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 ) 40 % , b ) 55 % , c ) 54.8 % , d ) 60 % , e ) 62 % | c | multiply(divide(10628, add(add(1136, 7636), 10628)), const_100) | 3 candidates in an election and received 1136 , 7636 and 10628 votes respectively . what % of the total votes did the winning candidate gotin that election ? | "total number of votes polled = ( 1136 + 7636 + 10628 ) = 19400 so , required percentage = 10628 / 19400 * 100 = 54.8 % c" | a = 1136 + 7636
b = a + 10628
c = 10628 / b
d = c * 100
|
a ) 124 , b ) 297 , c ) 394 , d ) 421 , e ) 842 | a | add(multiply(multiply(4, 3), const_10), 4) | a is the hundreds digit of the 3 digit integer x , b is the tens digit of x , and c is the units digit of x . 4 a = 2 b = c , and a > 0 . what is the difference between the two greatest possible values of x ? tip : dont stop till you have exhausted all answer choices to arrive at the correct one . | ratio of a : b : c = 1 : 2 : 4 two possible greatest single digit values for c are 8 and 4 if c is 8 , then x = 248 if c is 4 , then x = 124 difference = 248 - 124 = 124 a is the answer | a = 4 * 3
b = a * 10
c = b + 4
|
a ) 643 , b ) 652 , c ) 562 , d ) 578 , e ) 693 | c | multiply(divide(567, add(const_1, divide(27, const_100))), add(const_1, divide(26, const_100))) | if albert ’ s monthly earnings rise by 27 % , he would earn $ 567 . if , instead , his earnings rise by only 26 % , how much ( in $ ) would he earn this month ? | "= 567 / 1.27 ∗ 1.26 = 562 = 562 answer is c" | a = 27 / 100
b = 1 + a
c = 567 / b
d = 26 / 100
e = 1 + d
f = c * e
|
a ) 5 , b ) 2 , c ) 9 , d ) 5 , e ) 1 | b | subtract(subtract(multiply(1250, power(add(const_1, divide(4, const_100)), 2)), 1250), multiply(multiply(1250, divide(4, const_100)), 2)) | indu gave bindu rs . 1250 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ? | "1250 = d ( 100 / 4 ) 2 d = 2 answer : b" | a = 4 / 100
b = 1 + a
c = b ** 2
d = 1250 * c
e = d - 1250
f = 4 / 100
g = 1250 * f
h = g * 2
i = e - h
|
a ) 3 , b ) 4 , c ) 5 , d ) 0 , e ) 7 | d | subtract(4, reminder(4, 8)) | when n is divided by 24 , the remainder is 4 . what is the remainder when 4 n is divided by 8 ? | "let n = 4 ( leaves a remainder of 4 when divided by 24 ) 4 n = 4 ( 4 ) = 16 , which leaves a remainder of 0 when divided by 8 . answer d" | a = 4 - reminder
|
a ) 60 , b ) 72 , c ) 84 , d ) 96 , e ) 108 | d | multiply(subtract(divide(multiply(const_2, const_2), subtract(8, multiply(const_2, 3))), divide(const_2, subtract(8, 3))), const_60) | tom and linda stand at point a . linda begins to walk in a straight line away from tom at a constant rate of 3 miles per hour . one hour later , tom begins to jog in a straight line in the exact opposite direction at a constant rate of 8 miles per hour . if both tom and linda travel indefinitely , what is the positive ... | "d is the answer . . . . d = ts where d = distance , t = time and s = speed to travel half distance , ( 2 + 3 t ) = 8 t = = > t = 2 / 5 = = > 24 minutes to travel double distance , 2 ( 2 + 3 t ) = 8 t = = > 2 = = > 120 minutes difference , 96 minutes d" | a = 2 * 2
b = 2 * 3
c = 8 - b
d = a / c
e = 8 - 3
f = 2 / e
g = d - f
h = g * const_60
|
a ) 34 , b ) 32 , c ) 17 , d ) 27 , e ) 28 | b | subtract(35, const_3) | 35 - [ 23 - { 15 - x } ] = 12 × 2 ÷ 1 / 2 | explanation : 35 - [ 23 - { 19 - ( 15 - x ) } ] = 12 × 2 × 2 = 48 = > 35 - 23 + ( 19 - 15 + x ) = 48 = > 12 + 4 + x = 48 = > x = 48 - ( 4 + 12 ) = 32 answer : option b | a = 35 - 3
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a ) 600 m , b ) 200 m , c ) 300 m , d ) 400 m , e ) 100 m | c | divide(multiply(18, multiply(1.2, const_1000)), 48) | amar takes as much time in running 18 meters as a car takes in covering 48 meters . what will be the distance covered by amar during the time the car covers 1.2 km ? | "c 300 m distance covered by amar = 18 / 4.8 ( 1.6 km ) = 3 / 8 ( 1200 ) = 300 m answer is c" | a = 1 * 2
b = 18 * a
c = b / 48
|
a ) 9 , b ) 0 , c ) 1 , d ) 2 , e ) 4 | a | subtract(subtract(20, add(1, 4)), 6) | if n is an integer , f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 20 . what is the value of f ( 6 ) ? | "since f ( n ) = f ( n - 1 ) - n then : f ( 6 ) = f ( 5 ) - 6 and f ( 5 ) = f ( 4 ) - 5 . as given that f ( 4 ) = 20 then f ( 5 ) = 20 - 5 = 15 - - > substitute the value of f ( 5 ) back into the first equation : f ( 6 ) = f ( 5 ) - 6 = 15 - 6 = 9 . answer : a . questions on funtions to practice :" | a = 1 + 4
b = 20 - a
c = b - 6
|
a ) 22 hours , b ) 21 hours , c ) 23 hours , d ) 20 hours , e ) 28 hours | d | subtract(divide(multiply(divide(const_1, const_2), 40), subtract(50, 40)), divide(const_1, const_2)) | a thief goes away with a santro car at a speed of 40 kmph . the theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start ? | "d 20 hours | - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - | 50 40 d = 20 rs = 50 – 40 = 10 t = 20 / 10 = 2 hours" | a = 1 / 2
b = a * 40
c = 50 - 40
d = b / c
e = 1 / 2
f = d - e
|
a ) 11260 , b ) 11860 , c ) 12360 , d ) 12960 , e ) 13560 | d | add(multiply(const_100, const_100), subtract(lcm(lcm(lcm(lcm(5, 15), 32), 45), 54), reminder(multiply(const_100, const_100), lcm(lcm(lcm(lcm(5, 15), 32), 45), 54)))) | what is the smallest 5 digit number that is divisible by 15 , 32 , 45 , and 54 ? | 15 = 3 * 5 32 = 2 ^ 5 45 = 3 ^ 2 * 5 54 = 2 * 3 ^ 3 lcm = 2 ^ 5 * 3 ^ 3 * 5 = 4320 the smallest five - digit number that is a multiple of 4320 is 3 * 4320 = 12,960 the answer is d . | a = 100 * 100
b = math.lcm(5, 15)
c = math.lcm(b, 32)
d = math.lcm(c, 45)
e = math.lcm(d, 54)
f = 100 * 100
g = math.lcm(5, 15)
h = math.lcm(g, 32)
i = math.lcm(h, 45)
j = math.lcm(i, 54)
k = e - reminder
l = a + k
|
a ) 15 , b ) 88 , c ) 77 , d ) 20 , e ) 99 | a | subtract(multiply(const_1, const_60), multiply(divide(45, 60), const_60)) | excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 45 km / hr . for how many minutes does the bus stop per hour ? | "in 1 hr , the bus covers 60 km without stoppages and 45 km with stoppages . stoppage time = time take to travel ( 60 - 45 ) km i . e 15 km at 60 km / hr . stoppage time = 15 / 60 hrs = 15 min . answer : a" | a = 1 * const_60
b = 45 / 60
c = b * const_60
d = a - c
|
['a ) 14 cms', 'b ) 21 cms', 'c ) 42 cms', 'd ) none of these', 'e ) can not be determined'] | b | multiply(divide(divide(divide(divide(multiply(const_100, 3.78), const_3), const_3), const_3), const_2), const_3) | a rectangular courty 3.78 metres long and 5.25 metres wide is to be paved exactly with square tiles , all of the same size . what is the largest size of the tile which could be used for the purpose ? | solution largest size of the tile . h . c . f of 378 cm and 525 cm = 21 cms . answer b | a = 100 * 3
b = a / 3
c = b / 3
d = c / 3
e = d / 2
f = e * 3
|
