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 ) 250 , b ) 300 , c ) 350 , d ) 400 , e ) 450 | b | multiply(divide(multiply(40, const_1000), const_3600), 27) | a train running at the speed of 40 km / hr crosses a pole in 27 seconds . what is the length of the train ? | "speed = ( 40 * 5 / 18 ) m / sec = ( 100 / 9 ) m / sec length of the train = ( speed x time ) = ( 100 / 9 * 29 ) m = 300 m . answer : b" | a = 40 * 1000
b = a / 3600
c = b * 27
|
a ) 27 , b ) 37 , c ) 932 , d ) 12 , e ) 91 | a | add(divide(divide(multiply(floor(add(divide(subtract(multiply(const_10, const_1000), const_1), 89), const_1)), 89), const_4), const_100), const_2) | find the least number of 5 digits , which is exactly divisible by 89 . | answer : a | a = 10 * 1000
b = a - 1
c = b / 89
d = c + 1
e = math.floor(d)
f = e * 89
g = f / 4
h = g / 100
i = h + 2
|
a ) 1217 , b ) 1219 , c ) 1210 , d ) 1212 , e ) 858 | e | multiply(subtract(power(23, const_2), power(const_10, const_2)), divide(add(multiply(16, const_2), const_2), add(const_4, const_3))) | a rope of which a calf is tied is increased from 16 m to 23 m , how much additional grassy ground shall it graze ? | "π ( 232 – 162 ) = 858 answer : e" | a = 23 ** 2
b = 10 ** 2
c = a - b
d = 16 * 2
e = d + 2
f = 4 + 3
g = e / f
h = c * g
|
a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 10 | e | add(multiply(power(divide(128, multiply(1, multiply(1, const_2))), inverse(const_3)), multiply(1, const_2)), multiply(1, const_2)) | there is a rectangular prism made of 1 in cubes that has been covered in tin foil . there are exactly 128 cubes that are not touching any tin foil on any of their sides . if the width of the figure created by these 128 cubes is twice the length and twice the height , what is the measure m in inches of the width of the foil covered prism ? | "if the width is w , then length and height would be w / 2 . so , w * w / 2 * w / 2 = 128 = > w ^ 3 = ( 2 ^ 3 ) * 64 = ( 2 ^ 3 ) * ( 4 ^ 3 ) = > w = 2 * 4 m = 8 in . along the width of the cuboid , 8 cubes do n ' t touch the tin foil . so the actual width will be non - touching cubes + touching cubes = 8 + 2 = 10 ans e ." | a = 1 * 2
b = 1 * a
c = 128 / b
d = 1/(3)
e = c ** d
f = 1 * 2
g = e * f
h = 1 * 2
i = g + h
|
a ) 96 , b ) 112 , c ) 158 , d ) 192 , e ) 235 | b | add(add(add(add(23, const_2), add(add(23, const_2), const_2)), add(add(add(23, const_2), const_2), const_2)), 31) | the sum of all consecutive odd integers from − 23 to 31 , inclusive , is | the sum of the odd numbers from - 23 to + 23 is 0 . let ' s add the remaining numbers . 25 + 27 + 29 + 31 = 112 the answer is b . | a = 23 + 2
b = 23 + 2
c = b + 2
d = a + c
e = 23 + 2
f = e + 2
g = f + 2
h = d + g
i = h + 31
|
a ) 75 , b ) 37 , c ) 26 , d ) 97 , e ) 27 | a | divide(add(add(add(add(76, 65), 82), 67), 85), add(const_2, const_3)) | david obtained 76 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology what are his average marks ? | "average = ( 76 + 65 + 82 + 67 + 85 ) / 5 = 375 / 5 = 75 . answer : a" | a = 76 + 65
b = a + 82
c = b + 67
d = c + 85
e = 2 + 3
f = d / e
|
a ) 77 sec , b ) 92 sec , c ) 67 sec , d ) 16 sec , e ) 76 sec | b | subtract(divide(multiply(const_1, const_1000), divide(80, 8)), 8) | in a kilometer race , a beats b by 80 meters or 8 seconds . what time does a take to complete the race ? | time taken by b run 1000 meters = ( 1000 * 8 ) / 80 = 100 sec . time taken by a = 100 - 8 = 92 sec . answer : b | a = 1 * 1000
b = 80 / 8
c = a / b
d = c - 8
|
a ) 1677 , b ) 1683 , c ) 2523 , d ) 3363 , e ) none of these | b | multiply(lcm(lcm(lcm(5, 6), 7), 8), const_2) | the least number which when divided by 5 , 6 , 7 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder , is | explanation : l . c . m of 5 , 6 , 7 , 8 = 840 therefore required number is of the form 840 k + 3 . least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 therefore required number = ( 840 x 2 + 3 ) = 1683 . answer : b | a = math.lcm(5, 6)
b = math.lcm(a, 7)
c = math.lcm(b, 8)
d = c * 2
|
a ) 100 m , b ) 120 m , c ) 190 m , d ) 150 m , e ) none of these | c | subtract(240, multiply(divide(3, const_60), const_1000)) | a policeman noticed a criminal from a distance of 240 km . the criminal starts running and the policeman chases him . the criminal and the policeman run at the rate of 8 km and 9 km per hour respectively . what is the distance between them after 3 minutes ? | "explanation : solution : relative speed = ( 9 - 8 ) = 1 km / hr . distance covered in 3 minutes = ( 1 * 3 / 60 ) km = 1 / 20 km = 50 m . . ' . distance between the criminal and policeman = ( 240 - 50 ) m = 190 m . answer : c" | a = 3 / const_60
b = a * 1000
c = 240 - b
|
a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | e | subtract(multiply(add(multiply(const_4, const_10), const_2), 23), 1120) | what least number must be added to 1120 , so that the sum is completely divisible by 23 ? | "49 * 23 = 1127 1127 - 1120 = 7 answer : e" | a = 4 * 10
b = a + 2
c = b * 23
d = c - 1120
|
a ) 16 , b ) 24 , c ) 36 , d ) 48 , e ) 49 | b | subtract(multiply(24, 2), 24) | 24 men can complete a work in 16 days . 32 women can complete the same work in 24 days . 16 men and 16 women started working and worked for 12 days . how many more men are to be added to complete the remaining work in 2 days ? | explanation : 1 man ’ s 1 day work = 1 / 384 1 woman ’ s 1 day work = 1 / 768 work done in 12 days = 12 ( 16 / 384 + 16 / 768 ) = 12 * 3 / 48 = 3 / 4 remaining work = 1 / 4 ( 16 men + 16 women ) ’ s 2 day work = 2 ( 16 / 384 + 16 / 768 ) = 1 / 8 remaining work = 1 / 4 - 1 / 8 = 1 / 8 1 / 384 work is done in 1 day by 1 man 1 / 8 work will be done in 2 days by 384 x 1 / 8 x 1 / 2 = 24 men answer : option b | a = 24 * 2
b = a - 24
|
a ) 5 ⁄ 7 , b ) 7 ⁄ 10 , c ) 1 ⁄ 3 , d ) 7 ⁄ 30 , e ) 5 ⁄ 6 | e | subtract(const_1, divide(3, 4)) | at an elementary school , 60 % of the faculty members are women and 60 % of the faculty members are married . if 3 / 4 of the men are single , what fraction of the women are married ? | "2 x 2 table works perfect : - - - - - - - - - - - - - - - - - - - - m - - - - - - w - - - - - - - - total marrried - - - - - - - - - 10 - - - - - 50 - - - - - - - - - 60 not married - - - - - 30 - - - - - 10 - - - - - - - - - 40 total - - - - - - - - - - - - - 40 - - - - - 60 - - - - - - - - 100 need married woman / total woman , so 50 / 60 = 5 / 6 e" | a = 3 / 4
b = 1 - a
|
a ) $ 0.94 , b ) $ 0.96 , c ) $ 0.98 , d ) $ 1.00 , e ) $ 1.20 | b | multiply(add(const_1, divide(8, const_100)), divide(0.80, divide(subtract(const_100, 10), const_100))) | the manager of a produce market purchased a quantity of tomatoes for $ 0.80 per pound . due to improper handling , 10 percent of the tomatoes , by weight , were ruined and discarded . at what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 8 percent of the cost of the tomatoes . | "assume the manager bought 100 tomatoes . cost price = 80 given : 10 % are damaged - - > available tomatoes to sell = 90 90 * x - 80 = 0.08 * 80 90 x - 80 = 6.4 90 x = 86.64 x = 86.64 / 90 = 87 / 90 ( approx ) = 29 / 30 = 0.966 x is slightly under 0.9666 = 0.96 answer : b" | a = 8 / 100
