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 ) s . 2890 , b ) s . 2330 , c ) s . 3757 , d ) s . 1620 , e ) s . 2680 | c | multiply(divide(multiply(divide(637, 7), 17), 7), 17) | the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 637 , krishan has ? | "ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 637 : n & there n = 289 x 637 / 49 = rs . 3757 answer : c" | a = 637 / 7
b = a * 17
c = b / 7
d = c * 17
|
a ) 118.75 % , b ) 128.75 % , c ) 116.75 % , d ) 117.75 % , e ) 114.75 % | a | multiply(divide(multiply(divide(50, const_100), subtract(const_1, divide(5, const_100))), divide(40, const_100)), const_100) | last week david spent 40 percent of his wages on recreation . this week , his wages are 5 percent less than last week ΚΌ s wages and he spent 50 percent of his wages on recreation . the amount he spends on recreation this week is what percent of the amount he spent on recreation last week | say david ' s wages last week were $ 100 , so he spent 0.40 * 100 = $ 40 on recreation ; this week ' s wages is 0.95 * 100 = $ 95 , so he spends 0.5 * 95 = $ 47.5 on recreation ; 47.5 / 40 = 1.1875 , hence the amount he spends on recreation this week is 118.75 % of the amount he spent on recreation last week : 40 * 1.1875 = 47.5 answer : a | a = 50 / 100
b = 5 / 100
c = 1 - b
d = a * c
e = 40 / 100
f = d / e
g = f * 100
|
a ) 86 , b ) 92 , c ) 84 , d ) 102 , e ) 96 | e | add(add(add(12, multiply(12, 3)), multiply(12, 3)), 12) | the data a and b are equal to the data subtracted c ; the data b is 3 times the data a ; if the data a is equal to 12 what is the sum of the data a , b and c ? | the equations raised . a + b = c b = 3 a a = 12 then b = 36 and c = 48 a + b + c = 96 answer : e | a = 12 * 3
b = 12 + a
c = 12 * 3
d = b + c
e = d + 12
|
a ) 4300 , b ) 19200 , c ) 5120 , d ) 5230 , e ) 5366 | b | subtract(subtract(30000, multiply(30000, divide(20, const_100))), multiply(subtract(30000, multiply(30000, divide(20, const_100))), divide(20, const_100))) | the population of a town is 30000 . it decreases annually at the rate of 20 % p . a . what will be its population after 2 years ? | "30000 Γ 80 / 100 Γ 80 / 100 = 19200 answer ; b" | a = 20 / 100
b = 30000 * a
c = 30000 - b
d = 20 / 100
e = 30000 * d
f = 30000 - e
g = 20 / 100
h = f * g
i = c - h
|
a ) 2348 , b ) 7250 , c ) 4350 , d ) 1998 , e ) 2771 | c | multiply(add(add(multiply(3, 6), multiply(4, 5)), multiply(5, 4)), divide(150, subtract(multiply(4, 5), multiply(3, 6)))) | a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 150 more than a : | "explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \ inline \ frac { 18 xy } { 100 } \ inline \ frac { 20 xy } { 100 } \ inline \ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \ inline \ frac { 58 xy } { 100 } b ' s earnings - a ' s earnings = \ inline \ frac { 2 xy } { 100 } = 150 total earning = \ inline \ frac { 58 xy } { 100 } = 4350 answer : c ) rs . 4350" | a = 3 * 6
b = 4 * 5
c = a + b
d = 5 * 4
e = c + d
f = 4 * 5
g = 3 * 6
h = f - g
i = 150 / h
j = e * i
|
a ) 3 , b ) 5 , c ) 6 , d ) 4 , e ) 9 | c | divide(divide(add(18, 6), const_2), const_2) | a man can row downstream at 18 kmph and upstream at 6 kmph . find the speed of the man in still water and the speed of stream respectively ? | let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 18 - - - ( 1 ) and x - y = 6 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 24 = > x = 12 , y = 6 . answer : c | a = 18 + 6
b = a / 2
c = b / 2
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a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 14 , e ) e ) 9 | e | sqrt(divide(1701, add(power(4, 2), add(power(1, 2), power(2, 2))))) | the ratio of 3 numbers is 1 : 2 : 4 and the sum of their squares is 1701 . the sum of the numbers is ? | let the numbers be x , 2 x , 4 x then , x ^ 2 + 4 x ^ 2 + 16 x ^ 2 = 1701 21 x ^ 2 = 1701 x ^ 2 = 81 x = 9 answer is e | a = 4 ** 2
b = 1 ** 2
c = 2 ** 2
d = b + c
e = a + d
f = 1701 / e
g = math.sqrt(f)
|
a ) 107 , b ) 70 , c ) 78 , d ) 60 , e ) 111 | d | divide(multiply(multiply(10, 18), 4), 12) | a lady builds 10 cm length , 18 cm width , and 4 cm height box using 12 cubic cm cubes . what is the minimum number of cubes required to build the box ? | "number of cubes required = volume of box / volume of cube = 10 * 18 * 4 / 12 = 60 cubes answer : d" | a = 10 * 18
b = a * 4
c = b / 12
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a ) 5,050 , b ) 7,500 , c ) 10,500 , d ) 15,000 , e ) 19,600 | c | multiply(divide(add(200, 101), const_2), add(divide(subtract(200, 101), const_2), const_1)) | the sum of the first 80 positive even integers is 2,550 . what is the sum of the odd integers from 101 to 200 , inclusive ? | "101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 80 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) sum of 1 st 100 natural numbers = ( 100 * 101 ) / 2 = 5050 sum of 1 st 80 positive even integers = 2550 sum of 1 st 100 odd numbers = 5050 - 2550 = 2500 so 101 + 103 + . . . . . . . 199 = 80 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) = 8000 + 2500 = 10500 c is the answer ." | a = 200 + 101
b = a / 2
c = 200 - 101
d = c / 2
e = d + 1
f = b * e
|
a ) 287 , b ) 350 , c ) 828 , d ) 450 , e ) 122 | d | subtract(multiply(speed(300, 18), 45), 300) | a 300 m long train crosses a platform in 45 sec while it crosses a signal pole in 18 sec . what is the length of the platform ? | "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 45 = 50 / 3 3 x + 900 = 2250 = > x = 450 m . answer : d" | a = speed * (
b = a - 45
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a ) 30 , b ) 28 , c ) 25 , d ) 20 , e ) 10 | e | divide(subtract(45, 10), 3.5) | in assembling a bluetooth device , a factory uses one of two kinds of modules . one module costs $ 10 and the other one , that is cheaper , costs $ 3.5 . the factory holds a $ 45 worth stock of 11 modules . how many of the modules in the stock are of the cheaper kind ? | so the number of $ 3.50 modules must be 10 so that the leftover 1 modules are of $ 10 which will give a total value $ 45 . 10 * 3.50 + 1 * 10 = 35 + 10 = 45 answer : e | a = 45 - 10
b = a / 3
|
a ) 14 , b ) 21 , c ) 88 , d ) 37 , e ) 29 | a | add(7, divide(multiply(7, subtract(12000, 10000)), subtract(10000, 8000))) | the average salary of all the workers in a workshop is rs . 10000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 8000 . the total number of workers in the workshop is : | "explanation : lot the total number of workers be v then , 10000 v = ( 12000 * 7 ) + 8000 ( v - 7 ) < = > 2000 v = 28000 < = > v = 14 answer : a ) 14" | a = 12000 - 10000
b = 7 * a
c = 10000 - 8000
d = b / c
e = 7 + d
|
a ) 140 , b ) 149 , c ) 156 , d ) 195 , e ) 100 | b | divide(divide(multiply(add(multiply(4000, const_2), multiply(subtract(const_12, const_1), 100)), const_12), const_2), add(add(multiply(const_3, 100), multiply(multiply(const_2, const_3), const_10)), add(const_2, const_3))) | a salt manufacturing company produced a total of 4000 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its ave 66 rage daily production for that year ? | "total production of salt by the company in that year = 4000 + 4100 + 4200 + . . . . + 5100 = 54600 . average monthly production of salt for that year = 54600 / 365 Γ’ β° Λ 149 answer : b" | a = 4000 * 2
b = 12 - 1
c = b * 100
d = a + c
e = d * 12
f = e / 2
g = 3 * 100
h = 2 * 3
i = h * 10
