euclaise/mathqa_programs huggingface dataset:
Problem: weights of two friends ram and shyam are in the ratio 7 : 5 . if ram ' s weight is increased by 10 % and total weight of ram and shyam become 82.8 kg , with an increases of 15 % . by what percent did the weight of shyam has to be increased ?
Options: a ) 19 % , b ) 10 % , c ) 22 % , d ) 16 % , e ) none
Rationale: "solution : given ratio of ram and shayam ' s weight = 7 : 5 hence , ( x - 15 ) / ( 15 - 10 ) = 7 / 5 or , x = 22 % . answer : option c"
Answer: c
Python program:
a = 15 - 10
b = 7 / 5
c = a * b
d = 15 + c
Problem: in town x , 90 percent of the population are employed , and 20 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 66 % , c ) 77 % , d ) 88 % , e ) 52 %
Rationale: "total employed people 90 % , out of which 20 are employed males , hence 70 % are employed females . ( employed females ) / ( total employed people ) = 70 / 90 = 7 / 9 = 77 % answer : c ."
Answer: c
Python program:
a = 90 - 20
b = a / 90
c = b * 100
Problem: the ages of two persons differ by 16 years . 6 years ago , the elder one was 3 times as old as the younger one . what are their present ages of the elder person ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: let present age of the elder person = x and present age of the younger person = x − 16 ( x − 6 ) = 3 ( x − 16 − 6 ) x − 6 = 3 x − 66 2 x = 60 x = 60 / 2 = 30 answer : option c
Answer: c
Python program:
a = 3 * 6
b = 16 - 6
c = a + b 
d = c / 2
e = d + 16
Problem: how many positive integers less than 90 are multiples of 6 but not multiples of 9 ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "the lcm of 6 and 9 is 18 . if x < 90 and x is divisible by 6 not by 9 - - > x is not divisible by 18 . from 1 - - > 90 , we have 5 numbers which is divisible by 18 : 18 , 36 , 54 , 72 , 90 . from 1 - - > 90 , we have ( 90 - 6 ) / 6 + 1 = 15 numbers divisible by 6 . therefore , our answer is 15 - 5 = 10 numbers . d"
Answer: d
Python program:
a = 4 + 6 
b = a - 1
c = math.factorial(b)
d = math.factorial(6)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: two numbers are in the ratio of 6 : 8 . if 10 is subtracted from each , the new numbers are in the ratio 16 : 32 . find the smaller number .
Options: a ) 22 , b ) 12 , c ) 38 , d ) 15 , e ) 17
Rationale: "explanation : let the number be 6 x and 8 x . then , ( 6 x – 10 ) / ( 8 x – 10 ) = 1 / 2 2 ( 6 x – 10 ) = ( 8 x – 10 ) 12 x – 20 = 8 x – 10 4 x = 10 x = 2.5 the smaller number = ( 6 x 2.5 ) = 15 answer d"
Answer: d
Python program:
a = 32 * 10
b = 16 * 10
c = a - b
d = c * 6
e = 8 / 6
f = d * e
g = 32 * 10
h = 16 * 10
i = g - h
j = i * 6
k = f - j
Problem: a cistern 7 m long and 5 m wide contains water up to a breadth of 1 m 40 cm . find the total area of the wet surface .
Options: a ) 69 m sqaure , b ) 49 m sqaure , c ) 52 m sqaure , d ) 64 m sqaure , e ) none of these
Rationale: "explanation : area of the wet surface = 2 [ lb + bh + hl ] - lb = 2 [ bh + hl ] + lb = 2 [ ( 5 * 1.40 + 7 * 1.40 ) ] + 7 * 5 = 69 m square option a"
Answer: a
Python program:
a = 40 / 100
b = a + 1 
c = b * 5
d = 40 / 100
e = d + 1 
f = e * 7
g = c + f 
h = 2 * g
i = 5 * 7
j = h + i
Problem: in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 9 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .
Options: a ) 2 / 1 , b ) 4 / 1 , c ) 2 / 3 , d ) 3 / 4 , e ) 3 / 2
Rationale: "given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 9 ) = 36 / 18 = 2 / 1 . answer : a ."