b = 1 + a
c = 100 - 10
d = c / 100
e = 0 / 80
f = b * e
|
a ) 60 , b ) 50 , c ) 40 , d ) 100 , e ) 25 | a | divide(multiply(10, 60), subtract(60, 50)) | a group of men decided to do a work in 50 days , but 10 of them became absent . if the rest of the group did the work in 60 days , find the original number of men ? | "original number of men = 10 * 60 / ( 60 - 50 ) = 60 answer is a" | a = 10 * 60
b = 60 - 50
c = a / b
|
a ) 120 , b ) 200 , c ) 180 , d ) 300 , e ) 140 | b | divide(multiply(add(divide(multiply(50, 60), const_100), 30), const_100), 30) | 30 % of a number is more than 60 % of 50 by 30 . find the number ? | "( 30 / 100 ) * x – ( 60 / 100 ) * 50 = 30 2 / 7 x = 60 x = 200 answer : b" | a = 50 * 60
b = a / 100
c = b + 30
d = c * 100
e = d / 30
|
a ) 0 % , b ) 10 % , c ) 20 % , d ) 30 % , e ) 40 % | a | divide(add(8, add(10, const_3)), const_2) | operation # is defined as adding a randomly selected two digit multiple of 8 to a randomly selected two digit prime number and reducing the result by half . if operation # is repeated 10 times , what is the probability that it will yield at least two integers ? | any multiple of 8 is even . any two - digit prime number is odd . ( even + odd ) / 2 is not an integer . thus # does not yield an integer at all . therefore p = 0 . answer : a . | a = 10 + 3
b = 8 + a
c = b / 2
|
a ) 40 , b ) 85 , c ) 20 , d ) 60 , e ) 45 | c | divide(volume_rectangular_prism(sqrt(10), sqrt(10), 4), 10) | right triangle abc is the base of the prism in the figure above . if ab = ac = â ˆ š 10 and the height of the prism is 4 , what is the volume of the prism ? | "volume of prism = area of base * height = 1 / 2 * ( square root of 10 ) * ( square root of 10 ) * 4 = 20 answer : c" | a = math.sqrt(10)
b = math.sqrt(10)
c = volume_rectangular_prism / (
|
a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | d | divide(add(divide(54, 6), divide(6, 6)), const_2) | a woman swims downstream 54 km and upstream 6 km taking 6 hours each time , what is the speed of the woman in still water ? | "54 - - - 6 ds = 9 ? - - - - 1 6 - - - - 6 us = 1 ? - - - - 1 m = ? m = ( 9 + 1 ) / 2 = 5 answer : d" | a = 54 / 6
b = 6 / 6
c = a + b
d = c / 2
|
a ) 230 , b ) 240 , c ) 236 , d ) 256 , e ) 266 | d | add(lcm(lcm(7, 9), lcm(12, 18)), 4) | what is the least number which when divided by 7 , 9 , 12 and 18 leaves remainder 4 in each care ? | "explanation : lcm of 7 , 9 , 12 and 18 is 252 required number = 252 + 4 = 256 answer : option d" | a = math.lcm(7, 9)
b = math.lcm(12, 18)
c = math.lcm(a, b)
d = c + 4
|
a ) 1 , b ) 5 , c ) 7 , d ) 8 , e ) 9 | a | divide(7, 7) | how many points ( x , y ) lie on the line segment between ( 15 , 12 2 / 3 ) and ( 7 , 17 2 / 3 ) such that x and y are both integers ? | slope = ( 17 2 / 3 - 12 2 / 3 ) / ( 7 - 15 ) = - 5 / 8 y = mx + b = > 12 2 / 3 = - 15 * 5 / 8 + b = > b = 1 y = - 75 x / 8 + 22 only integer values work , and the only multiples of 8 between 7 and 15 for x value is 8 , thus 1 point . a | a = 7 / 7
|
a ) 105 kg , b ) 145 kg , c ) 165 kg , d ) 115 kg , e ) 100 kg | a | multiply(subtract(const_1, divide(25, const_100)), multiply(subtract(const_1, divide(20, const_100)), multiply(250, subtract(const_1, divide(30, const_100))))) | a statue is being carved by a sculptor . the original piece of marble weighed 250 kg . in the first week 30 per cent is cut away . in the second week 20 per cent of the remainder is cut away . in the third week the statue is completed when 25 percent of the remainder is cut away . what is the weight of the final statue ? | "a 105 kg = 250 ã — 0.7 ã — 0.8 ã — 0.75 ." | a = 25 / 100
b = 1 - a
c = 20 / 100
d = 1 - c
e = 30 / 100
f = 1 - e
g = 250 * f
h = d * g
i = b * h
|
a ) 0.004 % , b ) 0.04 % , c ) 0.40 % , d ) 4 % , e ) 40 % | d | multiply(divide(multiply(50, 0.008), 10), const_100) | a bowl was filled with 10 ounces of water , and 0.008 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ? | "total amount of water evaporated each day during a 50 - day period = . 008 * 50 = . 008 * 100 / 2 = . 8 / 2 = . 4 percent of the original amount of water evaporated during this period = ( . 4 / 10 ) * 100 % = 4 % answer d" | a = 50 * 0
b = a / 10
c = b * 100
|
a ) 278 , b ) 166 , c ) 151 , d ) 260 , e ) 109 | d | subtract(multiply(multiply(divide(72, const_3600), const_1000), 26), 260) | a goods train runs at the speed of 72 km / hr and crosses a 260 m long platform in 26 sec . what is the length of the goods train ? | speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 260 ) / 26 = 20 x = 260 m . answer : d | a = 72 / 3600
b = a * 1000
c = b * 26
d = c - 260
|
a ) 22 , b ) 56 , c ) 78 , d ) 112 , e ) 150 | e | divide(12, subtract(134.08, add(const_100, add(multiply(const_4, const_10), const_2)))) | when positive integer n is divided by positive integer j , the remainder is 12 . if n / j = 134.08 , what is value of j ? | "1 ) we know that decimal part of decimal quotient = { remainder / divisor } so 0.08 , the decimal part of the decimal quotient , must equal the remainder , 12 , divided by the divisor j . 0.08 = 12 / j 0.08 * j = 12 j = 12 / 0.08 = 1200 / 8 = 300 / 2 = 150 so j = 150 , answer = e ." | a = 4 * 10
b = a + 2
c = 100 + b
d = 134 - 8
e = 12 / d
|
a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 7 | b | add(divide(8, const_4), const_1) | q is a set of 8 distinct prime numbers . if the sum of the integers in q is even and the number x is a member of q , then what is the least value that x can be ? | 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 = 77 ( discard as sum is odd ) 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 = 98 ( sum is even ) least number = 3 b | a = 8 / 4
b = a + 1
|
a ) 320.40 $ , b ) 383.40 $ , c ) 420.40 $ , d ) 450.40 $ , e ) 473.40 $ | e | multiply(multiply(0.65, 58), 12) | in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 58 liters and they are all empty , how much money total will it cost to fuel all cars ? | "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 58 ) = 473.40 hence answer will be ( e )" | a = 0 * 65
b = a * 12
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a ) 4 / 7 , b ) 2 / 3 , c ) 3 / 5 , d ) 3 / 7 , e ) 1 / 2 | a | divide(const_4, add(0,0, const_10)) | in the xy - plane , a triangle has vertices ( 0,0 ) , ( 4,0 ) and ( 4,7 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ? | "the area of the right triangle is ( 1 / 2 ) * 4 * 7 = 14 . only the points ( a , b ) below the line y = x satisfy a - b > 0 . the part of the triangle which is below the line y = x has an area of ( 1 / 2 ) ( 4 ) ( 4 ) = 8 . p ( a - b > 0 ) = 8 / 14 = 4 / 7 the answer is a ." | a = 0 + 0
b = 4 / a