j = g + i
k = 2 + 3
l = j + k
m = f / l
|
a ) 882 , b ) 901 , c ) 1001 , d ) 1003 , e ) 1346 | a | add(multiply(add(subtract(330, const_100), const_1), const_3), add(multiply(const_3, const_3), multiply(multiply(multiply(const_3, const_3), const_10), const_2))) | a little girl is numbering her collection of butterflies by placing single - digit stickers under each specimen . if the girl has 330 butterflies , how many stickers does she need ? ( the numbers are consecutive and the number of the first butterfly is 1 ) . | for the first 9 butterflies we need 9 stickers . for the next 90 we need 2 stickers each or 180 stickers . for the next 900 butterflies we need 3 stickers each . the first 99 butterflies correspond to 189 stickers . subtract 99 from the total number of butterflies ( 330 ) . this leaves 231 butterflies that use 3 stickers each . so , multiply 231 by 3 to get 693 . add 693 to 189 stickers to get 882 stickers . answer : a | a = 330 - 100
b = a + 1
c = b * 3
d = 3 * 3
e = 3 * 3
f = e * 10
g = f * 2
h = d + g
i = c + h
|
a ) 48 , b ) 37 , c ) 39 , d ) 43 , e ) 42 | a | add(subtract(80, multiply(2, 17)), 2) | a batsman in his 17 th innings makes a score of 80 , and thereby increases his average by 2 . what is his average after the 17 th innings ? he had never been β not out β . | "average score before 17 th innings = 80 - 2 Γ 17 = 46 average score after 17 th innings = > 46 + 2 = 48 answer : a" | a = 2 * 17
b = 80 - a
c = b + 2
|
a ) 18 , b ) 19 , c ) 16 , d ) none , e ) can not be determined | a | divide(342, divide(342, 19)) | 19 times a number gives 342 . the number is | "explanation : let the number be ' n ' 19 Γ n = 342 β n = 18 correct option : a" | a = 342 / 19
b = 342 / a
|
a ) 17.3 , b ) 16.2 , c ) 15.3 , d ) 19.5 , e ) 18.1 | e | subtract(negate(8.11), multiply(subtract(2.56, 4.78), divide(subtract(2.56, 4.78), subtract(1.45, 2.56)))) | 1.45 , 2.56 , 4.78 , 8.11 , 12.55 , ( . . . . ) | "explanation : 1.11 , 2.22 , 3.33 , 4.44 , 5.55 , hence 5.55 = 18.1 answer : e" | a = negate - (
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a ) 114 , b ) 121 , c ) 122 , d ) 129 , e ) 136 | c | divide(factorial(subtract(add(const_4, 5), const_1)), multiply(factorial(5), factorial(subtract(const_4, const_1)))) | how many positive integers less than 1000 are multiples of 5 but not of 4 or 7 ? | "there are 1000 / 5 = 200 multiples of 5 . now we have to find the number of multiples of 5 and 4 that is 20 between 0 to 1000 and 5 and 7 that is 35 between 0 to 1000 . multiples of 20 = 1000 / 20 = 50 multiples . and multiples of 35 = 1000 / 35 = 28.5 so 28 multiples of 35 . so multiples of 5 between o to 1000 not including multiples of 20 and 35 are equal to 200 - 78 = 122 multiples . so the answer is c ." | a = 4 + 5
b = a - 1
c = math.factorial(b)
d = math.factorial(5)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
|
a ) a ) 10 % , b ) b ) 12 % , c ) c ) 16 % , d ) d ) 20 % , e ) e ) 22 % | c | multiply(subtract(divide(divide(multiply(subtract(const_100, 20), add(const_100, 45)), const_100), const_100), const_1), const_100) | a trader bought a car at 20 % discount on its original price . he sold it at a 45 % increase on the price he bought it . what percent of profit did he make on the original price ? | "original price = 100 cp = 80 s = 80 * ( 145 / 100 ) = 116 100 - 116 = 16 % c )" | a = 100 - 20
b = 100 + 45
c = a * b
d = c / 100
e = d / 100
f = e - 1
g = f * 100
|
a ) 45 minutes , b ) 50 minutes , c ) 55 minutes , d ) 52 minutes , e ) 35 minutes | c | subtract(const_60, divide(10, const_2)) | each day a man meets his wife at the train station after work , and then she drives him home . she always arrives exactly on time to pick him up . one day he catches an earlier train and arrives at the station an hour early . he immediately begins walking home along the same route the wife drives . eventually his wife sees him on her way to the station and drives him the rest of the way home . when they arrive home the man notices that they arrived 10 minutes earlier than usual . how much time did the man spend walking ? | as they arrived 10 minutes earlier than usual , they saved 10 minutes on round trip from home to station ( home - station - home ) - - > 5 minutes in each direction ( home - station ) - - > wife meets husband 5 minutes earlier the usual meeting time - - > husband arrived an hour earlier the usual meeting time , so he must have spent waking the rest of the time before their meeting , which is hour - 5 minutes = 55 minutes . answer : c | a = 10 / 2
b = const_60 - a
|
a ) 3 , b ) 5.4 , c ) 4.3 , d ) 6.5 , e ) 7 | b | divide(75, multiply(50, const_0_2778)) | in what time will a railway train 75 m long moving at the rate of 50 kmph pass a telegraph post on its way ? | "t = 75 / 50 * 18 / 5 = 5.4 sec answer : b" | a = 50 * const_0_2778
b = 75 / a
|
a ) 74 , b ) 78 , c ) 186 , d ) 92 , e ) 98 | c | add(multiply(add(multiply(6, const_3), 27), divide(add(multiply(6, const_3), 27), 5)), 6) | in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 27 to the thrice of the remainder . the dividend is | "divisor = ( 6 * 3 ) + 27 = 45 5 * quotient = 45 quotient = 9 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 9 ) + 6 = 186 . c )" | a = 6 * 3
b = a + 27
c = 6 * 3
d = c + 27
e = d / 5
f = b * e
g = f + 6
|
a ) 26 - 38 , b ) 50 - 34 , c ) 60 - 24 , d ) 42 - 42 , e ) 21 - 63 | a | divide(subtract(64, 12), const_2) | the sum of two numbers is 64 , and one of them is 12 more than the other . what are the two numbers ? | "in this problem , we are asked to find two numbers . therefore , we must let x be one of them . let x , then , be the first number . we are told that the other number is 12 more , x + 12 . the problem states that their sum is 64 : word problem = 64 the line over x + 12 is a grouping symbol called a vinculum . it saves us writing parentheses . we have : 2 x = 64 Γ’ Λ β 12 = 52 . x = 52 / 2 = 26 . this is the first number . therefore the other number is x + 12 = 26 + 12 = 38 . the sum of 26 + 38 is 64 . a" | a = 64 - 12
b = a / 2
|
a ) 2 : 4 , b ) 3 : 4 , c ) 3 : 6 , d ) 1 : 3 , e ) 3 : 36 | b | divide(divide(subtract(divide(36, const_2), const_10), const_2), add(divide(36, const_2), const_10)) | two whole numbers whose sum is 36 can not be in the ratio | b ) 3 : 4 | a = 36 / 2
b = a - 10
c = b / 2
d = 36 / 2
e = d + 10
f = c / e
|
a ) β 2 , b ) β 1 , c ) 1 , d ) 3 , e ) 5 | d | divide(9, 4) | if x β 2 + 3 β 4 = 9 β 4 , what is the value of x ? | "x β 2 + 3 β 4 = 9 β 4 let ' s multiply both sides by 4 . 2 x + 3 = 9 2 x = 6 x = 3 the answer is d ." | a = 9 / 4
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a ) 14 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) none | d | divide(subtract(24, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1)) | a man is 24 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is | "solution let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . then βΉ = βΊ ( x + 24 ) + 2 = 2 ( x + 2 ) βΉ = βΊ x + 26 = 2 x + 4 x = 22 . answer d" | a = 2 * 2
b = a - 2
c = 24 - b
d = 2 - 1
e = c / d