Answer: a
Python program:
a = 4 + 1 
b = 45 / a
c = 45 - b
d = 4 + 1 
e = 45 / d
f = e + 9 
g = c / f
Problem: find the area of a rhombus one side of which measures 20 cm and one diagonal is 27 cm .
Options: a ) 600 cm 2 , b ) 500 cm 2 , c ) 400 cm 2 , d ) 432 cm 2 , e ) 100 cm 2
Rationale: "explanation : let other diagonal = 2 x cm . since diagonals of a rhombus bisect each other at right angles , we have : ( 20 ) 2 = ( 12 ) 2 + ( x ) 2 = > x = √ ( 20 ) 2 – ( 12 ) 2 = √ 256 = 16 cm . _ i so , other diagonal = 32 cm . area of rhombus = ( 1 / 2 ) x ( product of diagonals ) = ( 1 / 2 × 27 x 32 ) cm 2 = 432 cm 2 answer : option d"
Answer: d
Python program:
a = 1 / 2
b = a * 27
c = 20 * 20
d = c * 4
e = 27 * 27
f = d - e
g = math.sqrt(f)
h = b * g
i = h + 27
Problem: on dividing a number by 56 , we get 28 as remainder . on dividing the same number by 8 , what will be the remainder ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "number = 56 x + 28 ( ∵ since the number gives 28 as remainder on dividing by 56 ) = ( 7 × 8 × x ) + ( 3 × 8 ) + 4 hence , if the number is divided by 8 , we will get 4 as remainder . answer : c"
Answer: c
Python program:
a = 28 ** 2
b = a / 56
c = 28 ** 2
d = c / 56
e = math.floor(d)
f = b - e
g = f * 56
Problem: a man sells an article at a profit of 25 % . if he had bought it at 20 % less and sold it for rs . 10.50 less , he would have gained 30 % . find the cost of the article .
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: let c . p = 100 gain = 25 % s . p = 125 supposed c . p = 80 gain = 30 % s . p = ( 130 * 80 ) / 100 = 104 diff = ( 125 - 104 ) = 21 diff 21 when c . p = 100 then diff 10.50 when c . p = ( 100 * 10.50 ) / 21 = 50 answer : c
Answer: c
Python program:
a = 10 * 5
b = 25 + 100 
c = 30 + 100 
d = 100 - 20
e = c * d
f = e / 100
g = b - f
h = a / g
Problem: how many three - element subsets of { 5 , 6,7 , 8,9 } are there that do not contain the pair of elements 6 and 9 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "required subsets are = { 5 , 6,7 } , { 5 , 7,8 } , { 5 , 8,9 } , { 6 , 7,8 } , { 7 , 8,9 } = 5 answer : e"
Answer: e
Python program:
a = 6 - 4
Problem: if a lends rs . 1500 to b at 10 % per annum and b lends the same sum to c at 11.5 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 112.5 , b ) 122.5 , c ) 132.5 , d ) 67.5 , e ) 212.5
Rationale: "( 1500 * 1.5 * 3 ) / 100 = > 67.5 answer : d"
Answer: d
Python program:
a = 1500 * 11
b = a * 3
c = b / 100
d = 1500 * 10
e = d * 3
f = e / 100
g = c - f
Problem: a man sitting in a train which is traveling at 45 kmph observes that a goods train , traveling in opposite direction , takes 8 seconds to pass him . if the goods train is 340 m long , find its speed
Options: a ) 102 kmph , b ) 106 kmph , c ) 108 kmph , d ) 62 kmph , e ) 72 kmph
Rationale: "explanation : relative speed = 340 / 8 m / sec = ( ( 340 / 8 ) × ( 18 / 5 ) ) kmph = 153 kmph . speed of goods train = ( 153 - 45 ) kmph = 108 kmph answer : option c"
Answer: c
Python program:
a = 340 / 8
b = a * const_3_6
c = b - 45
Problem: if x and y are both odd prime numbers and x < y , how many distinct positive integer q factors does 2 xy have ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: since 2 xy prime q factors are x ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer .
