 7,000 . answer : c ." | a = 12 * 100
b = a * 25
c = 400 * 10
d = 25 - 10
e = d - 1
f = e * 1
g = c + f
h = b - g
|
a ) $ 0.60 , b ) $ 0.80 , c ) $ 1.00 , d ) $ 1.20 , e ) $ 1.60 | a | divide(subtract(200.00, multiply(200, 0.40)), 200) | a caterer ordered 200 ice - cream bars and 200 sundaes . if the total price was $ 200.00 and the price of each ice - cream bar was $ 0.40 , what was the price of each sundae ? | "let price of a sundae = s price of ice cream bar = . 4 $ 200 * . 4 + 200 * s = 200 = > 200 * s = 200 = > s = 0.6 answer a" | a = 200 * 0
b = 200 - 0
c = b / 200
|
a ) 8 , b ) 7 , c ) 5 , d ) 6 , e ) 4 | a | divide(divide(divide(lcm(123, 578), 578), const_4), const_4) | what is the least value of k . so that 123 k 578 is divisible by 11 . | explanation : the difference of the sum of the digits at odd place and the sum of the digits at even place of the number , is either 0 or a number divisible by 11 . ( 1 + 3 + 5 + 8 ) - ( 2 + k + 7 ) = 17 - 9 - k = 8 - k therefore if k = 8 , then the value become zero . k = 8 is the least value so that 123 k 578 is divisible by 11 . answer : option a | a = math.lcm(123, 578)
b = a / 578
c = b / 4
d = c / 4
|
a ) 28 , b ) 26 , c ) 24 , d ) 32 , e ) 30 | d | multiply(8, 4) | local kennel has cats and dogs in the ratio of 3 : 4 . if there are 8 fewer cats than dogs , how many dogs are in the kennel ? | "lets work with the data given to us . we know that there ratio of cats to dogs is 3 : 4 or cats 3 dogs 4 we can write number of cats as 3 x and number of dogs as 4 x and we know that 4 x - 3 x = 8 ( therefore x = 8 ) then # of dogs = 4 x 8 = 32 answer is d" | a = 8 * 4
|
a ) 148 , b ) 152 , c ) 156 , d ) 145 , e ) none | d | multiply(39, divide(142, divide(add(add(37, 39), const_2), const_2))) | the ratio of ducks and frogs in a pond is 37 : 39 respectively . the average number of ducks and frogs in the pond is 142 . what is the number of frogs in the pond ? | "solution : ratio of ducks and frogs in pond , = 37 : 39 . average of ducks and frogs in pond , = 142 . so , total number of ducks and frogs in the pond , = 2 * 142 = 284 . therefore , number of frogs , = ( 284 * 39 ) / 76 = 145 . answer : option d" | a = 37 + 39
b = a + 2
c = b / 2
d = 142 / c
e = 39 * d
|
a ) 50.4 % , b ) 71.3 % , c ) 66.5 % , d ) 34.9 % , e ) 43.5 % | b | multiply(divide(subtract(1400, add(add(add(75, 50), add(64, 78)), 135)), 1400), const_100) | john had a stock of 1400 books in his bookshop . he sold 75 on monday , 50 on tuesday , 64 on wednesday , 78 on thursday and 135 on friday . what percentage of the books were not sold ? | "let n be the total number of books sold . hence n = 75 + 50 + 64 + 78 + 135 = 402 let m be the books not sold m = 1400 - n = 1400 - 402 = 998 percentage books not sold / total number of books = 998 / 1400 = 0.713 = 71.3 % correct answer b" | a = 75 + 50
b = 64 + 78
c = a + b
d = c + 135
e = 1400 - d
f = e / 1400
g = f * 100
|
a ) 2 : 1 , b ) 1 : 2 , c ) 4 : 3 , d ) 1 : 3 , e ) 3 : 2 | d | divide(subtract(divide(multiply(divide(8, const_100), 4), const_3), divide(4, const_100)), subtract(divide(8, const_100), divide(multiply(divide(6, const_100), 4), const_3))) | two numbers a and b are such that the sum of 8 % of a and 4 % of b is two - third of the sum of 6 % of a and 8 % of b . find the ratio of a : b . | "explanation : 8 % of a + 4 % of b = 2 / 3 ( 6 % of a + 8 % of b ) 8 a / 100 + 4 b / 100 = 2 / 3 ( 6 a / 100 + 8 b / 100 ) ⇒ 8 a + 4 b = 2 / 3 ( 6 a + 8 b ) ⇒ 24 a + 12 b = 12 a + 16 b ⇒ 12 a = 4 b ⇒ ab = 4 / 12 ⇒ a : b = 1 : 3 answer : option d" | a = 8 / 100
b = a * 4
c = b / 3
d = 4 / 100
e = c - d
f = 8 / 100
g = 6 / 100
h = g * 4
i = h / 3
j = f - i
k = e / j
|
a ) 1 : 1 , b ) 1 : 87 , c ) 1 : 6 , d ) 1 : 9 , e ) 1 : 2 | e | divide(divide(multiply(5, 3), multiply(6, 4)), divide(multiply(3, 4), multiply(4, 5))) | the compound ratio of 5 : 6 , 3 : 4 and 4 : 5 ? | "5 / 6 * 3 / 4 * 4 / 5 = 1 / 2 1 : 2 answer : e" | a = 5 * 3