a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 12 | b | multiply(multiply(add(inverse(multiply(const_2, const_4)), const_1), const_3), multiply(const_2, const_4)) | working together , wayne and his son can shovel the entire driveway in three hours . if wayne can shovel five times as fast as his son can , how many hours would it take for his son to shovel the entire driveway on his own ? | "w : the time for wyane to do the job s : the time for his son to do the job we have 1 / w + 1 / s = 1 / 5 and w = 5 s then we have 1 / ( 5 * s ) + 1 / s = 1 / 5 < = > 6 / ( 5 * s ) = 1 / 5 < = > s = 6 ans : b" | a = 2 * 4
b = 1/(a)
c = b + 1
d = c * 3
e = 2 * 4
f = d * e
|
a ) 240 seconds , b ) 120 seconds , c ) 60 seconds , d ) 180 seconds , e ) 100 seconds | b | divide(960, subtract(20, 12)) | 3 bodies x , y and z start moving around a circular track of length 960 m from the same point simultaneously in the same direction at speeds of 12 m / s , 20 m / s and 36 m / s respectively . when will they meet for the first time after they started moving ? | if they all meet after t seconds , it means they covered the distances 12 t , 20 t , and 36 t respectively . since they all arrive to the same spot , it means that the differences taken pairwise between the distances must be positive integer multiples of the length of the track , which is 960 m . so , 8 t , 16 t , and ... | a = 20 - 12
b = 960 / a
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a ) 4 : 2 , b ) 4 : 8 , c ) 4 : 3 , d ) 4 : 0 , e ) 6 : 5 | e | multiply(divide(12, const_100), 10) | a part of certain sum of money is invested at 10 % per annum and the rest at 12 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ? | "12 : 10 = 6 : 5 answer : e" | a = 12 / 100
b = a * 10
|
a ) 4 / 3 , b ) 2 / 3 , c ) 1 / 3 , d ) 3 / 4 , e ) 1 / 4 | b | divide(subtract(const_100, 60), 60) | kelly and chris are moving into a new city . both of them love books and thus packed several boxes with books . if chris packed 60 % of the total number of boxes , what was the ratio of the number of boxes kelly packed to the number of boxes chris packed ? | the ratio of the number of boxes kelly packed to the number of boxes chris packed = 40 / 60 = 2 / 3 answer : b | a = 100 - 60
b = a / 60
|
a ) 10 / 16 , b ) 9 / 15 , c ) 4 / 16 , d ) 6 / 10 , e ) 4 / 10 | b | divide(divide(subtract(24, 6), add(const_1, const_1)), add(divide(subtract(24, 6), add(const_1, const_1)), 6)) | there are 6 more women than there are men on a local co - ed softball team . if there are a total of 24 players on the team , what is the ratio of men to women ? | "w = m + 6 w + m = 24 m + 6 + m = 24 2 m = 18 m = 9 w = 15 ratio : 9 : 15 ans : b" | a = 24 - 6
b = 1 + 1
c = a / b
d = 24 - 6
e = 1 + 1
f = d / e
g = f + 6
h = c / g
|
a ) 0.75 , b ) 1 , c ) 1.25 , d ) 1.5 , e ) 2.0 | e | divide(60, add(13, 17)) | two cars start at the same time from opposite ends of a highway that is 60 miles long . one car is riding at 13 mph and the second car is riding at 17 mph . how long after they begin will they meet ? | "as cars are moving in opposite directions their speeds will be added . so their relative speeds : 17 + 13 = 30 mph total distance to be covered = 60 miles . time taken would be : 60 miles / 30 mph = 2.0 hours e is the answer ." | a = 13 + 17
b = 60 / a
|
a ) 2 , b ) 2.2 , c ) 1 , d ) 4 , e ) 5 | c | subtract(divide(42, 6), 6) | ( x + 6 ) is a factor in x ^ 2 - mx - 42 . what is the value of m ? | i solved the second degree equation and found it like this : x ^ 2 - mx - 42 = 0 ( x - 7 ) ( x + 6 ) = 0 x = 7 or x = - 6 substituting both values for x in the equation we find : x ^ 2 - mx - 42 = > ( - 6 ) ^ 2 - m ( - 6 ) = 42 = > 36 + 6 m = 42 = > 6 m = 42 - 36 = 6 = > m = 1 and with 7 , using a similar process we en... | a = 42 / 6
b = a - 6
|
a ) 30 , b ) 35 , c ) 45 , d ) 50 , e ) 40 | e | multiply(10, 8) | local kennel has cats and dogs in the ratio of 6 : 8 . if there are 10 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 6 : 8 or cats 6 dogs 8 we can write number of cats as 6 x and number of dogs as 8 x and we know that 8 x - 6 x = 10 ( therefore 2 x = 10 = > x = 5 ) then # of dogs = 8 x 5 = 40 answer is e" | a = 10 * 8
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a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24 | b | add(10, add(const_0_25, add(const_0_33, divide(divide(144, 10), const_2)))) | a rectangular field has a length 10 meters more than it is width . if the area of the field is 144 , what is the length ( in meters ) of the rectangular field ? | "area = l * w = ( l ) * ( l - 10 ) = 171 trial and error : 20 * 10 = 200 ( too high ) 19 * 9 = 171 ( too high ) 18 * 8 = 144 the length is 18 meters . the answer is b ." | a = 144 / 10
b = a / 2
c = const_0_33 + b
d = const_0_25 + c
e = 10 + d
|
a ) 9.2 , b ) 10.5 , c ) 11.5 , d ) 12.3 , e ) 15 | a | add(divide(multiply(15, 25), const_100), divide(multiply(12, 45), const_100)) | add 15 % of 25 and 12 % of 45 . | 15 % of 25 + 12 % of 45 25 * 15 / 100 + 45 * 12 / 100 3.8 + 5.4 = 9.2 answer a | a = 15 * 25
b = a / 100
c = 12 * 45
d = c / 100
e = b + d
|
a ) 941,1009 , b ) 991,1001 , c ) 991,1009 , d ) 791,1009 , e ) 931,1009 | c | divide(999919, add(multiply(const_100, const_10), add(const_3, const_2))) | there are cats got together and decided to kill the mice of 999919 . each cat kills equal number of mice and each cat kills more number of mice than cats there were . then what are the number of cats ? | "999919 can be written as 1000000 – 81 = 10002 – 92 ie of the form a 2 - b 2 = ( a + b ) ( a - b ) = ( 1000 + 9 ) * ( 1000 - 9 ) = ( 1009 ) * ( 991 ) given that number of cats is less than number if mice . so number of cats is 991 and number of mice were 1009 answer c" | a = 100 * 10
b = 3 + 2
c = a + b
d = 999919 / c
|
a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 12 | d | divide(divide(multiply(multiply(8, 12), 4), 12), 8) | a crate measures 4 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still... | "to fit the cylinder with largest radius inside this cuboid , we should make the base of the crate as wide as possible so we will take the base as 12 feet by 8 feet now since the limiting number in the base is 8 feet ; therefore a cylinder { we can visualise that a cylinder ' s width is its diameter } can only fit insi... | a = 8 * 12
b = a * 4
c = b / 12
d = c / 8
|
a ) 180 cm , b ) 220 cm , c ) 240 cm , d ) 270 cm , e ) 300 cm | d | add(triangle_perimeter(45, 45, 45), triangle_perimeter(45, 45, 45)) | an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 45 cm , find the sum of the perimeters of all the triangles... | "we have 45 for first triangle , when we join mid - points of first triangle we get the second equilateral triangle then the length of second one is 22.5 and continues . so we have 45 , 22.5 , 11.25 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 45 / 1 - ( 1 / 2 ) = 90 equil... | a = triangle_perimeter + (