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a ) 68463812 , b ) 68463813 , c ) 68479345 , d ) 68463814 , e ) 68463814 | c | multiply(565945, power(add(const_4, const_1), const_4)) | ( 565945 x 121 ) = ? | 565945 * 121 = 68479345 ans c | a = 4 + 1
b = a ** 4
c = 565945 * b
|
a ) 3 gallons , b ) 4 gallons , c ) 5 gallons , d ) 10 gallons , e ) 12 gallons | d | divide(divide(multiply(20, 50), 50), const_2) | mixture a is 20 percent alcohol , and mixture b is 50 percent alcohol . if the two are poured together to create a 15 gallon mixture that contains 30 percent alcohol , approximately how many gallons of mixture a are in the mixture ? | let a = number of gallons on mixture a in 15 gallon mixture b = number of gallons on mixture b in 15 gallon mixture ( 20 / 100 ) a + ( 50 / 100 ) b = ( 30 / 100 ) ( a + b ) - - 1 a + b = 15 - - 2 on solving equations 1 and 2 , we get a = 10 b = 5 answer d 10 gallons | a = 20 * 50
b = a / 50
c = b / 2
|
a ) 6 and 5 , b ) 8 and 5 , c ) 9 and 5 , d ) 8 and 5 , e ) 3 and 5 | c | add(45, 14) | sum of two numbers prime to each other is 14 and their l . c . m . is 45 . what are the numbers ? | "as two numbers are prime , satisfies all but option c will make the product of numbers i . e 45 answer : c" | a = 45 + 14
|
a ) - 8 , b ) - 4 , c ) - 3 , d ) 1 , e ) 6 | a | divide(subtract(10, add(power(5, 2), multiply(3, 5))), 5) | if 5 is one solution of the equation x ^ 2 + 3 x + k = 10 , where k is a constant , what is the other solution ? | "the phrase “ 5 is one solution of the equation ” means that one value of x is 5 . thus , we first must plug 5 for x into the given equation to determine the value of k . so we have 5 ^ 2 + ( 3 ) ( 5 ) + k = 10 25 + 15 + k = 10 40 + k = 10 k = - 30 next we plug - 30 into the given equation for k and then solve for x . x ^ 2 + 3 x – 30 = 10 x ^ 2 + 3 x – 40 = 0 ( x + 8 ) ( x - 5 ) = 0 x = - 8 or x = 5 thus , - 8 is the other solution . answer a ." | a = 5 ** 2
b = 3 * 5
c = a + b
d = 10 - c
e = d / 5
|
a ) 88 , b ) 82 , c ) 86 , d ) 87 , e ) 80 | c | add(divide(divide(350, add(const_4, const_1)), add(const_4, const_1)), divide(350, add(const_4, const_1))) | if 350 ! / 10 ^ n is an integer , what is the largest possible value of n ? | "the question actually asks the highest power of 10 which divides 350 ! ( for a number to be an integer - without any remainder all the trailing zeroe ' s must be divided by the denominator ) 10 = 2 x 5 350 factorial will have 86 as - 350 / 5 = 70 70 / 5 = 14 14 / 5 = 2 so answer will be ( c ) 86" | a = 4 + 1
b = 350 / a
c = 4 + 1
d = b / c
e = 4 + 1
f = 350 / e
g = d + f
|
a ) 40 , b ) 80 , c ) 70 , d ) 60 , e ) 50 | a | subtract(100, 80) | a person decided to build a house in 100 days . he employed 100 men in the beginning and 100 more after 80 days and completed the construction in stipulated time . if he had not employed the additional men , how many days behind schedule would it have been finished ? | "200 men do the rest of the work in 100 - 80 = 20 days 100 men can do the rest of the work in 20 * 200 / 100 = 40 days required number of days = 40 - 80 = 40 days answer is a" | a = 100 - 80
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a ) 30 % , b ) 40 % , c ) 85 % , d ) 19 % , e ) 20 % | e | divide(const_100, add(const_1, 4)) | solve the quickfire maths brain teaser â ˆ š 4 % = ? | â ˆ š 4 % = > â ˆ š 4 / â ˆ š 100 = > 2 / 10 = > 20 / 100 = > 20 % e | a = 1 + 4
b = 100 / a
|
a ) 52.7 m 2 , b ) 57.8 m 2 , c ) 52.8 metre sq , d ) 72.8 m 2 , e ) 52.8 m 2 | c | multiply(multiply(power(12, const_2), divide(add(multiply(const_2, const_10), const_2), add(const_4, const_3))), divide(42, divide(const_3600, const_10))) | the area of sector of a circle whose radius is 12 metre and whose angle at the center is 42 ° is ? | 42 / 360 * 22 / 7 * 12 * 12 = 52.8 m 2 answer : c | a = 12 ** 2
b = 2 * 10
c = b + 2
d = 4 + 3
e = c / d
f = a * e
g = 3600 / 10
h = 42 / g
i = f * h
|
a ) 125.5 meters , b ) 126.5 meters , c ) 127.5 meters , d ) 128.5 meters , e ) none of these | c | divide(multiply(600, subtract(1000, divide(multiply(subtract(1000, 100), subtract(800, 100)), 800))), 1000) | in a race of 1000 meters , a can beat b by 100 meters , in a race of 800 meters , b can beat c by 100 meters . by how many meters will a beat c in a race of 600 meters ? | explanation : when a runs 1000 meters , b runs 900 meters and when b runs 800 meters , c runs 700 meters . therefore , when b runs 900 meters , the distance that c runs = ( 900 x 700 ) / 800 = 6300 / 8 = 787.5 meters . so , in a race of 1000 meters , a beats c by ( 1000 - 787.5 ) = 212.5 meters to c . so , in a race of 600 meters , the number of meters by which a beats c = ( 600 x 212.5 ) / 1000 = 127.5 meters . answer : c | a = 1000 - 100
b = 800 - 100
c = a * b
d = c / 800
e = 1000 - d
f = 600 * e
g = f / 1000
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a ) 6 : 5 , b ) 1 : 4 , c ) 3 : 2 , d ) 2 : 3 , e ) 2 : 5 | a | divide(multiply(multiply(multiply(const_3, const_2), const_100), const_100), divide(multiply(multiply(multiply(const_3, const_2), const_100), const_100), multiply(add(const_2, const_3), const_2))) | if a and b get profits of rs . 18,000 and rs . 15,000 respectively at the end of year then ratio of their investments are | "ratio = 18000 / 15000 = 6 : 5 answer : a" | a = 3 * 2
b = a * 100
c = b * 100
d = 3 * 2
e = d * 100
f = e * 100
g = 2 + 3
h = g * 2
i = f / h
j = c / i
|
a ) 2 : 6 , b ) 2 : 9 , c ) 2 : 4 , d ) 5 : 2 , e ) 2 : 5 | d | inverse(subtract(const_1, divide(3, 5))) | he ratio between the sale price and the cost price of an article is 5 : 3 . what is the ratio between the profit and the cost price of that article ? | let c . p . = rs . 3 x and s . p . = rs . 5 x . then , gain = rs . 2 x required ratio = 5 x : 2 x = 5 : 2 answer : d | a = 3 / 5
b = 1 - a
c = 1/(b)
|
a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 7 | c | subtract(multiply(subtract(12, 1), add(6, 1)), multiply(12, 6)) | the average of 6 observations is 12 . a new observation is included and the new average is decreased by 1 . the seventh observation is ? | "let seventh observation = x . then , according to the question we have = > ( 72 + x ) / 7 = 11 = > x = 5 . hence , the seventh observation is 5 . answer : c" | a = 12 - 1
b = 6 + 1
c = a * b
d = 12 * 6
e = c - d
|
a ) 0.9 , b ) 0.75 , c ) 0.6 , d ) 0.8 , e ) 0.5 | d | divide(subtract(100, add(17, 3)), 100) | a certain bag contains 100 balls â € ” 50 white , 20 green , 10 yellow , 17 red , and 3 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ? | "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 50 + 20 + 10 ) / 100 = 80 / 100 = 0.8 . answer is d" | a = 17 + 3
b = 100 - a
c = b / 100
|
a ) 9872 , b ) 9782 , c ) 9827 , d ) 9287 , e ) none of them | a | add(multiply(8888, 888), multiply(88, 8)) | simplify : 8888 + 888 + 88 + 8 | "8888 888 88 8 - - - - - - - 9872 answer is a ." | a = 8888 * 888
b = 88 * 8
c = a + b