b = 6 * 4
c = a / b
d = 3 * 4
e = 4 * 5
f = d / e
g = c / f
|
a ) 7 : 6 , b ) 2 : 3 , c ) 9 : 3 , d ) 6 : 3 , e ) 2 : 5 | a | divide(subtract(15.8, 15.1), subtract(16.4, 15.8)) | the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.1 years , the ratio of the number of boys to the number of girls in the class is | explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.1 = ( k + 1 ) * 15.8 < = > ( 16.4 - 15.8 ) k = ( 15.8 - 15.1 ) < = > k = 0.7 / 0.6 = 7 / 6 . required ratio = 7 / 6 : 1 = 7 : 6 . answer : a | a = 15 - 8
b = 16 - 4
c = a / b
|
a ) a ) 300 , b ) b ) 350 , c ) c ) 450 , d ) d ) 470 , e ) e ) 500 | b | subtract(multiply(const_10, 150), add(multiply(4, 100), multiply(5, 150))) | a man purchased 4 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 4 * 100 + 5 * 150 = 1150 1500 – 1150 = 350 b" | a = 10 * 150
b = 4 * 100
c = 5 * 150
d = b + c
e = a - d
|
a ) 57 , b ) 59 , c ) 63 , d ) 71 , e ) 92 | a | add(multiply(subtract(const_1, divide(const_1, const_3)), subtract(70, 31)), 31) | of 70 players on a football team , 31 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ? | "total = 70 thrower = 31 rest = 70 - 31 = 39 left handed = 39 / 3 = 13 right handed = 26 if all thrower are right handed then total right handed is 31 + 26 = 57 so a . 57 is the right answer" | a = 1 / 3
b = 1 - a
c = 70 - 31
d = b * c
e = d + 31
|
a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 54 | e | add(divide(subtract(add(40, 2), 30), 1.5), 30) | each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 53 hours . if harry and james were paid the same amount last week , how many hours did harry work last week ? | "amount earned by james = 40 * x + 13 * 2 x = 66 x therefore , amount earned by harry = 66 x but we know the amount harry earned assuming working y hours ( y > 30 ) is 30 * x + ( y - 30 ) * 1.5 x [ [ we know y > 30 because in 30 h the most harry could earn is 30 x , but he has earned 66 x ] ] so x * ( 1.5 y - 45 + 30 ) = 66 x or x * ( 1.5 y - 15 ) = 66 x so 1.5 y - 15 = 66 so 1.5 y = 81 so y = 54 answer is e" | a = 40 + 2
b = a - 30
c = b / 1
d = c + 30
|
a ) 4 , b ) 4 √ 2 , c ) 8 , d ) 6 , e ) can not be determined from the information provided | d | sqrt(add(power(multiply(sqrt(9), sqrt(const_2)), const_2), power(multiply(sqrt(9), sqrt(const_2)), const_2))) | triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 9 , what is the measure of side xy ? | "ans d . . 6 . . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 9 or yz = 3 * \ sqrt { 2 } . . therefore hyp = xy = 6" | a = math.sqrt(9)
b = math.sqrt(2)
c = a * b
d = c ** 2
e = math.sqrt(9)
f = math.sqrt(2)
g = e * f
h = g ** 2
i = d + h
j = math.sqrt(i)
|
a ) 484 , b ) 1080 , c ) 1,100 , d ) 1,320 , e ) 1,694 | b | subtract(1980, divide(1980, add(divide(add(const_100, 20), const_100), const_1))) | yesterday ' s closing prices of 1980 different stocks listed on a certain stock exchange were all different from today ' s closing prices . the number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price . how many of the stocks closed at a higher price today than yesterday ? | lets consider the below - the number of stocks that closed at a higher price = h the number of stocks that closed at a lower price = l we understand from first statement - > h + l = 1980 - - - - ( 1 ) we understand from second statement - > h = ( 120 / 100 ) l = > h = 1.2 l - - - - ( 2 ) solve eq ( 1 ) ( 2 ) to get h = 1080 . b is my answer . | a = 100 + 20
b = a / 100
c = b + 1
d = 1980 / c
e = 1980 - d
|
a ) 2267 , b ) 1162 , c ) 2276 , d ) 1250 , e ) 1262 | d | multiply(divide(multiply(5, const_1000), const_60), 15) | a man walking at the rate of 5 km / hr crosses a bridge in 15 minutes . the length of the bridge ( in metres ) is ? | "explanation : speed = ( 5 x 5 / 18 ) m / sec = 25 / 18 m / sec . distance covered in 15 minutes = ( 25 / 18 x 15 x 60 ) m = 1250 m . answer : d" | a = 5 * 1000