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a ) $ 880 , b ) $ 990 , c ) $ 1,000 , d ) $ 1,100 , e ) $ 1,080 | e | subtract(multiply(120, divide(const_100, 10)), 120) | if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 120 , how much more remains to be paid ? | "10 / 100 p = 120 > > p = 120 * 100 / 10 = 1200 1200 - 120 = 1080 answer : e" | a = 100 / 10
b = 120 * a
c = b - 120
|
a ) 27 , b ) 22 , c ) 24 , d ) 26 , e ) 30 | a | subtract(power(3, 3), const_1) | a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 6 , which can be repeated . if the product of the digits in the area code must be even , how many different codes can be created ? | "total # of codes possible is 3 * 3 * 3 = 27 . oit of those 27 codes answer : a" | a = 3 ** 3
b = a - 1
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a ) 14300 , b ) 17280 , c ) 14500 , d ) 14600 , e ) 15400 | b | add(10000, multiply(divide(multiply(10000, 20), const_100), 3)) | the population of a town is 10000 . it increases annually at the rate of 20 % p . a . what will be its population after 3 years ? | "formula : ( after = 100 denominator ago = 100 numerator ) 10000 × 120 / 100 ^ 3 = 17280 b )" | a = 10000 * 20
b = a / 100
c = b * 3
d = 10000 + c
|
a ) 25 days , b ) 18 days , c ) 21 days , d ) 11 days , e ) 13 days | b | multiply(divide(multiply(6, add(const_2, const_1)), const_2), const_2) | a is twice as good a workman as b and they took 6 days together to do the work b alone can do it in ? | "wc = 2 : 1 2 x + x = 1 / 6 x = 1 / 18 = > 18 days answer : b" | a = 2 + 1
b = 6 * a
c = b / 2
d = c * 2
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a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 11 | b | add(divide(subtract(301, 149), multiply(15, const_2)), const_1) | how many even multiples of 15 are there between 149 and 301 ? | "150 = 10 * 15 300 = 20 * 15 the even multiples are 15 multiplied by 10 , 12 , 14 , 16 , 18 , and 20 for a total of 6 . the answer is b ." | a = 301 - 149
b = 15 * 2
c = a / b
d = c + 1
|
a ) a ) 4 , b ) b ) 1 , c ) c ) 2 , d ) d ) 3 , e ) e ) 5 | d | subtract(24, reminder(1101, 24)) | what least number should be added to 1101 , so that the sum is completely divisible by 24 | "explanation : ( 1056 / 24 ) gives remainder 21 21 + 3 = 24 , so we need to add 3 . answer : option d" | a = 24 - reminder
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a ) 12 / 24 , b ) 48 / 63 , c ) 45 / 56 , d ) 48 / 19 , e ) 28 / 12 | d | divide(const_1, divide(add(add(inverse(6), inverse(2)), inverse(8)), 6)) | a and b can do a work in 6 days , b and c in 2 days and c and a in 8 days . in how many days will the work be completed , if all three of them work together ? | "one day work of a and b = 1 / 6 one day work of b and c = 1 / 2 one day work of c and a = 1 / 8 2 ( a + b + c ) = 1 / 6 + 1 / 2 + 1 / 8 2 ( a + b + c ) = 19 / 24 ( a + b + c ) = 19 / 48 number of days required = 48 / 19 days . answer : d" | a = 1/(6)
b = 1/(2)
c = a + b
d = 1/(8)
e = c + d
f = e / 6
g = 1 / f
|
a ) 2 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours | a | inverse(add(multiply(divide(const_1, 5), add(divide(10, const_100), const_1)), multiply(divide(const_1, 3), divide(10, const_100)))) | working alone , mary can pave a driveway in 5 hours and hillary can pave the same driveway in 3 hours . when they work together , mary thrives on teamwork so her rate increases by 10 % , but hillary becomes distracted and her rate decreases by 10 % . if they both work together , how many hours will it take to pave the ... | "initial working rates : mary = 1 / 5 per hour hillary = 1 / 3 per hour rate when working together : mary = 1 / 5 + ( 1 / 10 * 1 / 5 ) = 2 / 9 per hour hillary = 1 / 3 - ( 1 / 10 * 1 / 3 ) = 3 / 10 per hour together they work 2 / 9 + 3 / 10 = 1 / 2 per hour so they will need 2 hours to complete the driveway . the corre... | a = 1 / 5
b = 10 / 100
c = b + 1
d = a * c
e = 1 / 3
f = 10 / 100
g = e * f
h = d + g
i = 1/(h)
|
a ) 24 , b ) 54 , c ) 60 , d ) 84 , e ) 94 | c | multiply(divide(multiply(add(add(subtract(add(const_4, const_4), divide(500, const_100)), const_1), add(const_4, const_4)), divide(500, const_100)), subtract(3, const_1)), const_2) | how many 3 digit no ' s are between 100 - 500 , where sum of two digit is 3 rd ? | total permutations possible = 18 + 16 + 14 + 12 = 60 answer : c | a = 4 + 4
b = 500 / 100
c = a - b
d = c + 1
e = 4 + 4
f = d + e
g = 500 / 100
h = f * g
i = 3 - 1
j = h / i
k = j * 2
|
a ) 2 / 1 , b ) 4 / 1 , c ) 6 / 5 , d ) 3 / 4 , e ) 3 / 2 | c | divide(subtract(45, divide(45, add(4, 1))), add(divide(45, add(4, 1)), 21)) | in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 21 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture . | "given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 21 ) = 36 / 30 = 6 / 5 . answer : c ." | a = 4 + 1
b = 45 / a
c = 45 - b
d = 4 + 1
e = 45 / d
f = e + 21
g = c / f
|
a ) 2 m , b ) 6 m , c ) 4 m , d ) 8 m , e ) 9 m | b | divide(subtract(640, multiply(multiply(80, divide(const_1, const_2)), 10)), multiply(80, divide(const_1, const_2))) | the cross - section of a stream is a trapezium in shape . if the stream is 10 m wide at the top and the area of cross - section is 640 sq m , the depth of stream is 80 m and width at the bottom is ? | 1 / 2 * 80 ( 10 + b ) = 640 b = 6 m answer : b | a = 1 / 2
b = 80 * a
c = b * 10
d = 640 - c
e = 1 / 2
f = 80 * e
g = d / f
|
a ) 8 , b ) 5 , c ) 7 , d ) 4 , e ) 6 | c | divide(subtract(multiply(2, 27), 26), subtract(multiply(2, 3), 2)) | the cost of 2 books and 2 magazines is $ 26 . the cost of 1 book and 3 magazines is $ 27 . how much does 1 magazine cost ? | let the cost of 1 book = x , let the cost of 1 magazine = y 2 x + 2 y = 26 x = ( 26 - 2 y ) / 2 x = 13 - y again , ( 13 - y ) + 3 y = 27 13 + 2 y = 27 2 y = 14 y = 7 answer : c | a = 2 * 27
b = a - 26
c = 2 * 3
d = c - 2
e = b / d
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a ) 22 , b ) 35 , c ) 27 , d ) 32 , e ) 161 | e | subtract(negate(81), multiply(subtract(21, 41), divide(subtract(21, 41), subtract(6,11, 21)))) | 6,11 , 21 , 41 , 81 , ( . . . ) | "explanation : 6 6 × 2 - 1 = 11 11 × 2 - 1 = 21 21 × 2 - 1 = 41 41 × 2 - 1 = 81 81 × 2 - 1 = 161 answer : option e" | a = negate - (
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a ) 45 % , b ) 56 % , c ) 64 % , d ) 75 % , e ) 80 % | c | multiply(divide(multiply(20, const_4), add(const_100, 25)), const_100) | the organizers of a fair projected a 25 percent increase in attendance this year over that of last year , but attendance this year actually decreased by 20 percent . what percent of the projected attendance was the actual attendance ? | last year attendance = 100 ( assume ) ; projected attendance = 125 ; actual attendance = 80 . the actual attendance therefore was ( actual ) / ( project ) = 80 / 125 * 100 = 64 $ of the projected attendance . answer : c . | a = 20 * 4