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a ) 2 , b ) 4 / 3 , c ) 15 / 4 , d ) 10 / 3 , e ) 17 / 5 | a | max(divide(subtract(const_1, multiply(add(divide(const_1, add(const_4, const_2)), divide(const_1, 4)), const_2)), divide(const_1, 4)), const_3) | two mechanics were working on your car . one can complete the given job in 4 hours , but the new guy takes eight hours . they worked together for the first two hours , but then the first guy left to help another mechanic on a different job . how long will it take the new guy to finish your car ? | "rate ( 1 ) = 1 / 4 rate ( 2 ) = 1 / 8 combined = 3 / 8 work done in 2 days = 3 / 4 work left = 1 / 4 rate * time = work left 1 / 8 * time = 1 / 4 time = 2 a" | a = 4 + 2
b = 1 / a
c = 1 / 4
d = b + c
e = d * 2
f = 1 - e
g = 1 / 4
h = f / g
i = max(h)
|
a ) 654 , b ) 655 , c ) 656 , d ) 657 , e ) 658 | e | multiply(divide(subtract(const_100, 30), const_100), 940.00) | yearly subscription to professional magazines cost a company $ 940.00 . to make a 30 % cut in the magazine budget , how much less must be spent ? | "total cost 940 940 * 30 / 100 = 282 so the cut in amount is 282 the less amount to be spend is 940 - 282 = 658 answer : e" | a = 100 - 30
b = a / 100
c = b * 940
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a ) 1 / 2 , b ) 1 / 3 , c ) 1.5 , d ) 3 , e ) 6 | b | divide(multiply(10, 0.31), 9) | water is leaking out from a cylinder container at the rate of 0.31 m ^ 3 per minute . after 10 minutes , the water level decreases 9 meters . what is value of the radius in meters ? | 10 * 0.31 = 3.1 = pi * r ^ 2 * h r ^ 2 = 3.1 / ( pi * 9 ) which is about 1 / 9 r = 1 / 3 the answer is b . | a = 10 * 0
b = a / 9
|
a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16 | d | subtract(6, 8) | what is 10 - 8 + 6 - 4 + . . . + ( - 16 ) ? | "the expression considers all even numbers between 10 and - 16 with alternate addition and subtraction of the numbers . the numbers to be used are : 10 , 8 , 6 , 4 , 2 , 0 , - 2 , - 4 , - 6 , - 8 , - 10 , - 12 , - 14 , and - 16 . now , the first term is positive and the next term is subtracted . so , the required expression becomes , 10 - 8 + 6 - 4 + 2 - 0 + ( - 2 ) - ( - 4 ) + ( - 6 ) - ( - 8 ) + ( - 10 ) - ( - 12 ) + ( - 14 ) - ( - 16 ) = 10 - 8 + 6 - 4 + 2 - 0 - 2 + 4 - 6 + 8 - 10 + 12 - 14 + 16 = 58 - 44 = 14 hence the correct answer choice is d ." | a = 6 - 8
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a ) 19 , b ) 20 , c ) 22 , d ) 23 , e ) 24 | a | divide(90, multiply(7, 1)) | how many 7 in between 1 to 90 ? | "7 , 17,27 , 37,47 , 57,67 , 70,71 , 72,73 , 74,75 , 76,77 ( two 7 ' s ) , 78 , 79,87 , 19 7 ' s between 1 to 90 answer : a" | a = 7 * 1
b = 90 / a
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a ) 232 m , b ) 238 m , c ) 224 m , d ) 331 m , e ) 236 m | c | subtract(224, multiply(16, speed(224, 32))) | for a race a distance of 224 meters can be covered by p in 16 seconds and q in 32 seconds . by what distance does p defeat q eventually ? | "explanation : this is a simple speed time problem . given conditions : = > speed of p = 224 / 16 = 14 m / s = > speed of q = 224 / 32 = 7 m / s = > difference in time taken = 16 seconds therefore , distance covered by p in that time = 14 m / s x 16 seconds = 224 metres answer : c" | a = 16 * speed
b = 224 - a
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a ) 52 % , b ) 40 % , c ) 30 % , d ) 20 % , e ) 10 % | c | multiply(divide(divide(25, const_100), subtract(const_1, divide(25, const_100))), const_100) | a merchant has selected two items to be placed on sale , one of which currently sells for 25 percent less than the other . if he wishes to raise the price of the cheaper item so that the two items are equally priced , by what percentage must he raise the price of the less expensive item ? | "expensive item = $ 100 ; cheap item = $ 75 ; we must increase $ 75 to $ 100 , so by $ 25 , which is approximately 30 % increase : ( 100 - 75 ) / 75 = 1 / 3 = ~ 0.33 answer : c ." | a = 25 / 100
b = 25 / 100
c = 1 - b
d = a / c
e = d * 100
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a ) 11 , b ) 14 , c ) 18 , d ) 12 , e ) 16 | e | divide(1540, multiply(multiply(const_2, divide(add(add(multiply(const_3, const_100), multiply(const_1, const_10)), const_4), const_100)), 15)) | if the wheel is 15 cm then the number of revolutions to cover a distance of 1540 cm is ? | "2 * 22 / 7 * 15 * x = 1540 = > x = 16 answer : e" | a = 3 * 100
b = 1 * 10
c = a + b
d = c + 4
e = d / 100
f = 2 * e
g = f * 15
h = 1540 / g
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a ) 13 % , b ) 9.22 % , c ) 9 % , d ) 14 % , e ) 12.28 % | e | multiply(subtract(const_1, multiply(subtract(const_1, divide(14, const_100)), add(const_1, divide(2, const_100)))), const_100) | you enter a weight loss challenge game and manage to lose 14 % of your body weight . for the final weigh in you are forced to wear clothes that add 2 % to your weight . what percentage of weight loss is measured at the final weigh in ? | "( 100 % - 14 % ) * ( 100 % + 2 % ) = 0.86 * 1.02 = 12.28 % the weigh in records your weight loss at 12.28 % ! the answer is e" | a = 14 / 100
b = 1 - a
c = 2 / 100
d = 1 + c
e = b * d
f = 1 - e
g = f * 100
|
a ) 1 : 3 , b ) 1 : 2 , c ) 1 : 1 , d ) 2 : 1 , e ) 3 : 1 | b | divide(0.865, add(0.8, 0.9)) | in what proportion must flour at $ 0.8 per pound be mixed with flour at $ 0.9 per pound so that the mixture costs $ 0.865 per pound ? | using weighted average method : let x be the proportion in which the $ 0.8 per pound flour is mixed with $ 0.9 per pound flour . thus 0.8 * x + 0.9 * ( 1 - x ) = 0.865 0.9 β 0.1 x = 0.865 x = 0.35 thus ratio of both flours is 1 : 2 b | a = 0 + 8
b = 0 / 865
|
a ) 135 , b ) 10 , c ) 15 , d ) 40 , e ) 22 | a | divide(add(subtract(divide(rectangle_area(const_360, const_1000), const_10), multiply(const_1000, multiply(const_3, const_2))), add(multiply(const_3, const_1000), multiply(36, const_10))), divide(add(subtract(divide(rectangle_area(const_360, const_1000), const_10), multiply(const_1000, multiply(const_3, const_2))), add(multiply(const_3, const_1000), multiply(36, const_10))), const_10)) | a rectangular block 12 cm by 20 cm by 36 cm is cut into an exact number of equal cubes . find the least possible number of cubes ? | "volume of the block = 12 * 20 * 36 = 8640 cm ^ 3 side of the largest cube = h . c . f of 12 , 20,36 = 4 cm volume of the cube = 4 * 4 * 4 = 64 cm ^ 3 number of cubes = 8640 / 64 = 135 answer is a" | a = rectangle_area / (
b = a - 10
c = 3 * 2
d = 1000 * c
e = b + d
f = 3 * 1000
g = 36 * 10
h = f + g
i = e / h
|
a ) 600 , b ) 480 , c ) 538 , d ) 650 , e ) 560 | c | subtract(subtract(multiply(45, 10), multiply(22, 20)), multiply(22, 16)) | the average of 45 results is 10 . the average of first 22 of them is 16 and that of last 22 is 20 . find the 23 result ? | "23 th result = sum of 45 results - sum of 44 results 10 * 45 - 16 * 22 + 20 * 22 = 450 - 352 + 440 = 538 answer is c" | a = 45 * 10
b = 22 * 20
c = a - b
d = 22 * 16
e = c - d
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a ) 5 sec , b ) 10 sec , c ) 20 sec , d ) 15 sec , e ) 25 sec | b | divide(200, add(15, 5)) | an escalator moves towards the top level at the rate of 15 ft . sec and its length is 200 feet . if a person walks on the moving escalator at the rate of 5 feet per second towards the top level , how much time does he take to cover the entire length . | "explanation : time taken to cover the entire length = tot . dist / resultant speed = 200 / ( 15 + 5 ) = 10 sec answer : b" | a = 15 + 5
b = 200 / a