b = a / const_60
c = b * 15
|
a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25 | a | divide(75, divide(multiply(54, const_1000), const_3600)) | a 75 m long train is running at 54 km / hr . in how much time will it cross an electric pole ? | speed of the train = ( 54 * 5 / 18 ) m / sec = 15 m / sec . length of the train = ( speed x time ) time = ( length of the train / speed ) = ( 75 / 15 ) = 5 sec answer : a | a = 54 * 1000
b = a / 3600
c = 75 / b
|
a ) s . 2.8 , b ) s . 2.4 , c ) s . 2.5 , d ) s . 2.2 , e ) s . 3.16 | e | multiply(divide(divide(multiply(divide(24, const_100), 100), 10), multiply(divide(24, const_100), 100)), const_100) | a reduction of 24 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ? | "100 * ( 24 / 100 ) = 24 - - - 10 ? - - - 1 = > rs . 2.4 100 - - - 76 ? - - - 2.4 = > rs . 3.16 answer : e" | a = 24 / 100
b = a * 100
c = b / 10
d = 24 / 100
e = d * 100
f = c / e
g = f * 100
|
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | d | multiply(subtract(add(const_1, floor(divide(1077, 23))), divide(1077, 23)), 23) | what is the least number that should be added to 1077 , so the sum of the number is divisible by 23 ? | "( 1077 / 23 ) gives a remainder 19 so we need to add 4 . the answer is d ." | a = 1077 / 23
b = math.floor(a)
c = 1 + b
d = 1077 / 23
e = c - d
f = e * 23
|
a ) 30 , b ) 40 , c ) 51 , d ) 60 , e ) 70 | c | divide(32.5, 0.63) | how many pieces of 0.63 meteres can be cut from a rod 32.5 meteres long | "explanation : we need so simple divide 32.5 / 0.63 , = ( 3250 / 63 ) = 51 option c" | a = 32 / 5
|
a ) 40 , b ) 48 , c ) 49 , d ) 55 , e ) 64 | c | add(divide(200, add(const_4, const_1)), divide(200, multiply(add(const_4, const_1), add(const_4, const_1)))) | how many terminating zeroes q does 200 ! have ? | you have 40 multiples of 5 , 8 of 25 and 1 of 125 . this will give 49 zeros . c | a = 4 + 1
b = 200 / a
c = 4 + 1
d = 4 + 1
e = c * d
f = 200 / e
g = b + f
|
a ) 1 : 2 , b ) 3 : 2 , c ) 4 : 1 , d ) 5 : 2 , e ) 6 : 5 | c | divide(subtract(17, 9), subtract(19, 17)) | gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 17 times as heavy as water ? | "g = 19 w c = 9 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 19 w + 9 wx = x + 1 * 17 w 19 + 9 x = 17 ( x + 1 ) x = 1 / 4 ratio of gold with copper = 1 : 1 / 4 = 4 : 1 answer is c" | a = 17 - 9
b = 19 - 17
c = a / b
|
a ) 344 , b ) 218 , c ) 400 , d ) 388 , e ) 211 | c | multiply(multiply(multiply(5, const_4.0), 10), 2) | a man bought an article and sold it at a gain of 5 % . if he had bought it at 5 % less and sold it for re 2 less , he would have made a profit of 10 % . the c . p . of the article was | "explanation : let original cost price is x its selling price = ( 105 / 100 ) * x = 21 x / 20 new cost price = ( 95 / 100 ) * x = 19 x / 20 new selling price = ( 110 / 100 ) * ( 19 x / 20 ) = 209 x / 200 [ ( 21 x / 20 ) - ( 209 x / 200 ) ] = 2 = > x = 400 answer : c ) rs 400" | a = 5 * 4
b = a * 10
c = b * 2
|
a ) 19,920 , b ) 19,940 , c ) 19,960 , d ) 19,980 , e ) 20,000 | e | divide(divide(subtract(multiply(const_1000, const_100), subtract(subtract(const_3600, const_100), const_1000)), const_1000), add(multiply(add(const_1, divide(10, const_100)), subtract(10, const_1)), const_1)) | a city with a population of 218,000 is to be divided into 10 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district . what is the minimum possible population that the least populated district could have ? | "the minimum possible population occurs when all the other districts have a population that is 10 % greater than the least populated district . let p be the population of the least populated district . then 218,000 = p + 9 ( 1.1 ) p 10.9 p = 218,000 p = 20,000 the answer is e ." | a = 1000 * 100