b = 100 + 25
c = a / b
d = c * 100
|
a ) 5 , b ) 35 , c ) 34 , d ) 36 , e ) 38 | a | sqrt(85) | the length of the longest tape in cm which can be used to measure exactly , the length 10 m ; 3 m 85 cm ; and 11 m 50 cm is : | "the three lengths in cm are 1000 , 385 & 1150 . hcf of 700 , 385 & 1295 is 5 . hence , the answer is 5 cm . answer : a" | a = math.sqrt(85)
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a ) 200 , b ) 235 , c ) 50 , d ) 115 , e ) 150 | b | divide(add(270, 200), const_2) | if x + y = 270 , x - y = 200 , for integers of x and y , y = ? | "x + y = 270 x - y = 200 2 x = 70 x = 35 y = 235 answer is b" | a = 270 + 200
b = a / 2
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a ) 12 days , b ) 15 days , c ) 66 / 5 days , d ) 21 days , e ) 22 / 5 days | c | inverse(subtract(inverse(6), inverse(11))) | a and b together can do a piece of work in 6 days and a alone can do it in 11 days . in how many days can b alone can do it ? | "explanation : a and b can do work 1 / 6 in 1 day a alone can do 1 / 11 work in 1 day b alone can do ( 1 / 6 - 1 / 11 ) = 5 / 66 work in 1 day = > complete work can be done in 66 / 5 days by b answer : option c" | a = 1/(6)
b = 1/(11)
c = a - b
d = 1/(c)
|
a ) 48.89 , b ) 42.25 , c ) 50 , d ) 51.25 , e ) 52.25 | a | divide(add(multiply(22, 50.25), multiply(8, 45.15)), add(22, 8)) | the average weight of 22 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class . | explanation : average weight of 22 boys = 50.25 total weight of 22 boys = 50.25 × 22 average weight of remaining 8 boys = 45.15 total weight of remaining 8 boys = 45.15 × 8 total weight of all boys in the class = ( 50.25 × 16 ) + ( 45.15 × 8 ) total boys = 22 + 8 = 30 average weight of all the boys = ( ( 50.25 × 22 ) +... | a = 22 * 50
b = 8 * 45
c = a + b
d = 22 + 8
e = c / d
|
a ) $ 150 , b ) $ 900 , c ) $ 600 , d ) $ 450 , e ) none | b | add(add(add(divide(300, 1), divide(300, 2)), divide(300, 2)), divide(300, 1)) | profits in the partnership of bess , bill and bob are shared in the ratio 1 : 2 : 3 . if bill ' s share of the profits is $ 300 , what is bob ' s share ? | ans is d given profit ratio , bess : bill : bob = 1 : 2 : 3 to make bill ' s portion $ 300 , multiply by $ 150 = > bess : bill : bob = $ 150 : $ 300 : $ 450 = > bob ' s share = $ 450 | a = 300 / 1
b = 300 / 2
c = a + b
d = 300 / 2
e = c + d
f = 300 / 1
g = e + f
|
a ) 24 , b ) 12 , c ) 8 , d ) 4 , e ) 2 | a | subtract(204, multiply(60, 3)) | a sporting goods store sold 60 frisbees in one week , some for $ 3 and the rest for $ 4 each . if receipts from frisbee sales for the week totaled $ 204 , what is the fewest number of $ 4 frisbees that could have been sold ? | "in this question however , because we are told that exactly 64 frisbees have been sold and revenue was exactly $ 204 , there is only one possible solution for the number of $ 3 and $ 4 frisbees sold . to solve , we have 2 equations and 2 unknowns let x = number of $ 3 frisbees sold let y = number of $ 4 frisbees sold ... | a = 60 * 3
b = 204 - a
|
a ) 0.75 , b ) 0.8 , c ) 1 , d ) 1.2 , e ) 1.44 | e | inverse(divide(90, add(90, 40))) | patrick purchased 90 pencils and sold them at a loss equal to the selling price of 40 pencils . the cost of 90 pencils is how many times the selling price of 90 pencils ? | "say the cost price of 90 pencils was $ 90 ( $ 1 per pencil ) and the selling price of 1 pencil was p . selling at a loss : 90 - 90 p = 40 p - - > p = 9 / 13 . ( cost price ) / ( selling price ) = 1 / ( 9 / 13 ) = 13 / 9 = 1.44 . answer : e ." | a = 90 + 40
b = 90 / a
c = 1/(b)
|
a ) a ) 1040 , b ) b ) 1045 , c ) c ) 1055 , d ) d ) 1060 , e ) e ) 1235 | e | add(multiply(8, 70), multiply(9, 75)) | tom purchased 8 kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 75 per kg . how much amount did he pay to the shopkeeper ? | cost of 8 kg apples = 70 × 8 = 560 . cost of 9 kg of mangoes = 75 × 9 = 675 . total cost he has to pay = 560 + 675 = 1235 . e ) | a = 8 * 70
b = 9 * 75
c = a + b
|
a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15 | b | divide(6, subtract(divide(multiply(const_2, 6), 8), 1)) | it takes joey the postman 1 hours to run a 6 mile long route every day . he delivers packages and then returns to the post office along the same path . if the average speed of the round trip is 8 mile / hour , what is the speed with which joey returns ? | "let his speed for one half of the journey be 6 miles an hour let the other half be x miles an hour now , avg speed = 8 mile an hour 2 * 6 * x / 6 + x = 8 12 x = 8 x + 48 = > x = 12 b" | a = 2 * 6
b = a / 8
c = b - 1
d = 6 / c
|
a ) 4 . , b ) 8 . , c ) 12 . , d ) 16 . , e ) 36 . | e | power(subtract(6, divide(add(18, 6), 2)), 2) | if ( a - b - c + d = 18 ) and ( a + b - c - d = 6 ) , what is the value of ( b - d ) ^ 2 ? | "eq 1 : a - b - c + d = 18 eq 2 : a + b - c - d = 6 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 18 - a + b - c - d = 6 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 12 ( 2 ) simplify - b + d = 6 b - d = - 6 ( b - d ) ^ 2 = ( - 6 ) ^ 2 = 36 my answer : e" | a = 18 + 6
b = a / 2
c = 6 - b
d = c ** 2
|
a ) 70 , b ) 72 , c ) 74 , d ) 75 , e ) 55 | e | divide(1, divide(add(multiply(const_3600, divide(1, 60)), 5), const_3600)) | a car traveling at a certain constant speed takes 5 seconds longer to travel 1 km than it would take to travel 1 km at 60 km / hour . at what speed , in km / hr , is the car traveling ? | "time to cover 1 kilometer at 80 kilometers per hour is 1 / 60 hours = 3,600 / 60 seconds = 60 seconds ; time to cover 1 kilometer at regular speed is 60 + 5 = 65 seconds = 65 / 3,600 hours = 1 / 55 hours ; so , we get that to cover 1 kilometer 1 / 55 hours is needed - - > regular speed 55 kilometers per hour ( rate is... | a = 1 / 60
b = 3600 * a
c = b + 5
d = c / 3600
e = 1 / d
|
a ) 1 / 7 , b ) 2 / 7 , c ) 3 / 7 , d ) 4 / 7 , e ) 5 / 7 | b | divide(const_2, choose(add(const_3, const_3), const_3)) | what is the probability of getting 53 mondays in a leap year ? | "in a leap year contains 52 monday ' s since 52 weeks are present and 2 days extra it may be sunday and monday 2 . monday and tuesday 3 . tuesday and thursday 4 . thursday and friday similary 7 alternatives are possible . among this only 2 are possible cases so 2 / 7 answer : b" | a = 3 + 3
b = math.comb(a, 3)
c = 2 / b
|
a ) 3125 , b ) 625 , c ) 5 , d ) 25 , e ) 125 | e | multiply(power(5, 5), 5) | if a and b are positive integers and ( 5 ^ a ) ^ b = 5 ^ 2 , what is the value of 2 ^ a * 2 ^ b ? | "5 ^ ab = 5 ^ 2 therefore ab = 2 either a = 1 or 2 or b = 2 or 1 therefore 5 ^ a * 5 ^ b = 5 ^ ( a + b ) = 5 ^ 3 = 125 e" | a = 5 ** 5
b = a * 5
|