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a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | b | subtract(subtract(add(multiply(8, const_2), multiply(4, const_2)), const_12), 10) | 4 barrels of water have an average capacity of 8 gallons . what is the maximum possible capacity of the smallest barrel e if the median is 10 gallons ? | suppose 4 barrels are b 1 , b 2 , b 3 , b 4 in ascending capacity . ( b 1 + b 2 + b 3 + b 4 ) / 4 = 8 b 1 + b 2 + b 3 + b 4 = 32 median is 10 . . . . . . . as the no . of terms are even i . e 4 , median = ( b 2 + b 3 ) / 2 = = > b 2 + b 3 = 20 now we have b 1 + b 4 = 32 - 20 = 12 only the following possible cases can be there : 19 , 1111 110 , 1011 210 , 1010 max value of smallest barrel e = 2 = b | a = 8 * 2
b = 4 * 2
c = a + b
d = c - 12
e = d - 10
|
a ) s . 800 , b ) s . 2400 , c ) s . 3000 , d ) s . 3200 , e ) s . 4200 | c | multiply(subtract(multiply(divide(1200, 2), 3), 1200), 5) | the ratio of incomes of two person p 1 and p 2 is 5 : 4 and the ratio of their expenditures is 3 : 2 . if at the end of the year , each saves rs . 1200 , then what is the income of p 1 ? | "let the income of p 1 and p 2 be rs . 5 x and rs . 4 x respectively and let their expenditures be rs . 3 y and 2 y respectively . then , 5 x β 3 y = 1200 β¦ ( i ) and 4 x β 2 y = 1200 β¦ β¦ . . ( ii ) on multiplying ( i ) by 2 , ( ii ) by 3 and subtracting , we get : 2 x = 1200 - > x = 600 p 1 β s income = rs 5 * 600 = rs . 3000 answer : c" | a = 1200 / 2
b = a * 3
c = b - 1200
d = c * 5
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a ) 24 , b ) 26 , c ) 42 , d ) 46 , e ) 48 | a | add(multiply(add(10, const_1), 2), 2) | in a two - digit number , if it is known that its unit ' s digit exceeds its 10 ' s digit by 2 and that the product of the given number and the sum of its digits is equal to 144 , then the number is : | let the ten ' s digit be x . then , unit ' s digit = x + 2 . number = 10 x + ( x + 2 ) = 11 x + 2 sum of digits = x + ( x + 2 ) = 2 x + 2 ( 11 x + 2 ) ( 2 x + 2 ) = 144 2 x 2 + 26 x - 140 = 0 ( x - 2 ) ( 11 x + 35 ) = 0 x = 2 hence , required number = 11 x + 2 = 24 . answer : a | a = 10 + 1
b = a * 2
c = b + 2
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a ) 120 , b ) 140 , c ) 130 , d ) 150 , e ) 160 | b | subtract(100, subtract(power(2, divide(100, 70)), const_1)) | what is the greatest value of positive integer x such that 2 ^ x is a factor of 100 ^ 70 ? | "put in simple words , we need to find the highest power of 2 in 100 ^ 70 100 = 2 ^ 2 * 5 ^ 2 therefore 100 ^ 70 = ( 2 ^ 2 * 5 ^ 2 ) ^ 70 = 2 ^ 140 * 5 ^ 140 answer : b" | a = 100 / 70
b = 2 ** a
c = b - 1
d = 100 - c
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a ) 1 / 11 , b ) 2 / 23 , c ) 3 / 34 , d ) 4 / 45 , e ) 5 / 56 | a | divide(const_4, divide(factorial(12), multiply(factorial(2), factorial(subtract(12, 2))))) | a certain box has 12 cards and each card has one of the integers from 1 to 12 inclusive . each card has a different number . if 2 different cards are selected at random , what is the probability that the sum of the numbers written on the 2 cards is less than the average ( arithmetic mean ) of all the numbers written on the 12 cards ? | "the average of the numbers is 6.5 the total number of ways to choose 2 cards from 12 cards is 12 c 2 = 66 . the ways to choose 2 cards with a sum less than the average are : { 1,2 } , { 1,3 } , { 1,4 } , { 1,5 } , { 2,3 } , { 2,4 } the probability is 6 / 66 = 1 / 11 the answer is a ." | a = math.factorial(12)
b = math.factorial(2)
c = 12 - 2
d = math.factorial(c)
e = b * d
f = a / e
g = 4 / f
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a ) 6 , b ) 8 , c ) 9 , d ) 5 , e ) 12 | e | add(4, const_1) | the average of first five multiples of 4 is ? | "average = 4 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 60 / 5 = 12 . answer : e" | a = 4 + 1
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a ) 3.0 , b ) 2.25 , c ) 2.08 , d ) 1.75 , e ) 2.0 | c | divide(divide(multiply(5, 50), const_2), 60) | priya takes a trip and drives 5 hours from town x to town z at a rate of 50 miles per hour . on her way back , priya drives 60 miles per hour and stops in town y which is midway between town x and town z . how many hours does it take scott to drive from town z to town y ? | distance from x to z = 5 hr * 50 mph = 250 miles hence distance from y to z = 1 / 2 * 250 = 125 time = 125 / 60 = 2.08 hrs imo : c | a = 5 * 50
b = a / 2
c = b / 60
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a ) 75 , b ) 85 , c ) 64 , d ) 51 , e ) 45 | a | add(50, divide(50, const_2)) | in a ratio which is equal to 4 : 6 , if the antecedent is 50 , then the consequent is ? | we have 4 / 6 = 50 / x 4 x = 50 * 6 x = 75 consequent = 75 answer is a | a = 50 / 2
b = 50 + a
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a ) 65 , b ) 69 , c ) 75 , d ) 85 , e ) 90 | c | divide(add(add(add(add(76, 65), 82), 67), 85), add(const_1, const_4)) | shekar scored 76 , 65 , 82 , 67 and 85 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ? | "explanation : average = ( 76 + 65 + 82 + 67 + 85 ) / 5 = 375 / 5 = 75 hence average = 75 answer : c" | a = 76 + 65
b = a + 82
c = b + 67
d = c + 85
e = 1 + 4
f = d / e
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a ) 15 sec , b ) 10 sec , c ) 12 sec , d ) 8 sec , e ) 9 sec | a | divide(210, add(12, 2)) | an escalator moves towards the top level at the rate of 12 ft . sec and its length is 210 feet . if a person walks on the moving escalator at the rate of 2 feet per second towards the top level , how much time does he take to cover the entire length . | "time taken to cover the entire length = tot . dist / resultant speed = 210 / ( 12 + 2 ) = 15 sec answer : a" | a = 12 + 2
b = 210 / a
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a ) s . 200.63 , b ) s . 250.63 , c ) s . 290.63 , d ) s . 300.63 , e ) s . 363.63 | e | divide(multiply(800, multiply(add(const_1, const_4), const_2)), multiply(add(multiply(add(const_1, const_4), const_2), const_1), const_2)) | two employees x and y are paid a total of rs . 800 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ? | "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 800 but x = 120 % of y = 120 y / 100 = 12 y / 10 β΄ 12 y / 10 + y = 800 β y [ 12 / 10 + 1 ] = 800 β 22 y / 10 = 800 β 22 y = 8000 β y = 8000 / 22 = rs . 363.63 e )" | a = 1 + 4
b = a * 2
c = 800 * b
d = 1 + 4
e = d * 2
f = e + 1
g = f * 2
h = c / g
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a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 28 | e | multiply(7, 4) | elena β s bread recipe calls for 5 ounces of butter for each 7 cups of flour used . she needs to make 4 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ? | solving through algebra route : 5 b + 7 f = x amount if we multiply this equation with 4 we get : 20 b + 28 f = 4 x therefore , we got 20 ounces of butter and 4 x amount of quantity when we use 28 ounces of floor . ans : e | a = 7 * 4
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a ) 40 , b ) 200 , c ) 266 , d ) 267 , e ) 600 | d | divide(subtract(75000, 45000), multiply(divide(15, const_100), 750)) | tom left a job paying $ 75000 per year to accept a sales job paying $ 45000 per year plus 15 percent commission . if each of his sales is for $ 750 , what is the least number of sales he must make per year if he is not to lose money because of the change ? | in order not to lose money because of the change tom ' s total commission must beat least $ 75000 - $ 45000 = $ 30000 , so total sales must beat least $ 30000 / 0.15 = $ 200000 . which means that he must makeat least $ 200000 / 750 = 800 / 3 = 266.6 sales , so 267 sales . answer : d . | a = 75000 - 45000