b = 3600 - 100
c = b - 1000
d = a - c
e = d / 1000
f = 10 / 100
g = 1 + f
h = 10 - 1
i = g * h
j = i + 1
k = e / j
|
a ) 50 , b ) 88 , c ) 66 , d ) 55 , e ) 22 | d | divide(multiply(36, divide(multiply(subtract(47, 36), const_1000), const_3600)), const_2) | two trains of equal are running on parallel lines in the same direction at 47 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ? | "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 47 - 36 = 11 km / hr . = 11 * 5 / 18 = 55 / 18 m / sec . 2 x / 36 = 55 / 18 = > x = 55 . answer : d" | a = 47 - 36
b = a * 1000
c = b / 3600
d = 36 * c
e = d / 2
|
a ) 450 . , b ) 412 . , c ) 432 . , d ) 502 . , e ) 522 . | a | multiply(divide(multiply(49, 6), subtract(49, 30)), 30) | a confectioner decides to sell all of his pastry due to the coming holiday . his pastry goods are equally divided among a group of 30 regular customers . if only 49 customers come to the bakery , each one will receive 6 less pastry goods . how much pastry does the confectioner needs to sell ? | pastry is divided in 30 customers equally . so , total number of pastry must be a multiple of 30 only option a satisfies the condition , and hence is the answer | a = 49 * 6
b = 49 - 30
c = a / b
d = c * 30
|
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | c | divide(add(7, const_1), 5) | if x and y are positive integers and x = 5 y + 7 , what is the remainder when x is divided by 5 ? | "this question asks what is . . . ( the answer ) , so we know that the answer will be consistent . as such , we can test values to quickly get the solution . we ' re told that x and y are positive integers and x = 5 y + 7 . we ' re asked for the remainder when x is divided by 5 . if . . . . y = 1 x = 12 12 / 5 = 2 remainder 2 final answer : c" | a = 7 + 1
b = a / 5
|
a ) 10.5 % , b ) 12.5 % , c ) 17.5 % , d ) 22 % , e ) 30 % | c | divide(const_100, multiply(multiply(divide(14, const_100), divide(20, const_100)), const_100)) | on a certain road 14 % 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 the road exceed the posted speed limit ? | "answer is c . this question is in the og and thus well explained by ets . those who exceed : x so x = 14 % + 0,2 x id est x = 17,5 %" | a = 14 / 100
b = 20 / 100
c = a * b
d = c * 100
e = 100 / d
|
a ) 90 , b ) 93 , c ) 56 , d ) 80.5 , e ) 78 | b | add(multiply(8, 6), 45) | the average weight of 8 person ' s increases by 6 kg when a new person comes in place of one of them weighing 45 kg . what is the weight of the new person ? | "total increase in weight = 8 × 6 = 48 if x is the weight of the new person , total increase in weight = x − 45 = > 48 = x - 45 = > x = 48 + 45 = 93 answer : b" | a = 8 * 6
b = a + 45
|
a ) 31 , b ) 35 , c ) 50 , d ) 91 , e ) 101 | d | floor(add(const_1, multiply(divide(log(2), log(const_10)), 300))) | how many digits 2 ^ 300 has ? | 2 ^ 10 = 1.024 * 10 ^ 3 = > 2 ^ 100 = ( 1.024 ) ^ 10 * 10 ^ 90 therefore 91 digits would be my best guess d | a = math.log(2)
b = math.log(10)
c = a / b
d = c * 300
e = 1 + d
f = math.floor(e)
|
a ) 328 , b ) 348 , c ) 358 , d ) 362 , e ) data inadequate | c | add(multiply(28, divide(subtract(25, const_1), const_2)), 22) | after distributing the sweets equally among 25 children , 8 sweets remain . had the number of children been 28 , 22 sweets would have been left after equal distribution . what was the total number of sweets ? | explanation : let the total number of sweets be ( 25 x + 8 ) . then , ( 25 x + 8 ) - 22 is divisible by 28 ( 25 x - 14 ) is divisible by 28 28 x - ( 3 x + 14 ) is divisible by 28 ( 3 x + 14 ) is divisible by 28 x = 14 . therefore total number of sweets = ( 25 x 14 + 8 ) = 358 . answer : c | a = 25 - 1
b = a / 2
c = 28 * b
d = c + 22
|