a ) 111 , b ) 28 , c ) 160 , d ) 213 , e ) 107 | d | subtract(add(floor(divide(subtract(332, 10), 3)), divide(subtract(332, 10), 2)), floor(divide(subtract(332, 10), multiply(2, 3)))) | if w is the set of all the integers between 10 and 332 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ? | "official solution : number of multiples of 3 step 1 . subtract the extreme multiples of 3 within the range ( the greatest is 330 , the smallest is 12 ) : 330 - 12 = 318 step 2 . divide by 3 : 318 / 3 = 106 step 3 . add 1 : 106 + 1 = 107 . so there are 107 multiples of 3 within the range : examples are 51 , 54 , 57 , 6... | a = 332 - 10
b = a / 3
c = math.floor(b)
d = 332 - 10
e = d / 2
f = c + e
g = 332 - 10
h = 2 * 3
i = g / h
j = math.floor(i)
k = f - j
|
['a ) 2345', 'b ) 3456', 'c ) 4567', 'd ) 5678', 'e ) 6789'] | b | divide(multiply(30, power(12, const_3)), subtract(add(12, 6), 3)) | a tank with a volume of 30 cubic feet has one inlet pipe and 2 outlet pipes . the inlet pipe fills water into the tank at the rate of 3 cubic inches / min and the 2 outlet pipes empty it out at the rates of 12 cubic inches / min and 6 cubic inches / min respectively . if all 3 pipes are opened when the tank is full , h... | the tank is emptied at this rate : 12 + 6 - 3 = 15 cubic inches / min the tank has a volume of 30 * 12 * 12 * 12 = 51840 cubic inches . the time it takes to empty the tank is 51840 / 15 = 3456 minutes . the answer is b . | a = 12 ** 3
b = 30 * a
c = 12 + 6
d = c - 3
e = b / d
|
a ) $ 28,300 , b ) $ 30,800 , c ) $ 31,300 , d ) $ 32,500 , e ) $ 35,100 | b | multiply(divide(231, divide(9, multiply(const_3, const_4))), const_100) | an investment yields an interest payment of $ 231 each month . if the simple annual interest rate is 9 % , what is the amount of the investment ? | "let the principal amount = p simple annual interest = 9 % simple monthly interest = ( 9 / 12 ) = ( 3 / 4 ) % ( 3 / 4 ) * ( p / 100 ) = 230 = > p = ( 231 * 4 * 10 ^ 2 ) / 3 = 77 * 4 * 10 ^ 2 = 308 * 10 ^ 2 = 30800 answer b" | a = 3 * 4
b = 9 / a
c = 231 / b
d = c * 100
|
a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) none | b | multiply(subtract(const_1, divide(multiply(const_1, 6), 7.50)), const_100) | if the price of sugar rises from rs . 6 per kg to rs . 7.50 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by | "sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 6 = x × 7.50 = x = 80 kg . ∴ reduction in consumption = 20 % . answer b" | a = 1 * 6
b = a / 7
c = 1 - b
d = c * 100
|
a ) 941,1009 , b ) 991,1001 , c ) 995,1005 , d ) 791,1009 , e ) 931,1009 | c | divide(999975, add(multiply(const_100, const_10), add(const_3, const_2))) | there are cats got together and decided to kill the mice of 999975 . each cat kills equal number of mice and each cat kills more number of mice than cats there were . then what are the number of cats ? | 999975 can be written as 1000000 â € “ 25 = 10002 â € “ 52 ie of the form a 2 - b 2 = ( a + b ) ( a - b ) = ( 1000 + 5 ) * ( 1000 - 5 ) = ( 1005 ) * ( 995 ) given that number of cats is less than number if mice . so number of cats is 995 and number of mice were 1005 answer c | a = 100 * 10
b = 3 + 2
c = a + b
d = 999975 / c
|
a ) 10 , b ) 14 , c ) 15 , d ) 16 , e ) 17 | a | divide(factorial(subtract(add(const_4, 01), const_1)), multiply(factorial(01), factorial(subtract(const_4, const_1)))) | how many positive integers less than 50 have a reminder 01 when divided by 5 ? | "1 also gives the remainder of 1 when divided by 5 . so , there are total of 10 numbers . answer : a ." | a = 4 + 1
b = a - 1
c = math.factorial(b)
d = math.factorial(1)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
|
a ) 2.125 , b ) 2.375 , c ) 2.625 , d ) 2.675 , e ) 2.825 | c | divide(divide(multiply(add(4, 2), 3.5), 2), 4) | natasha climbs up a hill , and descends along the same way she went up . it takes her 4 hours to reach the top and 2 hours to come back down . if her average speed along the whole journey is 3.5 kilometers per hour , what was her average speed ( in kilometers per hour ) while climbing to the top ? | "let the distance to the top be x , so the total distance traveled by natasha is 2 x . the total time is 4 + 2 = 6 hours the average speed = total distance / total time taken = 2 x / 6 = x / 3 the average speed of the complete journey is 3.5 km / hour x / 3 = 3.5 x = 10.5 km the average speed while climbing = distance ... | a = 4 + 2
b = a * 3
c = b / 2
d = c / 4
|
a ) 3 , b ) 16 , c ) 75 , d ) 24 , e ) 26 | e | subtract(add(const_100, const_1), subtract(add(add(add(add(divide(const_100, const_2), const_1), add(divide(subtract(const_100, const_1), const_3), const_1)), add(divide(const_100, 5), const_1)), add(divide(subtract(const_100, const_10), multiply(multiply(3, 5), 2)), const_1)), add(add(add(divide(subtract(const_100, mu... | how many positive integers d between 200 and 300 ( both inclusive ) are not divisible by 2 , 3 or 5 ? | 1 ) i figured there are 101 integers ( 300 - 200 + 1 = 101 ) . since the set begins with an even and ends with an even , there are 51 evens . 2 ) question says integers are not divisible by 2 , leaving all of the odds ( 101 - 51 = 50 integers ) . 3 ) question says integers are not divisible by 5 , removing all the inte... | a = 100 + 1
b = 100 / 2
c = b + 1
d = 100 - 1
e = d / 3
f = e + 1
g = c + f
h = 100 / 5
i = h + 1
j = g + i
k = 100 - 10
l = 3 * 5
m = l * 2
n = k / m
o = n + 1
p = j + o
q = 3 * 2
r = 100 - q
s = 3 * 2
t = r / s
u = t + 1
v = 100 - 10
w = 3 * 5
x = v / w
y = x + 1
z = u + y
A = 100 / 10
B = A + 1
C = z + B... |
a ) 63 , b ) 64.28 , c ) 65 , d ) 66 , e ) 68 | b | divide(const_100, add(add(add(divide(const_1, multiply(3, 3)), divide(const_1, multiply(3, 3))), const_1), const_0_33)) | in a certain flower shop , which stocks 4 types of flowers , there are 1 / 3 as many violets as carnations , and 1 / 3 as many tulips as violets . if there are equal numbers of roses and tulips , what percent of the flowers in the shop are carnations ? | given : - violets - c / 3 carnations - c tulip - c / 9 rose - c / 9 total flowers in terms of c = c / 3 + c + c / 9 + c / 9 = 14 c / 9 percentage of carnations = c / 14 c / 9 * 100 = 64.28 % answer b | a = 3 * 3
b = 1 / a
c = 3 * 3
d = 1 / c
e = b + d
f = e + 1
g = f + const_0_33
h = 100 / g
|
a ) 45 % , b ) 500 / 11 , c ) 42.22 % , d ) 55 % , e ) 35 % | c | multiply(divide(subtract(90, add(multiply(4, 6), multiply(6, 4))), 90), const_100) | a batsman scored 90 runs which included 4 boundaries and 6 sixes . what percent of his total score did he make by running between the wickets ? | "explanation : number of runs made by running , = > 90 − ( 4 × 4 + 6 × 6 ) . = > 90 − 52 = > 38 hence , the required percentage is : - = > 38 / 90 * 100 = > 42.22 % answer : c" | a = 4 * 6
b = 6 * 4
c = a + b
d = 90 - c
e = d / 90
f = e * 100
|