Answer: d
Python program:
a = 1 + 1 
b = 2 * a
c = 1 + 1 
d = b * c
Problem: what is the sum of all possible solutions to | x - 5 | ^ 2 + | x - 5 | = 20 ?
Options: a ) - 1 , b ) 6 , c ) 7 , d ) 10 , e ) 14
Rationale: "denote | x - 5 | as y : y ^ 2 + y = 20 - - > y = - 5 or y = 4 . discard the first solution since y = | x - 5 | , so it ' s an absolute value and thus can not be negative . y = | x - 5 | = 4 - - > x = 9 or x = - 1 . the sum = 10 answer : d ."
Answer: d
Python program:
a = 4 + 5 
b = 5 - 4
c = a + b
Problem: how many integers k greater than 100 and less than 1100 are there such that if the hundreds and the unit digits of k are reversed , the resulting integer is k + 99 ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "not sure if this is the shortest . . but this is how i did this there are 9 sets of integers with hundreds and units digits exchanged that satisfies k + 99 . 1 . 102 | 201 ( satisfies k + 99 , where k = 102 ) 2 . 203 | 302 ( satisfies k + 99 , where k = 203 ) 3 . . . . 4 . . . . 5 . . . . 6 . . . . 7 . 708 | 807 8 . 809 | 908 9 . 910 | 1001 each set has 10 such numbers . 1 . 102 | 201 ( still k + 99 holds good ) 2 . 112 | 211 3 . 122 | 221 4 . 132 | 231 5 . . . . 6 . . . . 7 . . . . 8 . . . . 9 . 182 | 281 10 . 192 | 291 therefore , 9 sets with 10 such number in each set will give 9 x 10 = 90 integers . e"
Answer: e
Python program:
a = 10 - 2
b = 10 * a
Problem: anil had to do a multiplication . instead of taking 35 as one of the multipliers , he took 53 . as a result , the product went up by 540 . what is the new product ?
Options: a ) 1590 , b ) 1600 , c ) 1950 , d ) 1630 , e ) 1760
Rationale: explanation : let the number that anil wanted to multiply be ' y ' . he was expected to find the value of 35 y . instead , he found the value of 53 y . the difference between the value that he got ( 53 y ) and what he was expected to get ( 35 y ) is 540 . = > 53 y - 35 y = 540 = > ( 53 - 35 ) * y = 540 = > y = 30 therefore , the correct product = 53 * 30 = 1590 answer : a
Answer: a
Python program:
a = 35 * 53
b = 3 * 10
c = a + b 
d = 4 * 100
e = c - d
f = e + 100
Problem: at what rate percent of simple interest will a sum of money double itself in 33 years ?
Options: a ) 6.54 % , b ) 4.54 % , c ) 8 . 2 % , d ) 3.03 % , e ) 5.54 %
Rationale: "let sum = x . then , s . i . = x . rate = ( 100 * s . i . ) / ( p * t ) = ( 100 * x ) / ( x * 33 ) = 100 / 33 = 3.03 % answer : d"
Answer: d
Python program:
a = 100 / 33
Problem: a 360 meter long train crosses a man standing on the platform in 6 sec . what is the speed of the train ?
Options: a ) 229 , b ) 108 , c ) 278 , d ) 216 , e ) 112
Rationale: "s = 360 / 6 * 18 / 5 = 216 kmph answer : d"
Answer: d
Python program:
a = 360 / 6
b = a * const_3_6
Problem: a trader bought a car at 30 % discount on its original price . he sold it at a 40 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 118 , b ) 110 , c ) 112 , d ) 113 , e ) 98
Rationale: "original price = 100 cp = 70 s = 70 * ( 140 / 100 ) = 98 100 - 112 = 2 % answer : e"
Answer: e
Python program:
a = 100 - 30
b = 100 + 40 
c = a * b
d = c / 100
e = d / 100
f = e - 1
g = f * 100
Problem: one - tenth of the students at a nursery school are 4 years old or older . if 20 students have not yet reached their third birthday , and a total of 25 students are not between 3 years old and 4 years old , how many children are in the nursery school ?