a ) 45 ( 4 / 11 ) % , b ) 60 % , c ) 45 ( 5 / 11 ) % , d ) 44 ( 5 / 11 ) % , e ) none of these | b | multiply(divide(subtract(150, add(multiply(3, 8), multiply(8, 3))), 150), const_100) | a batsman scored 150 runs which included 3 boundaries and 8 sixes . what percent of his total score did he make by running between the wickets ? | "explanation : total runs scored = 150 total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60 total runs scored by running between the wickets = 150 - 60 = 90 required % = ( 90 / 150 ) × 100 = 60 % answer : option b" | a = 3 * 8
b = 8 * 3
c = a + b
d = 150 - c
e = d / 150
f = e * 100
|
a ) 2333 , b ) 2777 , c ) 3000 , d ) 1000 , e ) 2871 | c | divide(subtract(120, divide(multiply(6, 2500), const_100)), subtract(divide(5, const_100), divide(6, const_100))) | rs . 2500 is divided into two parts such that if one part be put out at 5 % simple interest and the other at 6 % , the yearly annual income may be rs . 120 . how much was lent at 5 % ? | ( x * 5 * 1 ) / 100 + [ ( 2500 - x ) * 6 * 1 ] / 100 = 120 x = 3000 answer : c | a = 6 * 2500
b = a / 100
c = 120 - b
d = 5 / 100
e = 6 / 100
f = d - e
g = c / f
|
a ) 5 , b ) 6 , c ) 4 , d ) 3 , e ) 8 | e | divide(52.416, 0.000168) | when 52416 is divided by 312 , the quotient is 168 . what will be the quotient when 52.416 is divided by 0.000168 ? | for the 1 st no . there are 2 digits after decimal for the 2 nd no . there are 7 digits after decimal total no . of decimals = 9 req . no . of digits = ( n - 1 ) = ( 9 - 1 ) = 8 answer : e | a = 52 / 416
|
a ) 40 , b ) 41 , c ) 46 , d ) 42 , e ) 49 | c | subtract(multiply(add(23, 1), add(22, 1)), multiply(23, 22)) | the average age of a class of 23 students is 22 years . the average increased by 1 when the teacher ' s age also included . what is the age of the teacher ? | "total age of all students = 23 ã — 22 total age of all students + age of the teacher = 24 ã — 23 age of the teacher = 24 ã — 23 â ˆ ’ 23 ã — 22 = 23 ( 24 â ˆ ’ 22 ) = 23 ã — 2 = 46 answer is c ." | a = 23 + 1
b = 22 + 1
c = a * b
d = 23 * 22
e = c - d
|
a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25 | e | subtract(add(multiply(reminder(7, 600), 3), reminder(3, 600)), reminder(1, 600)) | x is a positive integer less than 600 . when x is divided by 7 , the remainder is 1 ; when x is divided by 3 , the remainder is 2 . how many x are there ? | "the nubmer which when divided by 7 leaves remainder 1 should be of the form 7 k + 1 this number when divided by 3 leaves remainder 2 . so , ( 7 k + 1 ) - 2 should be divisible by 3 or 7 k - 1 should be divisible by 3 . we now put the values of k starting from 0 to find first number divisible by 3 we find 1 st number at k = 1 thus smallest number will be 7 ( 1 ) + 1 = 8 now , next number will be = 8 + lcm of 37 i . e 29 now we will find number of all such values less than 500 by using the formula for last term of an a . p 8 + ( n - 1 ) 21 = 600 n = 25.42 or n = 25 answer : - e" | a = reminder * (
b = a + 3
c = b - reminder
|
a ) 44 % , b ) 69 % , c ) 144 % , d ) 40 % , e ) none of the above | b | multiply(subtract(divide(const_100, const_100), power(subtract(divide(const_100, const_100), divide(30, const_100)), const_2)), const_100) | if the radius of a circle is increased by 30 % then the area is increased by : | "initially a = pi * r 2 now r 2 = 130 / 100 r then area = pi * ( 130 r / 100 ) 2 area = 169 r / 100 that is area increases from 100 to 169 = increase in area = 69 % answer : b" | a = 100 / 100
b = 100 / 100
c = 30 / 100
d = b - c
e = d ** 2
f = a - e
g = f * 100
|
['a ) 15 m', 'b ) 22.5 m', 'c ) 25 m', 'd ) 30 m', 'e ) none of these'] | d | divide(divide(750, 5), 5) | the length of a rectangle hall is 5 m more than its breadth . the area of the hall is 750 m 2 . the length of the hall is : | solution let breadth = x metres . then , length = ( x + 5 ) metres . then x ( x + 5 ) = 750 ⇔ x 2 + 5 x − 750 = 0 ⇔ ( x + 30 ) ( x + 25 ) = 0 ⇔ x = 25 . ∴ length = ( x + 5 ) = 30 m . answer d | a = 750 / 5