a ) 11 : 00 , b ) 11 : 30 , c ) 12 : 00 , d ) 12 : 30 , e ) 1 : 00 | c | divide(add(70, multiply(70, divide(const_1, const_2))), subtract(84, 70)) | a train sets off at 9 : 00 am at the speed of 70 km / h . another train starts at 9 : 30 am in the same direction at the rate of 84 km / h . at what time will the second train catch the first train ? | "in thirty minutes the first train travels 35 km . the second train catches the first train at a rate of 84 km / h - 70 km / h = 14 km / h . the second train will catch the first train in 35 / 14 = 2.5 hours , so at 12 : 00 noon . the answer is c ." | a = 1 / 2
b = 70 * a
c = 70 + b
d = 84 - 70
e = c / d
|
a ) 2 / 35 , b ) 2 / 30 , c ) 2 / 63 , d ) 2 / 29 , e ) 2 / 10 | a | multiply(divide(1, 5), divide(2, 7)) | two brother x and y appeared for an exam . the probability of selection of x is 1 / 5 and that of b is 2 / 7 . find the probability that both of them are selected . | "explanation : let a be the event that x is selected and b is the event that y is selected . p ( a ) = 1 / 5 , p ( b ) = 2 / 7 . let c be the event that both are selected . p ( c ) = p ( a ) ã — p ( b ) as a and b are independent events : = ( 1 / 5 ) ã — ( 2 / 7 ) = 2 / 35 answer : a ) 2 / 35" | a = 1 / 5
b = 2 / 7
c = a * b
|
a ) 6 : 5 , b ) 6 : 9 , c ) 6 : 2 , d ) 2 : 2 , e ) 2 : 8 | a | divide(divide(1, 30), power(divide(1, 2), 2)) | the volumes of two cones are in the ratio 1 : 30 and the radii of the cones are in the ratio of 1 : 2 . what is the length of the wire ? | "the volume of the cone = ( 1 / 3 ) π r 2 h only radius ( r ) and height ( h ) are varying . hence , ( 1 / 3 ) π may be ignored . v 1 / v 2 = r 1 ^ 2 . h 1 / r 2 ^ 2 . h 2 = > 1 / 30 = ( 1 ) ^ 2 h 1 / ( 2 ) ^ 2 h 2 = > h 1 / h 2 = 6 / 5 i . e . h 1 : h 2 = 6 : 5 answer : a" | a = 1 / 30
b = 1 / 2
c = b ** 2
d = a / c
|
a ) 87 , b ) 86 , c ) 28 , d ) 76 , e ) 80 | b | subtract(multiply(add(10, const_1), add(4, 42)), multiply(10, 42)) | the average of runs of a cricket player of 10 innings was 42 . how many runs must he make in his next innings so as to increase his average of runs by 4 ? | "average after 11 innings = 46 required number of runs = ( 46 * 11 ) - ( 42 * 10 ) = 506 - 420 = 86 . answer : b" | a = 10 + 1
b = 4 + 42
c = a * b
d = 10 * 42
e = c - d
|
a ) 27 % , b ) 21 % , c ) 19 % , d ) 18 % , e ) 16 % | c | add(subtract(subtract(const_100, 40), multiply(divide(3, 4), subtract(const_100, 40))), subtract(40, multiply(divide(9, 10), 40))) | in a survey of parents , exactly 9 / 10 of the mothers and 3 / 4 of the fathers held full - time jobs . if 40 percent of the parents surveyed were women , what percent of the parents did not hold full - time jobs ? | "fathers without full - time jobs are 1 / 4 * 3 / 5 = 3 / 20 of all the parents surveyed . mothers without full - time jobs are 1 / 10 * 2 / 5 = 2 / 50 of all the parents surveyed . the percent of parents without full - time jobs is 3 / 20 + 2 / 50 = 19 / 100 = 19 % the answer is c ." | a = 100 - 40
b = 3 / 4
c = 100 - 40
d = b * c
e = a - d
f = 9 / 10
g = f * 40
h = 40 - g
i = e + h
|
a ) 2 : 9 , b ) 2 : 7 , c ) 1 : 2 , d ) 1 : 4 , e ) 1 : 3 | c | divide(subtract(4, 2), subtract(8, 4)) | cereal a is 8 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 4 % sugar , what should be the ratio of cereal a to cereal b , by weight ? | "( 8 / 100 ) a + ( 2 / 100 ) b = ( 4 / 100 ) ( a + b ) 4 a = 2 b = > a / b = 1 / 2 answer is c ." | a = 4 - 2
b = 8 - 4
c = a / b
|
a ) 30 , b ) 50 , c ) 70 , d ) 80 , e ) 90 | a | subtract(divide(multiply(divide(120, 2), 5), 2), 120) | the ratio of boarders to day students at a school was originally 2 to 5 . however , after a number of new boarders join the initial 120 boarders , the ratio changed to 1 to 2 . if no boarders became day students and vice versa , and no students left the school , how many new boarders joined the school ? | "let x be the number of new boarders . the ratio changed from 2 : 5 = 4 : 10 up to 1 : 2 = 5 : 10 . 120 / ( 120 + x ) = 4 / 5 x = 30 the answer is a ." | a = 120 / 2
b = a * 5
c = b / 2
d = c - 120
|
a ) 1 / 4 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3 | e | divide(divide(subtract(2, multiply(divide(0.375, 5), 20)), subtract(divide(1.375, 10), divide(0.375, 5))), subtract(20, divide(subtract(2, multiply(divide(0.375, 5), 20)), subtract(divide(1.375, 10), divide(0.375, 5))))) | a 20 kg metal bar made of alloy of tin and silver lost 2 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ? | "the bar lost certain percentage of its weight . we do n ' t know how much tin was lost and how much silver was lost but in all 2 kg was lost with is 10 % of its overall weight . tin loses 1.375 kg in 10 kg so 13.75 % of its weight when it is put in water . silver loses . 375 kg in 5 kg so . 375 / 5 * 100 = 7.5 % of it... | a = 0 / 375
b = a * 20
c = 2 - b
d = 1 / 375
e = 0 / 375
f = d - e
g = c / f
h = 0 / 375
i = h * 20
j = 2 - i
k = 1 / 375
l = 0 / 375
m = k - l
n = j / m
o = 20 - n
p = g / o
|
a ) 2200 , b ) 5500 , c ) 3300 , d ) 3771.4 , e ) 4400 | d | multiply(circumface(10), 12) | the radius of a cylinder is 10 m , height 12 m . the volume of the cylinder is : | "cylinder volume = ï € r ( power 2 ) h = 22 / 7 ã — 10 ã — 10 ã — 12 = 3771.4 m ( power 3 ) answer is d ." | a = circumface * (
|
a ) $ 6980 , b ) $ 7070 , c ) $ 7120 , d ) $ 7260 , e ) $ 7340 | d | multiply(6000, power(add(const_1, divide(10, const_100)), const_2)) | what amount does an investor receive if the investor invests $ 6000 at 10 % p . a . compound interest for two years , compounding done annually ? | a = ( 1 + r / 100 ) ^ n * p ( 1.1 ) ^ 2 * 6000 = 1.21 * 6000 = 7260 the answer is d . | a = 10 / 100
b = 1 + a
c = b ** 2
d = 6000 * c
|
a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15 | e | multiply(divide(multiply(multiply(50, divide(50, 40)), const_2), 50), const_2) | the racing magic takes 50 seconds to circle the racing track once . the charging bull makes 40 rounds of the track in an hour . if they left the starting point together , how many minutes will it take for them to meet at the starting point for the second time ? | "time taken by racing magic to make one circle = 50 seconds time taken bycharging bullto make one circle = 60 mins / 40 = 1.5 mins = 90 seconds lcm of 90 and 50 seconds = 450 seconds time taken for them to meet at the starting point for the second time = 450 * 2 = 900 seconds = 15 mins answer e" | a = 50 / 40
b = 50 * a
c = b * 2
d = c / 50
e = d * 2
|
a ) 2 hours , b ) 4 hours , c ) 3 hours , d ) 5 hours , e ) 6 hours | e | add(add(2, 2), 2) | three pipes , a , b , & c are attached to a tank . a & b can fill it in 20 & 30 minutes respectively while c can empty it in 15 minutes . if a , b & c are kept open successively for 2 minute each , how soon will the tank be filled ? | "in three minute 1 / 20 + 1 / 30 - 1 / 15 = 1 / 60 part is filled 6 min - - - - - - - - 1 / 60 parts x min - - - - - - - - - 1 part ( full ) x = 360 min = 6 hours answer : e" | a = 2 + 2
b = a + 2
|