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a ) 12 % , b ) 26 % , c ) 23 % , d ) 30 % , e ) 60 % | c | multiply(divide(add(multiply(divide(15, const_100), 300), multiply(divide(35, const_100), 200)), add(300, 200)), const_100) | for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 15 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ? | "in the first plot 15 % of 300 seeds germinated , so 0.15 x 300 = 45 seeds germinated . in the second plot , 35 % of 200 seeds germinated , so 0.35 x 200 = 70 seeds germinated . since 45 + 70 = 115 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 115 / 500 ) x 100 % , or 23 % . answer : c ." | a = 15 / 100
b = a * 300
c = 35 / 100
d = c * 200
e = b + d
f = 300 + 200
g = e / f
h = g * 100
|
a ) 62 kmph , b ) 58 kmph , c ) 52 kmph , d ) 50 kmph , e ) none of these | a | subtract(multiply(divide(280, 9), const_3_6), 50) | a man sitting in a train which is travelling at 50 kmph observes that a goods train , travelling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed . | "relative speed = ( 280 ⁄ 9 ) m / sec = ( 280 ⁄ 9 × 18 ⁄ 5 ) kmph = 112 kmph . ∴ speed of goods train = ( 112 – 50 ) kmph = 62 kmph . answer a" | a = 280 / 9
b = a * const_3_6
c = b - 50
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a ) 300 / 31 , b ) 300 / 35 , c ) 300 / 21 , d ) 300 / 15 , e ) 300 / 20 | b | inverse(add(divide(const_1, 15), divide(const_1, 20))) | a can do a work in 15 days and b in 20 days . if they work on it together then in how many days required to complete the work ? | person ( a ) ( b ) ( a + b ) time - ( 15 ) ( 20 ) ( 300 / 35 ) rate - ( 20 ) ( 15 ) ( 35 ) work - ( 300 ) ( 300 ) ( 300 ) therefore a + b requires ( 300 / 35 ) days to complete entire work = 300 / 35 answer is b | a = 1 / 15
b = 1 / 20
c = a + b
d = 1/(c)
|
a ) 1345 , b ) 1334 , c ) 1313.33 , d ) 1350 , e ) 1325 | c | divide(add(add(add(add(add(add(1200, 1300), 1400), 1510), 1520), 1530), 1200), add(const_3, const_4)) | what is the average of 1200 , 1300 , 1400 , 1510 , 1520 , 1530 , 1115 , 1120 , and 1125 ? | "add 1200 , 1300 , 1400 , 1510 , 1520 , 1530 , 1115 , 1120 , and 1125 grouping numbers together may quicken the addition sum = 11820 11820 / 9 = 1313.33 c" | a = 1200 + 1300
b = a + 1400
c = b + 1510
d = c + 1520
e = d + 1530
f = e + 1200
g = 3 + 4
h = f / g
|
a ) 70 , b ) 75 , c ) 88 , d ) 54 , e ) 15 | a | divide(add(90, 50), const_2) | the speed of a car is 90 km in the first hour and 50 km in the second hour . what is the average speed of the car ? | "s = ( 90 + 50 ) / 2 = 70 kmph answer : a" | a = 90 + 50
b = a / 2
|
a ) 65 , b ) 100 , c ) 115 , d ) 130 , e ) 135 | d | add(multiply(45, const_2), 55) | of the 200 employees in a certain company , 25 percent will be relocated to city x and the remaining 75 percent will be relocated to city y . however , 45 percent of the employees prefer city y and 55 percent prefer city x . what is the highest possible number of employees who will be relocated to the city they prefer ? | "110 prefer x ( group 1 ) ; 90 prefer y ( group 2 ) . city y needs 150 people : letall 90 who prefer y ( entire group 2 ) be relocated there , the rest 60 will be those who prefer x from group 1 ; city x needs 40 people : 110 - 60 = 40 from group 1 will be relocated to x , which they prefer . so , the highest possible number of employees who will be relocated to the city they prefer is 90 + 40 = 130 . answer : d ." | a = 45 * 2
b = a + 55
|
a ) 24887 , b ) 20778 , c ) 23788 , d ) 21000 , e ) 2811 | d | divide(multiply(multiply(3500, const_12), 3), multiply(subtract(const_12, 9), 2)) | a starts business with rs . 3500 and after 9 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ? | "explanation : a invested rs . 3500 for 12 months . let b joined with investment x . and he invested for 12 - 9 = 3 months . so there profit ratio = ( 3500 ã — 12 ) : ( 3 x ) = 2 : 3 â ‡ ’ x = 21000 answer : d" | a = 3500 * 12
b = a * 3
c = 12 - 9
d = c * 2
e = b / d
|
a ) 72 % , b ) 70 % , c ) 52 % , d ) 50 % , e ) 28 % | a | subtract(80, multiply(divide(80, const_100), 10)) | a shirt goes on sale for 80 % of its original price . one week later , the sale price is marked down 10 % . the final price is what percent of the original price ? | "just assume original price is 100 . sale price = 80 then it is marked down by 10 % = 80 - 8 = 72 . hence it is 72 % of the original price . hence answer is a" | a = 80 / 100
b = a * 10
c = 80 - b
|
a ) 15 , b ) 21 , c ) 35 , d ) 41 , e ) 64 | d | multiply(add(divide(subtract(subtract(330, 220), const_2), const_2), 220), divide(add(subtract(330, 220), const_2), const_2)) | what is the sum of all the prime factors of 220 and 330 ? | "prime factorization of both the numbers is as follows 220 = 2 * 2 * 5 * 11 sum of the prime factors of 220 = 20 330 = 2 * 3 * 5 * 11 sum of prime factors of 330 = 21 addition of both = 20 + 21 = 41 answer d" | a = 330 - 220
b = a - 2
c = b / 2
d = c + 220
e = 330 - 220
f = e + 2
g = f / 2
h = d * g
|
a ) 20 % , b ) 17 % , c ) 4.0 % , d ) 3.3 % , e ) 2.8 % | e | multiply(divide(divide(divide(const_100, const_3), 6), const_100), const_100) | mr . evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children . if mr . evans has 5 children and 6 grandchildren , then approximately what percentage of mr . evans estate will each grandchild receive ? | "share of each child ( 5 no ) and ( total share of grand children together ) 1 no = 1 / ( 5 + 1 ) = 1 / 6 as the grand children again equally share the part given to them : share of each grand child = [ ( 1 / 6 ) / 6 ] = 1 / 36 = 2.8 % answer : e" | a = 100 / 3
b = a / 6
c = b / 100
d = c * 100
|
a ) 11 , b ) 13 , c ) 15 , d ) 18 , e ) 19 | b | add(divide(subtract(multiply(floor(divide(50, 3)), 3), multiply(add(floor(divide(10, 3)), const_1), 3)), 3), const_1) | how many numbers from 10 to 50 are exactly divisible by 3 | "12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 , 45,48 . 13 numbers . 10 / 3 = 3 and 50 / 3 = 16 = = > 16 - 3 = 13 . therefore 13 digits b )" | a = 50 / 3
b = math.floor(a)
c = b * 3
d = 10 / 3
e = math.floor(d)
f = e + 1
g = f * 3
h = c - g
i = h / 3
j = i + 1
|
a ) 3 % , b ) 4 % , c ) 5 % , d ) 6 % , e ) 7 % | d | subtract(sqrt(divide(multiply(1348.32, const_100), divide(1200, const_100))), sqrt(divide(multiply(1200, const_100), divide(1200, const_100)))) | at what rate of compound interest per annum will a sum of rs . 1200 become rs . 1348.32 in 2 years | "explanation : let rate will be r % 1200 ( 1 + r / 100 ) 2 = 134832 / 100 ( 1 + r / 100 ) 2 = 134832 / 120000 ( 1 + r / 100 ) 2 = 11236 / 10000 ( 1 + r / 100 ) = 106 / 100 = > r = 6 % option d" | a = 1348 * 32
b = 1200 / 100
c = a / b
d = math.sqrt(c)
e = 1200 * 100
f = 1200 / 100
g = e / f
h = math.sqrt(g)
i = d - h
|
a ) 70 , b ) 105 , c ) 178 , d ) 177 , e ) 169 | a | add(add(multiply(divide(const_100, 45), 18), multiply(divide(30, 45), 18)), 18) | a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 18 , what is the total amount ? | "x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 18 35 - - - ? = > 70 answer : a" | a = 100 / 45