b = a / 5
|
['a ) 3 p / 4', 'b ) 3 p ^ 2 / 4', 'c ) p', 'd ) 3 p ^ 2', 'e ) 4 p / 3'] | c | multiply(sqrt(power(const_pi, divide(2, 16))), const_4) | what is the perimeter of a square with area p ^ 2 / 16 ? | area of square , ( side ) ^ 2 = ( p / 4 ) ^ 2 therefore side of the square = p / 4 perimeter of square = 4 * side = 4 * ( p / 4 ) = p answer is c . | a = 2 / 16
b = math.pi ** a
c = math.sqrt(b)
d = c * 4
|
['a ) 64', 'b ) 128', 'c ) 151', 'd ) 216', 'e ) 256'] | c | subtract(volume_cube(add(cube_edge_by_volume(65), const_2)), 65) | 65 small identical cubes are used to form a large cube . how many more cubes are needed to add one top layer of small cube all over the surface of the large cube ? | 65 small cube will make a large cube with 4 cubes in each line i . e . adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line . total number of small cubes in new cube = 6 ^ 3 = 216 extra cube required = 216 - 65 = 151 hence , c is the answer . | a = cube_edge_by_volume + (
b = volume_cube - (
|
a ) 1.42 sec , b ) 16.8 sec , c ) 5 sec , d ) 1.68 sec , e ) 3.6 sec | e | divide(add(100, 170), multiply(60, const_0_2778)) | how long does a train 100 m long traveling at 60 kmph takes to cross another train of 170 m in length has a speed of 40 kmph ? | "d = 100 m s = ( 60 + 40 ) * 5 / 18 = 250 / 3 t = 100 * 9 / 250 = 3.6 sec answer : e" | a = 100 + 170
b = 60 * const_0_2778
c = a / b
|
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | c | divide(subtract(subtract(10, 5), 1), 2) | in the coordinate plane , line a has a slope of - 1 and an x - intercept of 2 . line b has a slope of 5 and a y - intercept of - 10 . if the two lines intersect at the point ( a , b ) , what is the sum a + b ? | the equation of line a is y = - x + 2 the equation of line b is y = 5 x - 10 5 x - 10 = - x + 2 x = 2 y = 0 the point of intersection is ( 2,0 ) and then a + b = 2 . the answer is c . | a = 10 - 5
b = a - 1
c = b / 2
|
a ) - 7 , b ) - 8 , c ) - 9 , d ) - 10 , e ) - 11 | e | divide(subtract(multiply(9, 6), 10), subtract(7, multiply(const_3, 6))) | if 9 is added to thrice a number and this sum is multiplied by 6 , the result is the same as if the number is multiplied by 7 and 10 is added to the product . what is the number ? | let the number be x ; 6 ( 9 + 3 x ) = 7 x + 10 ; x = - 11 answer : e | a = 9 * 6
b = a - 10
c = 3 * 6
d = 7 - c
e = b / d
|
a ) 8 ° , b ) 10 ° , c ) 18 ° , d ) 36 ° , e ) 52 ° | c | divide(multiply(subtract(const_100, add(add(add(add(14, 24), 20), 29), 8)), divide(const_3600, const_10)), const_100) | a circle graph shows how the megatech corporation allocates its research and development budget : 14 % microphotonics ; 24 % home electronics ; 20 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ? | "14 % microphotonics ; 24 % home electronics ; 20 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; 100 - ( 14 + 24 + 20 + 29 + 8 ) = 5 % basic astrophysics . 5 % of 360 ° is 18 ° . answer : c ." | a = 14 + 24
b = a + 20
c = b + 29
d = c + 8
e = 100 - d
f = 3600 / 10
g = e * f
h = g / 100
|
a ) 5 / 2 , b ) 10 / 3 , c ) 7 / 2 , d ) 14 / 3 , e ) 11 / 2 | e | subtract(divide(add(5, sqrt(add(power(5, 2), multiply(multiply(2, 12), const_4)))), multiply(2, 2)), divide(subtract(5, sqrt(add(power(5, 2), multiply(multiply(2, 12), const_4)))), multiply(2, 2))) | by how much does the larger root of the equation 2 q ^ 2 + 5 q = 12 exceed the smaller root ? | "for 2 q ^ 2 + 5 q = 12 roots are [ - 5 + sqrt ( 25 + 96 ) ] / 4 or [ - 5 - sqrt ( 25 + 96 ) ] / 4 = 1.5 or - 4 hence larger root 1.5 is 1.5 - ( - 4 ) = 5.5 = 11 / 2 greater than smaller root ( - 4 ) . hence option ( e ) ." | a = 5 ** 2
b = 2 * 12
c = b * 4
d = a + c
e = math.sqrt(d)