a ) 38 sec , b ) 35 sec , c ) 44 sec , d ) 40 sec , e ) 56 | e | multiply(divide(add(divide(340, const_1000), divide(360, const_1000)), 45), const_3600) | a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 340 m long ? | "speed = 45 km / hr = 45 ã — ( 5 / 18 ) m / s = 150 / 12 = 50 / 4 = 25 / 2 m / s total distance = length of the train + length of the platform = 360 + 340 = 700 meter time taken to cross the platform = 700 / ( 25 / 2 ) = 700 ã — 2 / 25 = 56 seconds answer : e" | a = 340 / 1000
b = 360 / 1000
c = a + b
d = c / 45
e = d * 3600
|
a ) 15 , b ) 20 , c ) 18 , d ) 16.5 , e ) 25 | d | multiply(divide(subtract(add(25, add(const_0_25, const_0_25)), 5), add(const_100, subtract(add(25, add(const_0_25, const_0_25)), 5))), const_100) | in a certificate by mistake a candidate gave his height as 25 % more than actual height . in the interview panel , he clarified that his height was 5 feet 6 nches . find the % correction made by the candidate from his stated height to his actual height ? | his height was = 5 feet 6 inch = 6 + 60 = 66 inch . required % correction = 66 * ( 1.25 - 1 ) = 16.5 d | a = const_0_25 + const_0_25
b = 25 + a
c = b - 5
d = const_0_25 + const_0_25
e = 25 + d
f = e - 5
g = 100 + f
h = c / g
i = h * 100
|
a ) 1 / 25 , b ) 12 / 49 , c ) 1 / 4 , d ) 24 / 49 , e ) 1 / 2 | d | multiply(multiply(divide(subtract(divide(50, 2), const_1), subtract(50, const_1)), divide(divide(50, 2), 50)), 2) | there are 2 available positions and 50 candidates , one half of whom are democrats and another half are republicans . if it was decided that the positions would be filled at random , then what is the probability q that the both positions will be taken by members of just one party ? | "q probability of one party having both spots : ( 1 / 2 ) * ( 24 / 49 ) = 12 / 49 ( 1 / 2 ) or ( 25 / 50 ) because it does not matter which party or which person gets the first spot . ( 24 / 49 ) because after one person from a particular party is chosen , there are 24 members of the same party left out of 49 total can... | a = 50 / 2
b = a - 1
c = 50 - 1
d = b / c
e = 50 / 2
f = e / 50
g = d * f
h = g * 2
|
a ) 3 , b ) 9 , c ) 15 , d ) 25 , e ) 63 | a | add(const_3, const_4) | what is the smallest positive integer k such that the product of 3675 x k is a perfect square ? | "a perfect square , is just an integer that can be written as the square of some other integer . for example 16 = 4 ^ 2 , is a perfect square . now , 3675 = 5 ^ 2 * 7 ^ 2 * 3 , so if k = 3 then 3675 k = ( 5 * 7 * 3 ) ^ 2 , which is a perfect square ( basically the least positive value of k must complete only the power ... | a = 3 + 4
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a ) 144 mins , b ) 140 mins , c ) 136 mins , d ) 156 minw , e ) none of these | d | multiply(add(const_1, const_4), 39) | one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 39 minutes , then the slower pipe alone will be able to fill the tank in | "explanation : let the slower pipe alone fill the tank in x minutes then faster will fill in x / 3 minutes . part filled by slower pipe in 1 minute = 1 / x part filled by faster pipe in 1 minute = 3 / x part filled by both in 1 minute = 1 / x + 3 / x = 1 / 39 = > 4 / x = 1 / 39 x = 39 ∗ 4 = 156 mins option d" | a = 1 + 4
b = a * 39
|
a ) 22 , b ) 38 , c ) 35 , d ) 29 , e ) 18 | c | multiply(7, add(const_4, const_1)) | there are 7 non - collinear points . how many triangles can be drawn by joining these points ? | explanation : a triangle is formed by joining any three non - collinear points in pairs . there are 7 non - collinear points the number of triangles formed = \ inline { \ color { black } 7 c _ { 3 } } = 35 answer : c ) 35 | a = 4 + 1
b = 7 * a
|
a ) 7.6 % , b ) 7.7 % , c ) 24.82 % , d ) 13.6 % , e ) 27.82 % | c | multiply(const_100, divide(subtract(multiply(58, subtract(const_100, 1)), multiply(46, const_100)), multiply(46, const_100))) | a man buys 58 pens at marked price of 46 pens from a whole seller . if he sells these pens giving a discount of 1 % , what is the profit percent ? | "explanation : let marked price be re . 1 each c . p . of 58 pens = rs . 46 s . p . of 58 pens = 99 % of rs . 58 = rs . 57.42 profit % = ( profit / c . p . ) x 100 profit % = ( 11.42 / 46 ) x 100 = 24.82 % answer : c" | a = 100 - 1
b = 58 * a
c = 46 * 100
d = b - c
e = 46 * 100
f = d / e
g = 100 * f
|
a ) 187 , b ) 169 , c ) 172 , d ) 178 , e ) 171 | e | subtract(subtract(200, divide(multiply(200, 10), const_100)), divide(multiply(subtract(200, divide(multiply(200, 10), const_100)), 5), const_100)) | the sale price sarees listed for rs . 200 after successive discount is 10 % and 5 % is ? | "200 * ( 90 / 100 ) * ( 95 / 100 ) = 171 answer : e" | a = 200 * 10
b = a / 100
c = 200 - b
d = 200 * 10
e = d / 100
f = 200 - e
g = f * 5
h = g / 100
i = c - h
|
a ) $ 8 , b ) $ 9 , c ) $ 27 , d ) $ 32 , e ) $ 36 | d | multiply(divide(68, add(add(const_1, divide(const_4, const_3)), divide(const_1, const_2))), divide(const_4, const_3)) | if josh , doug , and brad have a total of $ 68 between them , and josh has two times as much money as brad but only 3 - fourths as much as doug , how much money does doug have ? | josh + doug + brad = 68 ; josh = 2 brad , josh = 3 / 4 doug josh + 1 / 2 josh + 4 / 3 josh = 68 ( substituted the given values ) josh = 24 . 24 = 3 / 4 doug = > doug = 32 answer is d . | a = 4 / 3
b = 1 + a
c = 1 / 2
d = b + c
e = 68 / d
f = 4 / 3
g = e * f
|
a ) 715 , b ) 716 , c ) 718 , d ) 720 , e ) 722 | d | divide(multiply(120, 144), subtract(144, 120)) | the bankers discount of a certain sum of money is rs . 144 and the true discount on the same sum for the same time is rs . 120 . the sum due is : | sum = ( b . d * t . d ) / ( b . d - t . d ) ( 144 * 120 ) / 144 - 120 ; 720 answer : d | a = 120 * 144
b = 144 - 120
c = a / b
|
a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 6 | c | add(divide(subtract(52, divide(subtract(divide(add(14, 2), 2), 2), 2)), add(subtract(divide(add(14, 2), 2), 2), divide(add(14, 2), 2))), divide(const_1, 2)) | tammy climbed a mountain in two days . she spent a total of 14 hours climbing the mountain . on the second day , she walked at an average speed that was half a kilometer per hour faster , but 2 hours less than what she walked on the first day . if the total distance she climbed during the two days is 52 kilometers , ho... | "ans : c total time = 14 hrs let time traveled during 1 st day = x let time traveled during 2 nd day = x - 2 total time = 14 x + x - 2 = 14 x = 8 speed * time = distance s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 solving s = 4.5 now speed for 2 nd day is 0.5 less than the 1 st day which is 4.5 thus speed for 2 nd day = 4 its s... | a = 14 + 2
b = a / 2
c = b - 2
d = c / 2
e = 52 - d
f = 14 + 2
g = f / 2
h = g - 2
i = 14 + 2
j = i / 2
k = h + j
l = e / k
m = 1 / 2
n = l + m
|