b = 15 / 100
c = b * 750
d = a / c
|
a ) 72 , b ) 85 , c ) 107 , d ) 98 , e ) 108 | c | subtract(add(subtract(192, 59), 23), 49) | there are 192 items that are members of set u . of these items , 49 are members of set b , 59 are not members of either of set a or set b , and 23 are members of both sets a and b . how many of the members of set u are members of set a ? | "you had the answer almost right . the x = 84 refers to only set a . however what ' s being asked is how many members are part of set a . this will include : 1 . only set a 2 . set a and set b so the answer is set a = 84 + set ab = 84 + 23 = 17 c" | a = 192 - 59
b = a + 23
c = b - 49
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a ) 270 km , b ) 890 km , c ) 684 km , d ) 320 km , e ) 560 km | e | divide(multiply(multiply(35, const_2), multiply(40, const_2)), subtract(multiply(multiply(40, const_2), const_1), multiply(multiply(35, const_2), const_1))) | a family travelled for 12 hours . they covered the first half of the distance at 35 kmph and remaining half of the distance at 40 kmph . find the distance travelled by the family ? | let the distance travelled be x km . total time = ( x / 2 ) / 35 + ( x / 2 ) / 40 = 12 = > x / 70 + x / 80 = 12 = > ( 8 x + 7 x ) / 560 = 12 = > x = 560 km answer : e | a = 35 * 2
b = 40 * 2
c = a * b
d = 40 * 2
e = d * 1
f = 35 * 2
g = f * 1
h = e - g
i = c / h
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a ) 20 , b ) 30 , c ) 50 , d ) 80 , e ) 100 | e | subtract(subtract(250, 80), 20) | of the 250 employees at company x , 80 are full - time , and 100 have worked at company x for at least a year . there are 20 employees at company x who aren β t full - time and haven β t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ? | "full time employee who have not worked for at least one year = a full time employee who have worked for at least one year = b non full time employee who have worked for at least one year = c non full time employee who have not worked for at least one year = d a + b + c + d = 150 a + b = 80 i . e . c + d = 70 b + c = 100 i . e . a + d = 50 d = 20 i . e . c = 70 - 20 = 50 i . e . b = 100 - 50 = 50 i . e . a = 80 - 50 = 30 b = 100 answer : option e" | a = 250 - 80
b = a - 20
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a ) 2277 , b ) 2667 , c ) 9000 , d ) 2766 , e ) 1811 | c | divide(360, subtract(power(add(divide(20, const_100), const_1), 2), add(multiply(divide(20, const_100), 2), const_1))) | the difference between the compound interest compounded annually and simple interest for 2 years at 20 % per annum is rs . 360 . find the principal ? | "p = 360 ( 100 / 5 ) ^ 2 = > p = 9000 answer : c" | a = 20 / 100
b = a + 1
c = b ** 2
d = 20 / 100
e = d * 2
f = e + 1
g = c - f
h = 360 / g
|
a ) 45 , b ) 62 , c ) 75 , d ) 83 , e ) 90 | d | subtract(subtract(multiply(6, 63), multiply(3, 65)), 100) | the average of 6 integers is 63 , and none of these integers is greater than 100 . if the average of 3 of the integers is 65 , what is the least possible value of one of the other two integers ? | when it comes to averages , we know thataverage value = ( sum of n values ) / n we can rewrite this into a useful formula : sum of n values = ( average value ) ( n ) the average of five integers is 63 so , the sum of all 5 integers = ( 63 ) ( 6 ) = 378 the average of three of the integers is 65 so , the sum of the 3 integers = ( 65 ) ( 3 ) = 195 so , the sum of the 2 remaining integers = 378 - 195 = 183 if the sum of the 2 remaining integers = 183 , and we want to minimize one value , we must maximize the other value . 100 is the maximum value so let 1 integer = 100 , which means the other must equal 83 answer : d | a = 6 * 63
b = 3 * 65
c = a - b
d = c - 100
|
a ) 3 hours , b ) 2.4 hours , c ) 1.4 hours , d ) 1 hour , e ) none of these | d | divide(600, divide(multiply(200, 30), const_10)) | in a flight of 600 km , an aircraft was slowed down due to bad weather . its average speed for the trip was reduced by 200 km / hr and the time of flight increased by 30 minutes . what is the duration of the flight ? | "explanation : let the duration of the flight be x hours . then 600 / x β 600 / x + 1 / 2 = 200 600 / x β 1200 / 2 x + 1 = 200 x ( 2 x + 1 ) = 3 2 x 2 + x β 3 = 0 = > ( 2 x + 3 ) ( x β 1 ) = 0 neglecting the negative value for x we get x = 1 option d" | a = 200 * 30
b = a / 10
c = 600 / b
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a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | e | floor(divide(reminder(power(7, reminder(1415, add(const_4, const_1))), const_100), const_10)) | what is the tens digit of 7 ^ 1415 ? | "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 2401 7 ^ 5 = 16807 7 ^ 6 = 117649 we should see this as pattern recognition . we have a cycle of 4 . ( we can multiply the last 2 digits only as we care about ten ' s digit ) 0 , 4 , 4 , 0 . 1415 = 4 * 353 + 3 the ten ' s digit will be 4 . answer e" | a = 4 + 1
b = 7 ** reminder
c = reminder / (
d = math.floor(c, 100)
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a ) 20 , b ) 24 , c ) 48 , d ) 36 , e ) 60 | c | sqrt(divide(4, add(power(4, 3), add(power(2, 3), power(3, const_2))))) | the ratio of 2 numbers is 3 : 4 and their h . c . f . is 4 . their l . c . m . is ? | "let the numbers be 3 x and 4 x their h . c . f . = 4 so the numbers are 3 * 4 , 4 * 4 = 12,16 l . c . m . = 48 answer is c" | a = 4 ** 3
b = 2 ** 3
c = 3 ** 2
d = b + c
e = a + d
f = 4 / e
g = math.sqrt(f)
|
a ) 35 , b ) 20 , c ) 47 , d ) 36 , e ) 40 | e | subtract(140, divide(140, add(divide(2, 5), const_1))) | a 140 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ? | "1 : 2 / 5 = 5 : 2 2 / 7 * 140 = 40 answer : e" | a = 2 / 5
b = a + 1
c = 140 / b
d = 140 - c
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a ) positive , b ) divisible by 2 . , c ) divisible by 3 , d ) divisible by 4 . , e ) divisible by 5 | c | add(add(power(add(add(divide(subtract(subtract(3, const_10), const_2), const_4), const_2), const_2), const_2), power(add(add(add(divide(subtract(subtract(3, const_10), const_2), const_4), const_2), const_2), const_2), const_2)), add(power(divide(subtract(subtract(3, const_10), const_2), const_4), const_2), power(add(divide(subtract(subtract(3, const_10), const_2), const_4), const_2), const_2))) | the sum of 3 consecutive numbers is definitely : | "if 1 st term is x : x + ( x + 1 ) + ( x + 2 ) = 3 x + 3 - - - > always divisible by 3 if 2 nd term is x : ( x - 1 ) + x + ( x + 1 ) = 3 x - - - > always divisible by 3 if 3 rd term is x : ( x - 2 ) + ( x - 1 ) + x = 3 x - 3 - - - > always divisible by 3 answer : c" | a = 3 - 10
b = a - 2
c = b / 4
d = c + 2
e = d + 2
f = e ** 2
g = 3 - 10
h = g - 2
i = h / 4
j = i + 2
k = j + 2
l = k + 2
m = l ** 2
n = f + m
o = 3 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 3 - 10
t = s - 2
u = t / 4
v = u + 2
w = v ** 2
x = r + w
y = n + x
|
a ) 150 m , b ) 200 m , c ) 125 m , d ) 115 m , e ) none | a | multiply(100, divide(12, 8)) | a tree is 12 m tall and casts an an 8 m long shadow . at the same time , a flag pole caste a 100 m long shadow . how long is the flag pole ? | answer β΅ 8 m shadow means original height = 12 m β΄ 1 m shadow means original height = 12 / 8 m β΄ 100 m shadow means original height = ( 12 / 8 ) x 100 m = ( 6 / 4 ) x 100 = 6 x 25 = 150 m correct option : a | a = 12 / 8