f = 5 + e
g = 2 * 2
h = f / g
i = 5 ** 2
j = 2 * 12
k = j * 4
l = i + k
m = math.sqrt(l)
n = 5 - m
o = 2 * 2
p = n / o
q = h - p
|
a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8 | b | divide(add(const_4, const_2), const_1) | a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 30,000 and at the same time n is a perfect square and a perfect cube ? | "if n is a perfect square and a perfect cube , then n = a ^ 6 for some integer a . the numbers are 1 ^ 6 = 1 , 2 ^ 6 = 64 , 3 ^ 6 = 729 , 4 ^ 6 = 4096 , 5 ^ 6 = 15,625 . the answer is b ." | a = 4 + 2
b = a / 1
|
a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 7 | d | subtract(divide(add(add(add(2, 4), 7), 27), add(4, const_1)), 4) | for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 27 , the mean is how much greater than the median ? | "mean = ( x + x + 2 + x + 4 + x + 7 + x + 27 ) / 5 = ( 5 x + 40 ) / 5 = x + 8 median = x + 4 thus mean - median = x + 8 - ( x + 4 ) = 4 answer = d" | a = 2 + 4
b = a + 7
c = b + 27
d = 4 + 1
e = c / d
f = e - 4
|
a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 % | d | subtract(const_100, divide(subtract(const_100, 68), const_2)) | a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 % of the distribution lies one standard deviation g of the mean , what percent of the distribution is less than m + g ? | "16 % ________________________________________________ m + g 34 % ________________________________________________ m 34 % ________________________________________________ m - g 16 % since 68 % lies one standard deviation from mean m , = > 50 % of 68 % lies on either side as it is symmetric about m . thus 16 % lie below m - g and 16 % lie above m + g now below m + g = 16 + 34 + 34 = 84 % hence d" | a = 100 - 68
b = a / 2
c = 100 - b
|
a ) 300 , b ) 600 , c ) 800 , d ) 1000 , e ) 900 | b | divide(add(185, 25), divide(35, const_100)) | pradeep has to obtain 35 % of the total marks to pass . he got 185 marks and failed by 25 marks . the maximum marks are | explanation : let their maximum marks be x . then , 35 % of x = 185 + 25 = > 35 / 100 x = 210 x = ( 210100 / 35 ) x = 600 . answer : b | a = 185 + 25
b = 35 / 100
c = a / b
|
a ) 42 , b ) 48 , c ) 64 , d ) 76 , e ) 88 | c | subtract(divide(multiply(subtract(subtract(subtract(const_100, multiply(divide(160, 800), const_100)), 22), subtract(const_100, 75)), 800), const_100), divide(multiply(subtract(const_100, 75), 800), const_100)) | in a sample of 800 high school students in which all students are either freshmen , sophomores , juniors , or seniors , 22 percent are juniors and 75 percent are not sophomores . if there are 160 seniors , how many more freshmen than sophomores are there among the sample of students ? | "200 are sophomores . the number of freshmen is 600 - 160 - 0.22 ( 800 ) = 264 the answer is c ." | a = 160 / 800
b = a * 100
c = 100 - b
d = c - 22
e = 100 - 75
f = d - e
g = f * 800
h = g / 100
i = 100 - 75
j = i * 800
k = j / 100
l = h - k
|
a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28 | b | divide(add(add(multiply(const_2, 6), multiply(const_2, 5)), sqrt(add(multiply(6, subtract(120, multiply(multiply(const_2, 5), multiply(const_2, 6)))), power(add(multiply(const_2, 6), multiply(const_2, 5)), const_2)))), const_2) | a tailor trims 6 feet from opposite edges of a square piece of cloth , and 5 feet from the other two edges . if 120 square feet of cloth remain , what was the length of a side of the original piece of cloth ? | "let the original side of the square be x . ( x - 12 ) * ( x - 10 ) = 120 = 10 * 12 x = 22 the answer is b ." | a = 2 * 6
b = 2 * 5
c = a + b
d = 2 * 5
e = 2 * 6
f = d * e
g = 120 - f
h = 6 * g
i = 2 * 6
j = 2 * 5
k = i + j
l = k ** 2
m = h + l
n = math.sqrt(m)
o = c + n
p = o / 2
|