a ) 22 , b ) 12 , c ) 67 , d ) 20 , e ) 81 | d | divide(add(120, 280), multiply(add(42, 30), const_0_2778)) | two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ? | "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 120 + 280 = 400 m . the time required = d / s = 400 / 20 = 20 sec . answer : d" | a = 120 + 280
b = 42 + 30
c = b * const_0_2778
d = a / c
|
a ) 57 minutes , b ) 14 minutes , c ) 39 minutes , d ) 40 minutes 20 seconds , e ) none of these | a | multiply(divide(950, subtract(add(40, 30), 20)), const_3) | pipe a fills a tank of capacity 950 liters at the rate of 40 liters a minute . another pipe b fills the same tank at the rate of 30 liters a minute . a pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute . if pipe a is kept open for a minute and then closed and pipe b is open for a minute a... | in one cycle they fill 40 + 30 - 20 = 50 liters 950 = 50 * n = > n = 19 here n = number of cycles . total time = 19 * 3 = 57 as in one cycle there are 3 minutes . thus 57 minutes answer : a | a = 40 + 30
b = a - 20
c = 950 / b
d = c * 3
|
a ) 9 % , b ) 10 % , c ) 11 % , d ) 14 % , e ) 90 % | d | divide(multiply(12, const_100), subtract(const_100, 12)) | during a sale , the price of a pair of shoes is marked down 12 % from the regular price . after the sale ends , the price goes back to the original price . what is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes ? | "assume the price = 100 price during sale = 88 price after sale = 100 percent increase = 12 / 88 * 100 = 14 % approx . correct option : d" | a = 12 * 100
b = 100 - 12
c = a / b
|
a ) 12 , b ) 14 , c ) 13 , d ) 15 , e ) 16 | b | add(multiply(5, 2), 4) | if p / q = 5 / 4 , then 2 p + q = ? | "let p = 5 , q = 4 then 2 * 5 + 4 = 14 so 2 p + q = 14 . answer : b" | a = 5 * 2
b = a + 4
|
a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12 | c | divide(0.06, divide(0.75, const_100)) | find the missing figures : 0.75 % of ? = 0.06 | "let 0.75 % of x = 0.06 . then , 0.75 * x / 100 = 0.06 x = [ ( 0.06 * 100 ) / 0.75 ] = 8 . answer is c ." | a = 0 / 75
b = 0 / 6
|
a ) 1 : 25 , b ) 2 : 25 , c ) 3 : 25 , d ) 4 : 25 , e ) 5 : 25 | c | divide(multiply(divide(30, const_100), divide(20, const_100)), divide(50, const_100)) | m is 30 % of q . q is 20 % of p . n is 50 % of p . find m : n ratio | let p be 100 n = 50 % of 100 ( p = 100 ) = 50 q = 20 % of 100 ( p = 100 ) = 20 m = 30 % of 20 ( q = 20 ) = 6 m : n = 6 : 50 m : n = 3 : 25 answer : c | a = 30 / 100
b = 20 / 100
c = a * b
d = 50 / 100
e = c / d
|
a ) s . 375 , b ) s . 425 , c ) s . 625 , d ) s . 800 , e ) s . 850 | c | multiply(multiply(subtract(inverse(3), add(inverse(8), inverse(6))), 5000), 3) | a alone can do a piece of work in 6 days and b alone in 8 days . a and b undertook to do it for rs . 5000 . with the help of c , they completed the work in 3 days . how much is to be paid to c ? | "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 3 - 7 / 24 = 1 / 24 a ' s wages : b ' s wages : c ' s wages = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 c ' s share ( for 3 days ) = rs . ( 3 * 1 / 24 * 5000 ) = rs . 625 answer = c" | a = 1/(3)
b = 1/(8)
c = 1/(6)
d = b + c
e = a - d
f = e * 5000
g = f * 3
|
a ) 1 / 190 , b ) 1 / 17 , c ) 1 / 19 , d ) 1 / 10 , e ) 1 / 9 | b | divide(const_1, subtract(18, const_1)) | a box contains 9 pairs of shoes ( 18 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ? | "the problem with your solution is that we do n ' t choose 1 shoe from 18 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 17 ( as after taking one at random there are 17 shoes left and only one is the pair of the fir... | a = 18 - 1
b = 1 / a
|
a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) x = 8 | e | divide(240, 30) | a marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each . there can be no less than 8 musicians per row and no more than 30 musicians per row . how many different rectangular formations x are possible ? | the combinations could be { ( 1,240 ) , ( 2,120 ) , ( 3,80 ) , ( 4,60 ) , ( 5,48 ) , ( 6,40 ) , ( 8,30 ) , ( 10,24 ) , ( 12,20 ) , ) 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) , ( 40,6 ) , ( 48,5 ) , ( 60,4 ) , ( 80,3 ) , ( 120,2 ) , ( 240,1 ) } of these we are told 8 < = t < = 30 so we can remove these pai... | a = 240 / 30
|
a ) 420 , b ) 840 , c ) 1,260 , d ) 2,520 , e ) 5,040 | a | lcm(1, 7) | what is the lowest positive integer that is divisible by each of the integers 1 through 7 , inclusive ? | "the integer should be divisible by : 2 , 3 , 4 ( = 2 ^ 2 ) , 5 , 6 ( = 2 * 3 ) , and 7 . the least common multiple of these integers is lcm = 2 ^ 2 * 3 * 5 * 7 = 420 . answer : a ." | a = math.lcm(1, 7)
|
a ) 2277 , b ) 5000 , c ) 1000 , d ) 2651 , e ) 1971 | b | divide(5225, multiply(add(const_1, divide(10, const_100)), subtract(const_1, divide(5, const_100)))) | the salary of a typist was at first raised by 10 % and then the same was reduced by 5 % . if he presently draws rs . 5225 . what was his original salary ? | "x * ( 110 / 100 ) * ( 95 / 100 ) = 5225 x * ( 11 / 10 ) * ( 1 / 100 ) = 55 x = 5000 answer : b" | a = 10 / 100
b = 1 + a
c = 5 / 100
d = 1 - c
e = b * d
f = 5225 / e
|
a ) $ 16.32 , b ) $ 18.00 , c ) $ 10.125 , d ) $ 24.48 , e ) $ 28.80 | c | multiply(divide(subtract(const_100, 10), const_100), multiply(0.15, 75)) | the regular price per can of a certain brand of soda is $ 0.15 . if the regular price per can is discounted 10 percent when the soda is purchased in 24 - can cases , what is the price of 75 cans of this brand of soda purchased in 24 - can cases ? | the discounted price of one can of soda is ( 0.9 ) ( $ 0.15 ) , or $ 0.135 therefore , the price of 75 cans of soda at the discounted price would be ( 75 ) ( $ 0.135 ) = 10.125 answer : c . | a = 100 - 10
b = a / 100
c = 0 * 15
d = b * c
|
a ) 888 , b ) 333 , c ) 555 , d ) 1221 , e ) 889 | d | divide(add(multiply(multiply(666, 666), 666), multiply(multiply(555, 555), 555)), subtract(add(multiply(666, 666), multiply(555, 555)), multiply(666, 555))) | solve : - 666 x 666 x 666 + 555 x 555 x 555 = ? ( 666 x 666 - 666 x 555 + 555 x 555 ) | given exp . = ( a 3 + b 3 ) = ( a + b ) = ( 666 + 555 ) = 1221 ( a 2 - ab + b 2 ) answer d | a = 666 * 666
b = a * 666
c = 555 * 555
d = c * 555
e = b + d
f = 666 * 666
g = 555 * 555
h = f + g
i = 666 * 555
j = h - i
k = e / j
|
a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12 | a | divide(11.52, subtract(96.12, floor(96.12))) | when positive integer x is divided by positive integer y , the remainder is 11.52 . if x / y = 96.12 , what is the value of y ? | "when positive integer x is divided by positive integer y , the remainder is 11.52 - - > x = qy + 11.52 ; x / y = 96.12 - - > x = 96 y + 0.12 y ( so q above equals to 96 ) ; 0.12 y = 11.52 - - > y = 96 . answer : a ." | a = math.floor(96, 12)
b = 96 - 12
c = 11 / 52
|
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