b = a * 18
c = 30 / 45
d = c * 18
e = b + d
f = e + 18
|
a ) 1000 , b ) 908 , c ) 930 , d ) 1075 , e ) 1080 | b | add(multiply(7, 68), multiply(9, 48)) | andrew purchased 7 kg of grapes at the rate of 68 per kg and 9 kg of mangoes at the rate of 48 per kg . how much amount did he pay to the shopkeeper ? | "cost of 7 kg grapes = 68 × 7 = 476 . cost of 9 kg of mangoes = 48 × 9 = 432 . total cost he has to pay = 476 + 432 = 908 b" | a = 7 * 68
b = 9 * 48
c = a + b
|
a ) 2 : 1 , b ) 1 : 2 , c ) 7 : 3 , d ) 1 : 1 , e ) 3 : 2 | c | divide(subtract(divide(multiply(divide(8, const_100), 3), const_3), divide(3, const_100)), subtract(divide(5, const_100), divide(multiply(divide(6, const_100), const_2), const_3))) | two numbers a and b are such that the sum of 5 % of a and 3 % of b is two - third of the sum of 6 % of a and 8 % of b . find the ratio of a : b . | "explanation : 5 % of a + 3 % of b = 2 / 3 ( 6 % of a + 8 % of b ) 5 a / 100 + 3 b / 100 = 2 / 3 ( 6 a / 100 + 8 b / 100 ) ⇒ 5 a + 3 b = 2 / 3 ( 6 a + 8 b ) ⇒ 15 a + 9 b = 12 a + 16 b ⇒ 3 a = 7 b ⇒ ab = 7 / 3 ⇒ a : b = 7 : 3 answer : option c" | a = 8 / 100
b = a * 3
c = b / 3
d = 3 / 100
e = c - d
f = 5 / 100
g = 6 / 100
h = g * 2
i = h / 3
j = f - i
k = e / j
|
a ) rs . 72 , b ) rs . 78 , c ) rs . 80 , d ) rs . 90 , e ) rs . 92 | d | add(divide(subtract(sqrt(add(multiply(const_100, const_100), multiply(multiply(const_100, 144), const_4))), const_100), const_2), const_10) | radha bought a watch for rs . 144 and got a percentage of profit equal to the cost price of the watch . what is the cost price of the watch ? | sp = 144 cp = x profit % = x c . p . = ( 100 / ( 100 + gain % ) ) * s . p . x = ( 100 / 100 + x ) * 144 x ^ 2 + 100 x = 14400 x ^ 2 + 180 x - 80 x - 14400 = 0 ( x + 180 ) ( x - 80 ) = 0 x = - 180 x = 80 answer : d | a = 100 * 100
b = 100 * 144
c = b * 4
d = a + c
e = math.sqrt(d)
f = e - 100
g = f / 2
h = g + 10
|
a ) 36 / 5 , b ) 13 , c ) 17 , d ) 21 , e ) 23 | a | divide(multiply(add(add(3, const_3), const_2), divide(3, const_2)), add(const_2, divide(const_1, const_2))) | a and b are two partially filled buckets of water . if 3 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 3 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ? | "let bucket a be a and bucket b be b scenario 1 a - 3 = 1 / 3 ( b + 3 ) - - - - > 3 a - 9 = b + 3 scenario 2 b - 3 = 1 / 2 ( a + 3 ) - - - - - > 2 b - 6 = a + 3 from scenario 1 , b = 3 a - 12 substitute b with this information in stmt 2 2 ( 3 a - 12 ) - 9 = a + 3 - - - - - - > 6 a - 24 - 9 = a + 3 - - - - - - > 6 a - a = 33 + 3 - - - > 5 a = 36 a = 36 / 5 , answer choice a" | a = 3 + 3
b = a + 2
c = 3 / 2
d = b * c
e = 1 / 2
f = 2 + e
g = d / f
|
['a ) 2', 'b ) 4', 'c ) 6', 'd ) 8', 'e ) 10'] | c | sqrt(add(27, multiply(const_2, multiply(const_2, const_2)))) | 27 is a perfect cube . when x is perfect cube which is added to the prime factor of 27 , the result is not a prime number . what is the square root of x ? | 27 is 3 * 3 * 3 2 * 2 = 4 , 3 + 4 = 7 4 * 4 = 16 , 3 + 16 = 17 6 * 6 = 36 , 3 + 36 = 39 8 * 8 = 64 , 3 + 64 = 67 10 * 10 = 100 , 3 + 100 = 103 here c is the only addition that is not a prime number . so the answer is c | a = 2 * 2
b = 2 * a
c = 27 + b
d = math.sqrt(c)
|
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | a | divide(multiply(add(4, 3), const_2), 8) | | x + 3 | – | 4 - x | = | 8 + x | how many k solutions will this equation have ? | "| x | = x when x > = 0 ( x is either positive or 0 ) | x | = - x when x < 0 ( note here that you can put the equal to sign here as well x < = 0 because if x = 0 , | 0 | = 0 = - 0 ( all are the same ) so the ' = ' sign can be put with x > 0 or with x < 0 . we usually put it with ' x > 0 ' for consistency . a" | a = 4 + 3
b = a * 2
c = b / 8
|
a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0 | a | add(reminder(multiply(reminder(55, const_4), 93), const_10), reminder(35, const_10)) | the units digit of ( 35 ) ^ ( 87 ) + ( 93 ) ^ ( 55 ) is : | "the units digit of powers of 3 , cycles in a group of 4 : { 3 , 9 , 7 , 1 } 55 has the form 4 k + 3 , so the units digit of 93 ^ 55 is 7 . the units digit of powers of 5 is always 5 . 7 + 5 = 12 , so the units digit is 2 . the answer is a ." | a = reminder * (
b = reminder + (
|
a ) 120 meters , b ) 360 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined | a | subtract(multiply(divide(multiply(36, const_1000), const_3600), 30), multiply(divide(multiply(36, const_1000), const_3600), 12)) | a train traveling at 36 kmph crosses a platform in 30 seconds and a man standing on the platform in 12 seconds . what is the length of the platform in meters ? | "answer distance covered by the train when crossing a man and when crossing a platform when a train crosses a man standing on a platform , the distance covered by the train is equal to the length of the train . however , when the same train crosses a platform , the distance covered by the train is equal to the length of the train plus the length of the platform . the extra time that the train takes when crossing the platform is on account of the extra distance that it has to cover . i . e . , length of the platform . compute length of platform length of the platform = speed of train * extra time taken to cross the platform . length of platform = 36 kmph * 12 seconds convert 36 kmph into m / sec 1 kmph = 5 / 18 m / s ( this can be easily derived . but if you can remember this conversion , it saves a good 30 seconds ) . ∴ 36 kmph = 5 / 18 ∗ 36 = 10 m / sec therefore , length of the platform = 10 m / s * 12 sec = 120 meters . choice a" | a = 36 * 1000
b = a / 3600
c = b * 30
d = 36 * 1000
e = d / 3600
f = e * 12
g = c - f
|
a ) 22 , b ) 56 , c ) 280 , d ) 112 , e ) 175 | c | divide(14, subtract(134.05, add(const_100, add(multiply(const_4, const_10), const_2)))) | when positive integer n is divided by positive integer j , the remainder is 14 . if n / j = 134.05 , what is value of j ? | "1 ) we know that decimal part of decimal quotient = { remainder / divisor } so 0.08 , the decimal part of the decimal quotient , must equal the remainder , 14 , divided by the divisor j . 0.05 = 14 / j 0.05 * j = 14 j = 14 / 0.05 = 1400 / 5 = 280 so j = 280 , answer = c ." | a = 4 * 10
b = a + 2
c = 100 + b
d = 134 - 5
e = 14 / d
|
a ) 61,600 , b ) 64,850 , c ) 64,749 , d ) 49,700 , e ) 56,720 | a | multiply(divide(add(divide(subtract(subtract(const_1000, 3), add(add(multiply(multiply(3, 3), const_10), multiply(3, 3)), 3)), 8), const_1), 2), add(subtract(const_1000, 3), add(add(multiply(multiply(3, 3), const_10), multiply(3, 3)), 3))) | what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 8 ? | "find the number , upon sum of 3 digits of a number gives a reminder 2 when it is divided by 8 seeing the options after dividing an finding the reminder of 2 my answer was a" | a = 1000 - 3