a ) 336 , b ) 384 , c ) 345 , d ) 244 , e ) 242 | a | multiply(14, 24) | find the area of a parallelogram with base 14 cm and height 24 cm . | "area of a parallelogram = base * height = 14 * 24 = 336 cm 2 answer : option a" | a = 14 * 24
|
a ) 25 % , b ) 28 % , c ) 30 % , d ) 32.5 % , e ) 35 % | e | multiply(divide(subtract(add(add(100, 35), 100), multiply(2, 100)), 100), 100) | a man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses . next year his income increases by 35 % but his savings increase by 100 % . if his total expenditure in 2 years is double his expenditure in 1 st year , what % age of his income in the first year did he save ? | "1 st year income = i 1 st year savings = s 1 st year expense = e 1 2 nd year income = 1.35 i 2 nd year savings = 2 s ( 100 % increase ) 2 nd year expense = e 2 e 1 + e 2 = 2 e 1 e 2 = e 1 that means expenses are same during both years . with increase of 35 % income the savings increased by 100 % . or s = . 35 i or s = 35 % of income e is the answer" | a = 100 + 35
b = a + 100
c = 2 * 100
d = b - c
e = d / 100
f = e * 100
|
a ) 0.5 , b ) 0.05 , c ) 0.005 , d ) 0.0005 , e ) 5 | b | divide(5, const_100) | how is 5 % expressed as a decimal fraction ? | "5 / 100 = 0.05 answer : b" | a = 5 / 100
|
a ) 7 , b ) 10 , c ) 8 , d ) 12 , e ) 15 | c | sqrt(subtract(power(10, const_2), power(6, const_2))) | 34 . the side surface of a cylinder is rolled with a rectangular plate . if the perimeter of the circular base is 6 feet , and the diagonal of the rectangular plate was 10 ft . what is height of the of the cylinder ? | think of a pringles can . if you took off the bottom and top and cut a slit down the length , it would flatten to a rectangle . the dimensions of the rectangle are the height of the can and the circumference of the circle . since you know both , one side and thehypothenuse use pythagoreans theorem or properties of 3 - 4 - 5 triangles to solve for the other side , 8 . correct answer c . | a = 10 ** 2
b = 6 ** 2
c = a - b
d = math.sqrt(c)
|
a ) 400 meters , b ) 1111 meters , c ) 160 meters , d ) 850 meters , e ) none of these | d | multiply(multiply(subtract(100, 64), const_0_2778), 85) | a train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 85 seconds . what is the length of the train in meters ? | train overtakes a bike means that we are talking about total length of the train . ( train ' s head is close to bike when it started and its tail crosses the bike when it overtakes the bike ) relative speed = 100 - 64 = 36 km / h = 36000 m / h time = 85 seconds distance = speed * time 36000 * 85 / 3600 = 850 meters . d is the answer . | a = 100 - 64
b = a * const_0_2778
c = b * 85
|
a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22 | b | add(subtract(subtract(const_1000, const_10), multiply(multiply(const_10, multiply(78, 78)), multiply(const_4, const_2))), const_10) | how many three digit numbers q are divisible by 78 or 91 ? | "the answer will be 19 . explanation : 78 = 2 * 3 * 13 now multiples of 78 , 156 . . . . 780 , now 1000 - 780 = 220 only two more muktiples of 78 can exists . so total number of 3 digit multiples of 78 are 9 + 2 = 11 91 = 13 * 7 - - total number of three digit multiples - - 9 no remember we have a common multiples as well - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples q - - 11 + 9 - 1 = 19 . hence answer is 19 . b" | a = 1000 - 10
b = 78 * 78
c = 10 * b
d = 4 * 2
e = c * d
f = a - e
g = f + 10
|
a ) a ) 2 , b ) b ) 3 , c ) c ) 5 , d ) d ) 4 , e ) e ) 8 | d | add(divide(subtract(multiply(floor(divide(9, 2)), 2), multiply(add(floor(divide(2, 2)), const_1), 2)), 2), const_1) | how many numbers from 2 to 9 are exactly divisible by 2 ? | "2 / 2 = 1 and 9 / 2 = 4 4 - 1 = 3 3 + 1 = 4 numbers . answer : d" | a = 9 / 2
b = math.floor(a)
c = b * 2
d = 2 / 2
e = math.floor(d)
f = e + 1
g = f * 2
h = c - g
i = h / 2
j = i + 1
|
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