b = 100 * a
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a ) 53 , b ) 58 , c ) 51 , d ) 60 , e ) 62 | a | add(multiply(add(multiply(4, const_3), 2), divide(add(multiply(4, const_3), 2), 3)), 4) | in a division sum , the remainder is 4 and the divisor is 3 times the quotient and is obtained by adding 2 to the thrice of the remainder . the dividend is : | "diver = ( 4 * 3 ) + 2 = 14 4 * quotient = 14 quotient = 3.5 dividend = ( divisor * quotient ) + remainder dividend = ( 14 * 3.5 ) + 4 = 53 a" | a = 4 * 3
b = a + 2
c = 4 * 3
d = c + 2
e = d / 3
f = b * e
g = f + 4
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a ) 171 , b ) 281 , c ) 361 , d ) 461 , e ) 561 | b | add(multiply(divide(add(20, 30), const_2), add(subtract(30, 20), const_1)), add(divide(subtract(30, 20), const_2), const_1)) | if x is equal to the sum of the integers from 20 to 30 , inclusive , and y is the number of even integers from 20 to 30 , inclusive , what is the value of x + y ? | "sum s = n / 2 { 2 a + ( n - 1 ) d } = 11 / 2 { 2 * 20 + ( 11 - 1 ) * 1 } = 11 * 25 = 275 = x number of even number = ( 30 - 20 ) / 2 + 1 = 6 = y x + y = 275 + 6 = 281 b" | a = 20 + 30
b = a / 2
c = 30 - 20
d = c + 1
e = b * d
f = 30 - 20
g = f / 2
h = g + 1
i = e + h
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a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 % | b | sqrt(36) | the difference between c . i . and s . i . on an amount of $ 10,000 for 2 years is $ 36 . what is the rate of interest per annum ? | "$ 36 is the interest on the first year of interest . let x be the interest rate . the interest after the first year is 10000 * x . the interest on the first year ' s interest is 10000 * x * x 10000 * x ^ 2 = 36 x = 0.06 the answer is b ." | a = math.sqrt(36)
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['a ) 1', 'b ) 5', 'c ) 41', 'd ) 45', 'e ) 46'] | c | multiply(subtract(divide(2200, 60), floor(divide(2200, 60))), 60) | there are 60 slots around a circle , numbered 1 to 60 . a man starts fromthe first slot and jumps to the 5 th slot . from there he jumps to the 9 th slot andso on . in which slot will he land in his 2200 th jump ? | every 15 th jump , he comes back to 1 st position so , 2200 / 15 = remainder 10 hence 10 th position is 41 st slot answer : c | a = 2200 / 60
b = 2200 / 60
c = math.floor(b)
d = a - c
e = d * 60
|
a ) 5.2 hrs , b ) 2.9 hrs , c ) 1.9 hrs , d ) 6 hrs , e ) 5 hrs | d | divide(const_1, subtract(divide(const_1, 3), divide(const_1, 6))) | a cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 6 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ? | "net part filled in 1 hour = ( 1 / 3 - 1 / 6 ) = 1 / 6 the cistern will be filled in 6 / 1 hrs i . e . , 6 hrs . answer : d" | a = 1 / 3
b = 1 / 6
c = a - b
d = 1 / c
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a ) 23000 , b ) 22000 , c ) 20000 , d ) 25000 , e ) 30000 | e | divide(3000, divide(10, const_100)) | in an election between two candidates , the winner has a margin of 10 % of the votes polled . if 3000 people change their mind and vote for the loser , the loser would have won by a margin of 10 % of the votes polled . find the total number of votes polled in the election ? | "winner - looser 55 % - 45 % if 3000 people change their mind and vote for the loser : winner - looser 45 % - 55 % thus 3,000 people compose 10 % of all voters , which means that the total number of votes is 30,000 . answer : e ." | a = 10 / 100
b = 3000 / a
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a ) $ 3556.25 , b ) $ 3988.89 , c ) $ 3836.56 , d ) $ 3745.56 , e ) $ 3428.56 | b | subtract(multiply(floor(divide(divide(divide(add(multiply(9, 1300), multiply(18, 12000)), add(9, 18)), const_2), const_1000)), const_1000), add(const_10, const_1)) | a departmental store has 9 managers and 18 associates . the 9 managers have an average salary of $ 1300 . the 18 associates have an average salary of $ 12000 . what is the average salary for the departmental store ? | number of managers is 9 their average salary is $ 1300 number of associates is 18 their average salary is $ 12,000 total salary of managers is 9 * 1300 = $ 11700 total salary of associates is 18 * 12,000 = $ 96,000 total salary for the departmental store is 96,000 + 11700 = 107700 average salary for the departmental store is 107700 / 9 + 18 = 3988.89 answer is b | a = 9 * 1300
b = 18 * 12000
c = a + b
d = 9 + 18
e = c / d
f = e / 2
g = f / 1000
h = math.floor(g)
i = h * 1000
j = 10 + 1
k = i - j
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a ) 4 , b ) 6 , c ) 8 , d ) 16 , e ) 18 | d | add(power(const_2, const_2), const_2) | how many different positive integers are factors of 256 ? | "16 Γ 16 = 4 ^ 2 Γ 4 ^ 2 so total factors = ( 3 + 1 ) ( 3 + 1 ) = 16 answer : d" | a = 2 ** 2
b = a + 2
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a ) 240 / 1576 , b ) 240 / 1542 , c ) 240 / 1547 , d ) 240 / 1528 , e ) 240 / 1529 | c | multiply(divide(divide(5, 34), divide(7, 48)), divide(2, 13)) | find the fraction which has the same ratio to 2 / 13 that 5 / 34 has to 7 / 48 ? | "p : 2 / 13 = 5 / 34 : 7 / 48 as the product of the means is equal to the product of the extremes . p * 7 / 48 = 2 / 13 * 5 / 34 p * 7 / 48 = 10 / 442 p = 480 / 3094 = > p = 240 / 1547 answer : c" | a = 5 / 34
b = 7 / 48
c = a / b
d = 2 / 13
e = c * d
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a ) 10 % , b ) 15 % , c ) 20 % , d ) 36 % , e ) 50 % | d | subtract(multiply(multiply(subtract(const_1, divide(20, const_100)), add(const_1, divide(70, const_100))), const_100), const_100) | a furniture store owner decided to drop the price of her recliners by 20 % to spur business . by the end of the week she had sold 70 % more recliners . what is the percentage increase of the gross ? | say a recliner is actually worth $ 100 if she sells 100 recliners then she earns $ 10000 after the discount of 20 % , she will earn $ 80 per recliner and she sells 70 % more ie . , 170 recliners hence her sales tields 170 * 80 = $ 13600 increase in sales = 13600 - 10000 = $ 3600 so % increase = 3600 * 100 / 10000 = 36 % d is the answer | a = 20 / 100
b = 1 - a
c = 70 / 100
d = 1 + c
e = b * d
f = e * 100
g = f - 100
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a ) 448 , b ) 488 , c ) 16748 , d ) 548 , e ) 560 | c | multiply(54, const_10) | the least number , which when divided by 12 , 31 , 20 and 54 leaves in each case a remainder of 8 is : | "required number = ( l . c . m . of 12 , 31 , 20 , 54 ) + 8 = 16740 + 8 = 16748 . answer : c" | a = 54 * 10
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a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 5 , d ) 3 / 4 , e ) 3 / 5 | d | divide(divide(subtract(40, 10), subtract(50, 40)), const_4) | timothy drove at an average speed of 10 mph for some time and then at an average speed of 50 mph for the rest of the journey . if he made no stops during the trip and his average speed for the entire journey was 40 mph , for what fraction of the total time did he drive at 50 mph ? | we do n ' t need to get into calculations for solving this question . we can use the concept of weighted averages . we know that if the average speed for the entire journey was 40 mph , then he drove at 50 mph for a longer duration of time . 10 30 10 - - 40 - - - - - - 50 this shows that you can divide the entire journey into 4 equal parts . thus , 3 / 4 part he drove at 50 mph and 1 / 4 part he drove at 10 mph . answer : d | a = 40 - 10