b = 3 * 3
c = b * 10
d = 3 * 3
e = c + d
f = e + 3
g = a - f
h = g / 8
i = h + 1
j = i / 2
k = 1000 - 3
l = 3 * 3
m = l * 10
n = 3 * 3
o = m + n
p = o + 3
q = k + p
r = j * q
|
a ) a . 43 , b ) b . 53 , c ) c . 55 , d ) d . 68 , e ) e . 60 | b | subtract(divide(multiply(multiply(35, subtract(15, 2.5)), 100), multiply(2.5, subtract(300, 100))), 35) | an engineer undertakes a project to build a road 15 km long in 300 days and employs 35 men for the purpose . after 100 days , he finds only 2.5 km of the road has been completed . find the ( approximate ) number of extra men he must employ to finish the work in time . | "35 workers working already let x be the total men required to finish the task in next 200 days 2.5 km done hence remaining is 12.5 km also , work has to be completed in next 200 days ( 300 - 100 = 200 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 35 * 12.5 * 100 ) / ( 2.5 * 200 ) thus , x = 87.5 that is approximately 88 thus , more men needed to finish the task = 88 - 35 = 53 hence answer is b" | a = 15 - 2
b = 35 * a
c = b * 100
d = 300 - 100
e = 2 * 5
f = c / e
g = f - 35
|
a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | e | subtract(1,439, add(multiply(multiply(multiply(5, 11), 13), const_2), 3)) | what least number should be subtracted from 1,439 so that the remainder when divided by 5 , 11 , and 13 will leave in each case the same remainder 3 ? | "the lcm of 5 , 11 , and 13 is 715 . the next multiple is 2 * 715 = 1,430 . 1,430 + { remainder } = 1,430 + 3 = 1,433 , which is 6 less than 1,439 . answer : e ." | a = 5 * 11
b = a * 13
c = b * 2
d = c + 3
e = 1 - 439
|
a ) 2 : 3 , b ) 82 : 31 , c ) 32 : 45 , d ) 34 : 89 , e ) 35 : 21 | a | divide(add(multiply(5000, 4), multiply(divide(6000, const_3), multiply(2, 4))), add(multiply(6000, multiply(2, const_3)), multiply(subtract(6000, divide(6000, const_3)), multiply(2, const_3)))) | a and b invests rs . 5000 and rs . 6000 in a business . after 4 months , a withdraws half of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ? | "a : b ( 5000 * 4 ) + ( 2500 * 8 ) : ( 6000 * 6 ) + ( 4000 * 6 ) 40000 : 60000 2 : 3 answer : a" | a = 5000 * 4
b = 6000 / 3
c = 2 * 4
d = b * c
e = a + d
f = 2 * 3
g = 6000 * f
h = 6000 / 3
i = 6000 - h
j = 2 * 3
k = i * j
l = g + k
m = e / l
|
a ) 52 sec , b ) 45 sec , c ) 60 sec , d ) 24 sec , e ) 39 sec | d | divide(multiply(20, const_4), multiply(12, divide(const_1000, const_3600))) | how long will a boy take to run round a square field of side 20 meters , if he runs at the rate of 12 km / hr ? | "speed = 12 km / hr = 12 * 5 / 18 = 10 / 3 m / sec distance = 20 * 4 = 80 m time taken = 80 * 3 / 10 = 24 sec answer is d" | a = 20 * 4
b = 1000 / 3600
c = 12 * b
d = a / c
|
a ) 1865113 , b ) 1775123 , c ) 1765113 , d ) 1675123 , e ) none of them | c | multiply(4300731, power(add(const_4, const_1), const_4)) | ( 4300731 ) - ? = 2535618 | "let 4300731 - x = 2535618 then x = 4300731 - 2535618 = 1765113 answer is c" | a = 4 + 1
b = a ** 4
c = 4300731 * b
|
a ) 95 , b ) 99 , c ) 26 , d ) 73 , e ) none of the above | c | add(multiply(const_10, add(subtract(11, 4), const_1)), 4) | what two - digit number is less than the sum of the square of its digits by 11 and exceeds their doubled product by 4 ? | "let the digits be x and y . the number would be 10 x + y . we are given that 2 xy + 4 = 10 x + y = x ^ 2 y ^ 2 - 11 thus 2 xy + 4 = x ^ 2 + y ^ 2 - 11 x ^ 2 + y ^ 2 - 2 xy = 16 ( x - y ) ^ 2 = 16 ( x - y ) = 4 or - 4 substituting the values of ( x - y ) in the equation 2 xy + 5 = 10 x + y x comes out to be 1 or 9 . . . thus the two numbers can be 26 or 98 thus the answer is c" | a = 11 - 4
b = a + 1
c = 10 * b
d = c + 4
|
['a ) 100 π', 'b ) 101 / π', 'c ) 99 π / 12', 'd ) 54 / 13 π', 'e ) 22 / 10 π'] | a | multiply(multiply(power(power(divide(multiply(divide(multiply(multiply(divide(const_4, const_3), power(10, const_3)), const_pi), 8), const_3), multiply(const_4, const_pi)), inverse(const_3)), const_2), const_4), const_pi) | if a solid sphere of radius 10 cms is moulded into 8 spherical solid balls of equal radius , then surface area of each ball ( in sq . cm ) is ? | explanation : 4 / 3 π x 10 x 10 x 10 = 8 x 4 / 3 π rxrxr r = 5 4 π x 5 x 5 = 100 π answer is a | a = 4 / 3
b = 10 ** 3
c = a * b
d = c * math.pi
e = d / 8
f = e * 3
g = 4 * math.pi
h = f / g
i = 1/(3)
j = h ** i
k = j ** 2
l = k * 4
m = l * math.pi
|
a ) 419 , b ) 551 , c ) 601 , d ) 620 , e ) 858.54 | e | divide(add(add(add(add(add(add(add(add(add(add(12, 13), 14), 510), 520), 530), 1115), 1120), add(1115, const_10)), subtract(2345, add(add(multiply(const_100, const_2), const_4), const_1))), 2345), add(const_10, const_1)) | what is the average of 12 , 13 , 14 , 510 , 520 , 530 , 1115 , 1120 , and 1 , 1252140 , 2345 ? | add 12 , 13 , 14 , 510 , 520 , 530 , 1,115 , 1,120 , and 1,125 , 2140 , 2345 grouping numbers together may quicken the addition sum = 9444 4959 / 11 = 858.54 . e | a = 12 + 13
b = a + 14
c = b + 510
d = c + 520
e = d + 530
f = e + 1115
g = f + 1120
h = 1115 + 10
i = g + h
j = 100 * 2
k = j + 4
l = k + 1
m = 2345 - l
n = i + m
o = n + 2345
p = 10 + 1
q = o / p
|
a ) 102 % , b ) 90 % , c ) 120 % , d ) 85 % , e ) 95 % | b | add(subtract(subtract(20, 25), divide(multiply(25, 20), const_100)), const_100) | the price of a certain painting increased by 20 % during the first year and decreased by 25 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ? | "easiest thing to do : assume that price is 100 price at the end of yr 1 : 100 + 20 = 120 price at the end of year 2 = 120 - 120 * 0.25 = 120 * 0.75 = 90 hence required answer = ( 90 / 100 ) * 100 % = 90 % answer is b ." | a = 20 - 25
b = 25 * 20
c = b / 100
d = a - c
e = d + 100
|
a ) 11 , b ) 16 , c ) 13 , d ) 14 , e ) 15 | b | subtract(multiply(15, 15), add(multiply(5, 13), multiply(9, 16))) | the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 13 years and that of the other 9 students is 16 years , the age of the 15 th student is | explanation : age of the 15 th student = [ 15 * 15 - ( 13 * 5 + 16 * 9 ) ] = 16 years . answer : b | a = 15 * 15
b = 5 * 13
c = 9 * 16
d = b + c
e = a - d
|
a ) – 2 , b ) – 1 , c ) 0 , d ) - 6 , e ) 5 | d | divide(log(divide(1, 64)), log(2)) | if 64 ( 2 ^ x ) = 1 then x = | "2 ^ x = 1 / 64 2 ^ x = 1 / 2 ^ 6 2 ^ x = 2 ^ - 6 x = - 6 d" | a = 1 / 64
b = math.log(a)
c = math.log(2)
d = b / c
|
a ) $ 160 , b ) $ 289 , c ) $ 334 , d ) $ 274 , e ) $ 286 | c | add(multiply(18.00, add(const_3, const_4)), multiply(13.00, subtract(23, add(const_3, const_4)))) | if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 13.00 / day for each additional week , how much does it cost to stay for 23 days ? | "total number of days of stay = 23 charge of staying in first week = 18 * 7 = 126 $ charge of staying for additional days = ( 23 - 7 ) * 13 = 16 * 13 = 208 $ total charge = 126 + 208 = 334 $ answer c" | a = 3 + 4