b = 50 - 40
c = a / b
d = c / 4
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a ) 2 , b ) 4 , c ) 6 , d ) 7 , e ) 10 | d | subtract(divide(420, 10), divide(420, 12)) | a certain car uses 12 gallons of gasoline in traveling 420 miles . in order for the car to travel the same distance using 10 gallons of gasoline , by how many miles per gallon must the car β s gas mileage be increased ? | "420 / 10 = 42 the difference is 42 - 35 = 7 . answer d" | a = 420 / 10
b = 420 / 12
c = a - b
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a ) 40 , b ) 52 , c ) 65 , d ) 80 , e ) 98 | c | divide(subtract(multiply(divide(52, const_100), 120), multiply(divide(26, const_100), 120)), subtract(const_1, divide(52, const_100))) | in august , a cricket team that played 120 matches won 26 % of the games it played . after a continuous winning streak , this team raised its average to 52 % . how many matches did the team win to attain this average ? | "let the no of matches played more = x so , ( 120 + x ) * 52 / 100 = 31.2 + x by solving we get x = 65 answer : c" | a = 52 / 100
b = a * 120
c = 26 / 100
d = c * 120
e = b - d
f = 52 / 100
g = 1 - f
h = e / g
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a ) 55 kg , b ) 65 kg , c ) 75 kg , d ) 45 kg , e ) 63 kg | a | subtract(add(multiply(60, const_2), multiply(70, const_2)), multiply(65, const_3)) | the average weight of a , b and c is 65 kg . if the average weight of a and b be 60 kg and that of b and c be 70 kg , then the weight of a is : | "explanation let a , b , c represent their respective weights . then , we have : a + b + c = ( 65 x 3 ) = 195 Γ’ β¬ Β¦ . ( i ) a + b = ( 60 x 2 ) = 120 Γ’ β¬ Β¦ . ( ii ) b + c = ( 70 x 2 ) = 140 Γ’ β¬ Β¦ . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 260 Γ’ β¬ Β¦ . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 65 . substituting b in ( ii ) a + 65 = 120 a = 55 a Γ’ β¬ β’ s weight = 55 kg . answer a" | a = 60 * 2
b = 70 * 2
c = a + b
d = 65 * 3
e = c - d
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a ) 4 , b ) 3 , c ) 5 , d ) 2 , e ) 1 | a | inverse(add(inverse(28), add(inverse(7), inverse(14)))) | a , b and c can do a piece of work in 7 days , 14 days and 28 days respectively . how long will they taken , if all the three work together ? | "1 / 7 + 1 / 14 + 1 / 28 = 7 / 28 = 1 / 4 = > 4 days answer a" | a = 1/(28)
b = 1/(7)
c = 1/(14)
d = b + c
e = a + d
f = 1/(e)
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a ) 10 , b ) 20 , c ) 60 , d ) 30 , e ) 70 | d | add(multiply(sqrt(15), const_10), const_3) | if a ^ 2 + b ^ 2 = 15 and ab = 10 , what is the value of the expression ( a - b ) ^ 2 + ( a + b ) ^ 2 | "( a - b ) ^ 2 = a ^ 2 + b ^ 2 - 2 ab = 15 - 20 = - 5 ( a + b ) ^ 2 = a ^ 2 + b ^ 2 + 2 ab = 15 + 20 = 35 so ( a + b ) ^ 2 + ( a - b ) ^ 2 = 35 - 5 = 30 d" | a = math.sqrt(15)
b = a * 10
c = b + 3
|
a ) 35 , b ) 27 , c ) 25 , d ) 15 , e ) 55 | b | multiply(105, divide(multiply(15, 3), add(add(multiply(10, 7), multiply(12, 5)), multiply(15, 3)))) | a , b and c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 105 , then how much amount should c pay as his share of rent ? | "a : b : c = 10 Γ 7 : 12 Γ 5 : 15 Γ 3 = 2 Γ 7 : 12 Γ 1 : 3 Γ 3 = 14 : 12 : 9 amount that c should pay = 105 Γ 9 / 35 = 3 Γ 9 = 27 answer is b ." | a = 15 * 3
b = 10 * 7
c = 12 * 5
d = b + c
e = 15 * 3
f = d + e
g = a / f
h = 105 * g
|
a ) 35 , b ) 15 , c ) 20 , d ) 25 , e ) 30 | d | multiply(const_60, divide(multiply(50, divide(15, const_60)), subtract(80, 50))) | mary passed a certain gas station on a highway while traveling west at a constant speed of 50 miles per hour . then , 15 minutes later , paul passed the same gas station while traveling west at a constant speed of 80 miles per hour . if both drivers maintained their speeds and both remained on the highway for at least 2 hours , how long after he passed the gas station did paul catch up with mary ? | d = rt m : r = 50 mph , t = t + 1 / 4 hr d = 50 ( t + 1 / 4 ) p : r = 80 , t = t d = 80 t since they went the same distance : 50 t + 50 / 4 = 80 t 30 t = 50 / 4 = 50 / 120 * 60 = 25 min t = 25 min d | a = 15 / const_60
b = 50 * a
c = 80 - 50
d = b / c
e = const_60 * d
|
a ) 2,000 , b ) 3,000 , c ) 6,000 , d ) 8,000 , e ) 9,000 | d | multiply(divide(divide(subtract(subtract(multiply(multiply(2, const_4), const_1000), multiply(multiply(multiply(2, const_4), const_1000), divide(3, 7))), multiply(subtract(multiply(multiply(2, const_4), const_1000), multiply(multiply(multiply(2, const_4), const_1000), divide(3, 7))), divide(2, 9))), const_1000), const_4), 2) | in a recent head - to - head run - off election , 18,000 absentee ballets were cast . 3 / 7 of the absentee ballets were thrown out and 2 / 9 of the remaining absentee ballets were cast for candidate a . how many absentee votes did candidate b receive ? | "4 / 7 * 7 / 9 ( total absentee votes ) = 4 / 9 ( total votes ) = 4 / 9 * 18000 = 8000 answer is d" | a = 2 * 4
b = a * 1000
c = 2 * 4
d = c * 1000
e = 3 / 7
f = d * e
g = b - f
h = 2 * 4
i = h * 1000
j = 2 * 4
k = j * 1000
l = 3 / 7
m = k * l
n = i - m
o = 2 / 9
p = n * o
q = g - p
r = q / 1000
s = r / 4
t = s * 2
|
a ) 2 , b ) 7 , c ) 6 , d ) 46 , e ) 3 | d | add(divide(subtract(100, 10), 2), const_1) | how many multiples of 2 are there between 10 and 100 ( both are inclusive ) ? | the answer is ( 100 - 10 ) / 2 + 1 = 46 answer is d | a = 100 - 10
b = a / 2
c = b + 1
|
a ) 76 , b ) 70 , c ) 55 , d ) 65 , e ) 22 | b | add(divide(11.9, divide(subtract(25, 8), const_100)), 8) | if 25 % of a number exceeds 8 % of it by 11.9 , then find the number ? | "use the elimination method to find the correct option . of all the options only 70 fits 25 % of 70 = 17.5 8 % of 70 = 5.6 17.5 - 5.6 = 11.9 required number is 70 . answer : b" | a = 25 - 8
b = a / 100
c = 11 / 9
d = c + 8
|
a ) 3 , b ) 2 , c ) 8 , d ) 6 , e ) 5 | e | subtract(multiply(multiply(20, divide(1, add(1, 3))), 4), multiply(20, divide(3, 4))) | in a 20 litre mixture ratio of milk and water is 3 : 1 . how much milk should added so that mixture ratio become 4 : 1 ? | amount of milk = 20 Γ 3 / 4 = 15 litre and water = 5 litre let x litre milk to be added then 15 + x / 5 = 4 / 1 = 15 + x = 20 , x = 5 answer e | a = 1 + 3
b = 1 / a
c = 20 * b
d = c * 4
e = 3 / 4
f = 20 * e
g = d - f
|
a ) 80 % , b ) 82.5 % , c ) 83 % , d ) 84 % , e ) 85.5 % | e | add(multiply(divide(divide(10, const_100), subtract(1, divide(1, 5))), const_100), 2) | the price of an item is discounted 5 percent on day 1 of a sale . on day 2 , the item is discounted another 5.00001 percent , and on day 3 , it is discounted an additional 10 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ? | "let initial price be 100 price in day 1 after 5 % discount = 95 price in day 2 after 5 % discount = 90.25 price in day 3 after 10 % discount = 81.23 so , price in day 3 as percentage of the sale price on day 1 will be = 81.23 / 95 * 100 = > 85.5 % answer will definitely be ( e )" | a = 10 / 100
b = 1 / 5
c = 1 - b
d = a / c
e = d * 100
f = e + 2
|
a ) 12 , b ) 20 , c ) 88 , d ) 77 , e ) 4 | e | subtract(14, divide(14, add(divide(2, 5), const_1))) | a 14 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ? | "1 : 2 / 5 = 5 : 2 2 / 7 * 14 = 4 answer : e" | a = 2 / 5
b = a + 1
c = 14 / b
d = 14 - c
|
a ) 100 , b ) 225 , c ) 900 , d ) 1,600 , e ) 4,900 | b | add(multiply(multiply(multiply(9, power(const_3, const_2)), 15), const_2), multiply(15, 25)) | what is the smallest positive perfect square that is divisible by 9 , 15 , and 25 ? | "the number needs to be divisible by 3 ^ 2 , 3 * 5 , and 5 ^ 2 . the smallest such perfect square is 3 ^ 2 * 5 ^ 2 = 225 the answer is b ." | a = 3 ** 2
b = 9 * a
c = b * 15
d = c * 2
e = 15 * 25
f = d + e
|
a ) 15.6 , b ) 18.1 , c ) 17.5 , d ) 18.7 , e ) 19.1 | b | add(2.5, multiply(subtract(divide(8, divide(1, 5)), 1), 0.4)) | a certain taxi company charges $ 2.50 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? | a certain taxi company charges $ 2.50 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 2.50 for the first 0.2 miles plus ( 8 - 0.2 ) / 0.2 * 0.4 = $ 2.50 + $ 15.6 = $ 18.1 . answer : b . | a = 1 / 5
b = 8 / a
c = b - 1
d = c * 0
e = 2 + 5
|
['a ) 40', 'b ) 45', 'c ) 50', 'd ) 55', 'e ) 60'] | e | divide(volume_rectangular_prism(10, 6, 5), 5) | water is poured into a tank so that the tank is being filled at the rate of 5 cubic feet per hour . if the empty rectangular tank is 10 feet long , 6 feet wide , and 5 feet deep , approximately how many hours does it take to fill the tank ? | the volume the tank is : length * width * depth = 10 * 6 * 5 = 300 cubic feet . 300 cubic feet / 5 cubic feet per hour = 60 hours . it will take 60 hours to fill the tank . the answer is e . | a = volume_rectangular_prism / (
|
a ) 3.6 hr , b ) 5.25 hr , c ) 8.25 hr , d ) 2.25 hr , e ) 2.50 hr | a | divide(69, add(13, 6)) | a boat can travel with a speed of 13 km / hr in still water . if the speed of the stream is 6 km / hr , find the time taken by the boat to go 69 km downstream . | "speed of boat in still water = 13 km / hr speed of the stream = 6 km / hr speed downstream = ( 13 + 6 ) = 19 km / hr time taken to travel 69 km downstream = 69 Γ’ Β β 19 = 17 Γ’ Β β 4 = 3.6 hours answer is a" | a = 13 + 6
b = 69 / a
|
a ) 0.05 , b ) ( 0.05 ) ^ 50 , c ) 1 - ( 0.96 ) ^ 50 , d ) 1 - ( 0.95 ) ^ 50 , e ) ( 0.95 ) ^ 50 | d | subtract(const_1, power(subtract(const_1, 0.05), 50)) | a string of 50 light bulbs is wired in such a way that if any individual light bulb fails , the entire string fails . if for each individual light bulb the probability of failing during time period t is 0.05 , what is the probability that the string of light bulbs will fail during the time period t ? | the string of light bulbs will fail if at least one light bulb fails . so , let ' s find the probability of the opposite event and subtract that value from 1 . the opposite event is when none of the 50 light bulbs fails , since the probability of each light bulb not to fail is 1 - 0.05 = 0.95 the the probability that none of the 50 light bulbs fails is 0.95 ^ 50 . hence , the probability that at least one light bulb fails is 1 - 0.95 ^ 50 . answer : d . now , you should have spotted that your reasoning was not right because of one simple thing , consider the case when we have 100 light bulbs instead of 50 , then according to your logic the probability that the string of light bulbs will fail would be 100 * 0.05 = 5 , which is not possible since the probability of an event can not be more than 1 ( 100 % ) . | a = 1 - 0
b = a ** 50
c = 1 - b
|
a ) 500 , b ) 750 , c ) 1000 , d ) 1250 , e ) 1500 | c | divide(140, multiply(divide(2, const_100), 7)) | a sum was put at simple interest at a certain rate for 7 years had it been put at 2 % higher rate , it would have fetched 140 more . find the sum . | "difference in s . i . = p Γ t / 100 ( r 1 β r 2 ) β 140 = p Γ 7 x 2 / 100 ( β΅ r 1 - r 2 = 2 ) β p = 140 Γ 100 / 7 Γ 2 = 1000 answer c" | a = 2 / 100
b = a * 7
c = 140 / b
|
a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10 | c | divide(add(subtract(multiply(2, subtract(8, 2)), multiply(3, 2)), 31), add(3, 2)) | zachary is helping his younger brother , sterling , learn his multiplication tables . for every question that sterling answers correctly , zachary gives him 3 pieces of candy . for every question that sterling answers incorrectly , zachary takes away two pieces of candy . after 8 questions , if sterling had answered 2 more questions correctly , he would have earned 31 pieces of candy . how many of the 8 questions did zachary answer correctly ? | "i got two equations : 3 x - 2 y = 25 x + y = 8 3 x - 2 ( 8 - x ) = 25 3 x - 16 + 2 x = 25 5 x = 41 x = 8.2 or between 8 and 9 . 9 ans c )" | a = 8 - 2
b = 2 * a
c = 3 * 2
d = b - c
e = d + 31
f = 3 + 2
g = e / f
|
a ) 7 / 3 , b ) 3 / 2 , c ) 4 / 3 , d ) 2 / 3 , e ) 1 / 2 | a | divide(7, 3) | a positive number x is multiplied by 7 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ? | "sq rt ( 7 x / 3 ) = x = > 7 x / 3 = x ^ 2 = > x = 7 / 3 ans - a" | a = 7 / 3
|
a ) 23 , b ) 19 , c ) 42 , d ) 20 , e ) 21 | c | add(7, divide(multiply(7, subtract(18000, 8000)), subtract(8000, 6000))) | the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 18000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is : | "let the total number of workers be x . then , 8000 x = ( 18000 * 7 ) + 6000 ( x - 7 ) = 2000 x = 84000 = x = 42 . answer : c" | a = 18000 - 8000
b = 7 * a
c = 8000 - 6000
d = b / c
e = 7 + d
|
a ) 28 % , b ) 25 % , c ) 18.5 % , d ) 16 % , e ) none of these | a | multiply(divide(subtract(divide(350, 150), divide(add(multiply(subtract(250, 200), 1.4), 350), 250)), divide(350, 150)), const_100) | a company charges a fixed rental of rs . 350 per month . it allows 200 calls free per month . each call is charge at rs . 1.4 when the number of calls exceed 200 per month and it charges rs . 1.6 when the number of calls exceeds 400 per month and so on . a customer made 150 calls in february and 250 calls in march . by how much percent each call is cheaper in march than each call in february . | solution : charge per call in february = 350 / 150 = 7 / 3 = 2.33 charge per call in march = [ 350 + ( 50 * 1.4 ) ] / 250 = 420 / 250 = 42 / 25 = 1.68 % cheaper call rate in march = [ ( 2.33 - 1.68 ) / 2.33 ] * 100 = 28 % . answer : option a | a = 350 / 150
b = 250 - 200
c = b * 1
d = c + 350
e = d / 250
f = a - e
g = 350 / 150
h = f / g
i = h * 100
|
a ) 122 , b ) 126 , c ) 134 , d ) 148 , e ) 151 | c | add(add(add(multiply(3, 12), multiply(3, 13)), multiply(3, 16)), 11) | 3 * 12 + 3 * 13 + 3 * 16 + 11 = ? | 3 * 12 + 3 * 13 + 3 * 16 + 11 = 36 + 39 + 48 + 11 = 134 the answer is c . | a = 3 * 12
b = 3 * 13
c = a + b
d = 3 * 16
e = c + d
f = e + 11
|
a ) 0 , b ) 1 / 9 , c ) 2 / 9 , d ) 720 / 16807 , e ) 1 | d | multiply(factorial(7), power(divide(1, 7), 7)) | a certain roller coaster has 7 cars , and a passenger is equally likely to ride in any 1 of the 7 cars each time that passenger rides the roller coaster . if a certain passenger is to ride the roller coaster 7 times , what is the probability that the passenger will ride in each of the 7 cars ? | "if he is to ride 6 times and since he can choose any of the 6 cars each time , total number of ways is = 7 * 7 * 7 * 7 * 7 * 7 = 117649 now the number of ways if he is to choose a different car each time is = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040 so the probability is = 5040 / 117649 = 720 / 16807 answer : d" | a = math.factorial(7)
b = 1 / 7
c = b ** 7
d = a * c
|
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