b = 18 * 0
c = 3 + 4
d = 23 - c
e = 13 * 0
f = b + e
|
a ) 80 , b ) 240 , c ) 288 , d ) 277 , e ) 221 | a | multiply(20, multiply(18, const_0_2778)) | a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 18 km / hr . what is the length of the platform ? | "speed = 18 * 5 / 18 = 5 m / sec . length of the train = 5 * 20 = 100 m . let the length of the platform be x m . then , ( x + 100 ) / 36 = 5 = > x = 80 m . answer : a" | a = 18 * const_0_2778
b = 20 * a
|
a ) 17 , b ) 12 , c ) 15 , d ) 13 , e ) 11 | c | divide(multiply(60, 3), 12) | if the lcm and hcf of 12 and another number is 60 and 3 respectively . find the other number ? | "hcf x lcm = product of numbers 3 x 60 = 12 x the other number other number = ( 3 x 60 ) / 12 other number = 15 answer : c" | a = 60 * 3
b = a / 12
|
a ) $ 11 , b ) $ 5 , c ) $ 45 , d ) $ 400 , e ) $ 6.2 | e | divide(subtract(280, multiply(subtract(const_1, divide(10, const_100)), 280)), subtract(5, divide(const_1, const_2))) | a reduction in the price of petrol by 10 % enables a motorist to buy 5 gallons more for $ 280 . find the original price of petrol ? | price decreased by 10 % , so 9 / 10 times , which means that original gallons bought increased 10 / 9 times . since this increase equals to 5 gallons then 45 gallons were bought originally ( 45 * 10 / 9 = 50 - - > increase 5 gallons ) . hence original price was 280 / 45 = $ 6.2 answer : e . | a = 10 / 100
b = 1 - a
c = b * 280
d = 280 - c
e = 1 / 2
f = 5 - e
g = d / f
|
a ) 100 m , b ) 120 m , c ) 140 m , d ) 160 m , e ) 170 cm | b | divide(const_100.0, subtract(divide(const_100.0, 10), 6)) | a train covers a distance of 12 km in 10 minutes . if it takes 6 seconds to pass a telegraph post , then the length of the train is | "explanation : speed = 12 / 10 x 60 km / hr = 72 x 5 / 18 m / sec = 20 m / sec . length of the train = ( speed x time ) = ( 20 x 6 ) m = 120 m answer : option b" | a = 100 / 0
b = a - 6
c = 100 / 0
|
a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 6 , d ) 1 / 8 , e ) none of these | e | add(add(const_1, divide(2, 6)), divide(2, const_3)) | if x / 2 = y / 4 = z / 6 , then find the value of ( x + y + z ) / z | explanation : x / 2 = y / 4 = z / 6 = k , then x = 2 k , y = 4 k and z = 6 k . now , ( x + y + z ) / z = ( 2 k + 4 k + 6 k ) / 6 k = 12 k / 6 k = 2 answer : option e | a = 2 / 6
b = 1 + a
c = 2 / 3
d = b + c
|
a ) $ 40,000 , b ) $ 50,000 , c ) $ 64,000 , d ) $ 66,667 , e ) $ 80,000 | b | add(divide(subtract(8000, multiply(divide(15, const_100), 40000)), divide(20, const_100)), 40000) | country x taxes each of its citizens an amount equal to 15 percent of the first $ 40000 of income , plus 20 percent of all income in excess of $ 40000 . if a citizen of country x is taxed a total of $ 8000 , what is her income ? | equation is correct , so math must be a problem . 0.15 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 6,000 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 10,000 - - > x = 50,000 . answer : b . | a = 15 / 100
b = a * 40000
c = 8000 - b
d = 20 / 100
e = c / d
f = e + 40000
|
a ) 1 / 49 , b ) 1 / 42 , c ) 1 / 09 , d ) 1 / 77 , e ) 1 / 12 | b | inverse(multiply(2, 7)) | the compound ratio of 2 / 3 , 6 / 7 , 1 / 3 and 1 / 8 is given by ? | "2 / 3 * 6 / 7 * 1 / 3 * 1 / 8 = 1 / 42 answer : b" | a = 2 * 7
b = 1/(a)
|
a ) 26 , b ) 32 , c ) 33 , d ) 34 , e ) 40 | e | subtract(add(floor(divide(subtract(99, 39), 3)), divide(subtract(99, 39), 2)), floor(divide(subtract(99, 39), multiply(2, 3)))) | if w is the set of all the integers between 39 and 99 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ? | "multiples of 2 from 39 to 99 = multiples of 2 from 1 to 99 - multiples of 2 from 1 to 38 = [ 99 / 2 ] - [ 38 / 2 ] = 49 - 19 = 30 multiples of 3 from 39 to 99 = multiples of 3 from 1 to 99 - multiples of 3 from 1 to 38 = [ 99 / 3 ] - [ 38 / 3 ] = 33 - 13 = 20 multiples of 2 and 3 bothi . e . 6 from 39 to 99 = multiples of 6 from 1 to 99 - multiples of 6 from 1 to 38 = [ 99 / 6 ] - [ 38 / 6 ] = 16 - 6 = 10 these 8 numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3 i . e . total numbers in w = 30 + 20 - 10 = 40 answer option e" | a = 99 - 39
b = a / 3
c = math.floor(b)
d = 99 - 39
e = d / 2
f = c + e
g = 99 - 39
h = 2 * 3
i = g / h
j = math.floor(i)
k = f - j
|
a ) 17 , b ) 16 , c ) 15 , d ) 18 , e ) 13 | d | add(add(add(const_4, 2), add(2, const_2)), 2) | the number 500 can be written as the sum of the squares of 2 different positive integers . what is the difference of these 2 integers ? | "22 ^ 2 + 4 ^ 2 = 500 - - > 22 - 4 = 18 . d" | a = 4 + 2
b = 2 + 2
c = a + b
d = c + 2
|
a ) 14.04 % , b ) 15.04 % , c ) 13.64 % , d ) 12.04 % , e ) 10.04 % | c | divide(multiply(15, const_100), add(15, const_100)) | the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 15 percent , what was the annual interest rate last year ? | "let i = interest rate i ( this year ) = i ( last year ) + 0.1 i ( last year ) = 1.1 i ( last year ) 15 = 1.1 x i ( last year ) i ( last year ) = 15 / 1.1 = 150 / 11 = 13.64 % answer : c" | a = 15 * 100
b = 15 + 100
c = a / b
|
a ) s . 650 , b ) s . 690 , c ) s . 698 , d ) s . 700 , e ) s . 728 | e | subtract(845, divide(multiply(subtract(854, 845), 3), 4)) | a sum of money at simple interest amounts to rs . 845 in 3 years and to rs . 854 in 4 years . the sum is : | "s . i . for 1 year = rs . ( 854 - 815 ) = rs . 39 . s . i . for 3 years = rs . ( 39 x 3 ) = rs . 117 . principal = rs . ( 845 - 117 ) = rs . 728 . answer : option e" | a = 854 - 845
b = a * 3
c = b / 4
d = 845 - c
|
a ) 18 , b ) 22 , c ) 24 , d ) 26 , e ) 98 | c | divide(multiply(80, 70), const_100) | find number which is 70 % less than 80 . | "explanation : 70 % less is 30 % of the given number therefore , 30 % of 80 is 24 . answer : c" | a = 80 * 70
b = a / 100
|
a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 10 | c | add(divide(subtract(20, add(const_2, const_4)), subtract(3, const_1)), const_2) | the sum of 3 consecutive odd numbers is 20 more than the first of these numbers . what is the middle number ? | solution let the numbers be x , x + 2 , x + 4 then x , ( x + 2 ) + ( x + 4 ) = x + 20 ‹ = › 2 x = 14 ‹ = › x = 7 . therefore middle number = x + 2 = 9 . answer c | a = 2 + 4
b = 20 - a
c = 3 - 1
d = b / c
e = d + 2
|
a ) 8 , b ) 9 , c ) 16 , d ) 17 , e ) 18 | e | divide(add(add(add(add(4, const_4), add(4, const_4)), add(const_4, const_4)), 48), 4) | the sum of ages of 4 children born 4 years different each is 48 yrs . what is the age of the elder child ? | "let the ages of children be x , ( x + 4 ) , ( x + 8 ) , ( x + 12 ) years . then , x + ( x + 4 ) + ( x + 8 ) + ( x + 12 ) = 48 4 x = 24 x = 6 x + 12 = 6 + 12 = 18 answer : e" | a = 4 + 4
b = 4 + 4
c = a + b
d = 4 + 4
e = c + d
f = e + 48
g = f / 4
|
a ) 1.25 % , b ) 3.75 % , c ) 9.33 % , d ) 10.67 % , e ) 11.7 % | c | multiply(divide(multiply(multiply(const_100, const_100), divide(7, const_100)), subtract(multiply(const_100, const_100), add(multiply(add(const_2, const_3), multiply(multiply(add(const_2, const_3), const_2), const_100)), multiply(add(const_2, const_3), const_100)))), const_100) | a tank contains 10,000 gallons of a solution that is 7 percent sodium chloride by volume . if 2,500 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ? | "the remaining solution will be approximately what percent sodium chloride ? means : what percent of the remaining solution is sodium chloride . now , since the remaining solution is 10,000 - 2,500 = 7,500 gallons and sodium chloride is 700 gallons ( 7 % of initial solution of 10,000 gallons ) then sodium chloride is 700 / 7,500 * 100 = ~ 9.33 % of the remaining solution of 7,500 gallons . answer : c ." | a = 100 * 100
b = 7 / 100
c = a * b
d = 100 * 100
e = 2 + 3
f = 2 + 3
g = f * 2
h = g * 100
i = e * h
j = 2 + 3
k = j * 100
l = i + k
m = d - l
n = c / m
o = n * 100
|
a ) 4 kmph , b ) 5 kmph , c ) 6 kmph , d ) 7 kmph , e ) 8 kmph | c | divide(18, add(const_1, const_2)) | the speed of a boat in still water is 18 kmph . what is the speed of the stream if the boat can cover 48 km downstream or 32 km upstream in the same time ? | "x = the speed of the stream ( 18 + x ) / ( 18 - x ) = 2 / 1 18 + x = 36 - 2 x 3 x = 18 x = 6 km / hour if the speed of the stream is 6 km / hour , then the ' downstream ' speed of the boat is 18 + 6 = 24 km / hour and the ' upstream ' speed of the boat is 18 - 6 = 12 km / hour . in that way , if the boat traveled for 2 hours , it would travel 2 x 24 = 48 km downstream and 2 x 12 = 24 km / hour upstream . answer : c" | a = 1 + 2
b = 18 / a
|
a ) 322 , b ) 324 , c ) 326 , d ) 328 , e ) 330 | b | divide(divide(2000, const_1000), divide(25, const_3600)) | a train 2000 m long can cross an electric pole in 25 sec and then find the speed of the train ? | "length = speed * time speed = l / t s = 2000 / 25 s = 80 m / sec speed = 80 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 324 kmph answer : b" | a = 2000 / 1000
b = 25 / 3600
c = a / b
|
a ) 27.5 % , b ) 33.3 % , c ) 35.5 % , d ) 42.5 % , e ) 47.5 % | d | multiply(divide(divide(subtract(32, add(divide(divide(const_100, add(const_2, const_3)), const_2), divide(divide(divide(const_100, add(const_2, const_3)), const_2), const_2))), const_2), divide(const_100, add(const_2, const_3))), const_100) | a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 32 % of the original number . what percent of the red candies remain ? | "let x be the original number of each color so there are a total of 5 x candies . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = 1.6 x red + yellow = 0.85 x red = 0.425 x , since red = yellow . the answer is d ." | a = 2 + 3
b = 100 / a
c = b / 2
d = 2 + 3
e = 100 / d
f = e / 2
g = f / 2
h = c + g
i = 32 - h
j = i / 2
k = 2 + 3
l = 100 / k
m = j / l
n = m * 100
|
a ) 58 kgs , b ) 58.65 kgs , c ) 58.95 kgs , d ) 59 kgs , e ) 59.85 kgs | b | divide(add(multiply(58.4, 20), subtract(61, 56)), 20) | the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 61 kg . what is the correct weight ? | "actual total weight is ( 20 x 58.4 - 56 + 61 ) = 1173 kgs actual average weight is 1177 / 20 = 58.65 kgs b" | a = 58 * 4
b = 61 - 56
c = a + b
d = c / 20
|
['a ) 11', 'b ) 12', 'c ) 13', 'd ) 14', 'e ) 15'] | d | divide(28, 2) | n people were sitting on a circular manner , if each of two present in the party except the pairs were adjacent sang a song , if a song lasted for 2 mins and 28 minutes was taken for singing song , find n | each of 2 present in the party = > no . of pairs possible = nc 2 possible adjacent pairs = n total required combinations = nc 2 - n time taken by each combination to sing a song = 2 min total time taken = 2 ( nc 2 - n ) = 28 on solving the above equation , we get n = 14 answer : d | a = 28 / 2
|
a ) 53 , b ) 56 , c ) 60 , d ) 64 , e ) 68 | a | subtract(add(divide(405, 9), 9), const_1) | in the floor of a particular kitchen owned by an abstract artist , each row of tiles to the right of the first row contains two fewer tiles than the row directly to its left . if there are 9 rows in all and a total of 405 tiles in the floor , how many tiles does the leftmost row contain ? | this question can be solved in a variety of ways : with algebra , by testing the answers and by using a great number property shortcut involving consecutive integers . we ' re given a few facts to work with : 1 ) there are 9 rows of tiles . 2 ) when going from ' left to right ' , each row contains two fewer tiles than the one next to it . 3 ) there are a total of 405 tiles we ' re asked how many tiles the left - most most row holds ( meaning the one with the most tiles ) . to start , 405 is divisible by 9 , so we can figure out the average number of tiles per row . that is 405 / 9 = 45 . since we ' re dealing with a set of 9 consecutive integers that differ by 2 each , we know that the ' 5 th row ' will have 45 tiles ( the average ) . then we just have to ' add 2 s ' until we get to the first row . . . 45 + 2 + 2 + 2 + 2 = 53 . final answer : a | a = 405 / 9
b = a + 9
c = b - 1
|
a ) 8 , b ) 13 , c ) 16 , d ) 24 , e ) 27 | b | subtract(subtract(multiply(3, 8), 8), 3) | each of 3 charities in novel grove estates has 8 persons serving on its board of directors . if exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors , then how many distinct persons serve on one or more boards of directors ? a . b . c . d . e . | each group has 8 = 8 + 8 + 8 = 24 max 4 people are in 2 groups , subtract 4 people twice as they are counted twice each pair of groups has 5 in common , so in addition to the 4 people subtract 1 from each group ans : 8 + 8 + 8 - ( 2 ( 4 ) ) - 3 = 13 answer : b | a = 3 * 8
b = a - 8
c = b - 3
|
a ) 4 kg , b ) 5 kg , c ) 8 kg , d ) 30 kg , e ) 35 kg | a | divide(subtract(multiply(divide(25, const_100), 20), divide(20, 10)), subtract(const_1, divide(25, const_100))) | a mixture of 20 kg of spirit and water contains 10 % water . how much water must be added to this mixture to raise the percentage of water to 25 % | exp . water in the given mixture = 10 * 20 / 100 = 2 kg , and spirit = ( 20 - 2 ) = 18 kg let x kg of water added , then , x + 2 / 20 + x * 100 = = 25 4 x + 8 = 20 + x , or x = 4 kg answer : a | a = 25 / 100
b = a * 20
c = 20 / 10
d = b - c
e = 25 / 100
f = 1 - e
g = d / f
|
a ) rs . 8082 , b ) rs . 7800 , c ) rs . 8100 , d ) rs . 8112 , e ) none | d | multiply(7500, multiply(divide(add(const_100, 4), const_100), divide(add(const_100, 4), const_100))) | if rs . 7500 are borrowed at c . i at the rate of 4 % per annum , then after 2 years the amount to be paid is : | "explanation : amount = rs . [ 7500 ( 1 + 4 / 100 ) 2 ] = rs . [ 7500 × 26 / 25 × 26 / 25 ] = rs . 8112 . correct option : d" | a = 100 + 4
b = a / 100
c = 100 + 4
d = c / 100
e = b * d
f = 7500 * e
|
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