Options: a ) 51 , b ) 20 , c ) 40 , d ) 50 , e ) 55
Rationale: "x / 10 students are > 4 yrs 20 students are < 3 yrs x / 10 + 20 = 25 x / 10 = 5 x = 50 answer : d"
Answer: d
Python program:
a = 25 - 20
b = a * 10
Problem: a train is 310 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 36 seconds , b ) 18 seconds , c ) 40 seconds , d ) 19 seconds , e ) 45 seconds
Rationale: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 310 + 140 = 500 meter time = distance / speed = 450 * ( 2 / 25 ) = 36 seconds answer : a"
Answer: a
Python program:
a = 310 + 140 
b = 45 * 1000
c = b / 3600
d = a / c
Problem: a 49 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 ?
Options: a ) 12 , b ) 20 , c ) 88 , d ) 77 , e ) 14
Rationale: "1 : 2 / 5 = 5 : 2 2 / 7 * 49 = 14 answer : e"
Answer: e
Python program:
a = 2 / 5
b = a + 1 
c = 49 / b
d = 49 - c
Problem: there are 6 boxes numbered 1 , 2 , . . . 6 . each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered . the total number of ways in which this can be done is :
Options: a ) 5 , b ) 21 , c ) 33 , d ) 60 , e ) 6
Rationale: "explanatory answer list down possibilities : from only 1 box all the way to all 6 if only one of the boxes has a green ball , it can be any of the 6 boxes . so , we have 6 possibilities . if two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes . 12 , 23 , 34 , 45 , 56 . if 3 of the boxes have green balls , there are 4 possibilities : 123 , 234 , 345 , 456 . if 4 boxes have green balls , there are 3 possibilities : 1234 , 2345 , 3456 . if 5 boxes have green balls , there are 2 possibilities : 12345 , 23456 . if all 6 boxes have green balls , there is just 1 possibility . total number of possibilities = 6 + 5 + 4 + 3 + 2 + 1 = 21 . choice b"
Answer: b
Python program:
a = 6 - 1
b = 6 + a 
c = 6 - 1
d = c - 1
e = b + d 
f = 6 - 1
g = f - 1
h = g - 1
i = e + h 
j = i + 2
Problem: the overall age of x and y is 18 year greater than the overall age of y and z . z is how many decades younger that x ?
Options: a ) 11 , b ) 15 , c ) 12 , d ) 17 , e ) 18
Rationale: "e 18 ( x + y ) â € “ ( y + z ) = 18 x â € “ z = 18"
Answer: e
Python program:
a = 18 / 1
Problem: tom , working alone , can paint a room in 8 hours . peter and john , working independently , can paint the same room in 4 hours and 2 hours , respectively . tom starts painting the room and works on his own for two hour . he is then joined by peter and they work together for two hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ?
Options: a ) 4 / 7 , b ) 5 / 7 , c ) 6 / 7 , d ) 1 / 7 , e ) 3 / 7
Rationale: "let the time when all three were working together be t hours . then : tom worked for t + 4 hour and has done 1 / 8 * ( t + 4 ) part of the job ; peter worked for t + 2 hour and has done 1 / 4 * ( t + 2 ) part of the job ; john worked for t hours and has done 1 / 2 * t part of the job : 1 / 8 * ( t + 4 ) + 1 / 4 * ( t + 2 ) + 1 / 2 * t = 1 - - > multiply by 8 - - > ( t + 4 ) + ( 2 t + 2 ) + 4 t = 8 - - > t = 2 / 7 ; hence peter has done 1 / 4 * ( 2 / 7 + 2 ) = 1 / 4 * 16 / 7 = 16 / 28 = 8 / 14 = 4 / 7 answer : a"
Answer: a
Python program:
a = 4 * 2
b = a + 1 
c = 4 / b
Problem: a boy rides his bicycle 10 km at an average sped of 12 km / hr and again travels 12 km at an average speed of 10 km / hr . his average speed for the entire trip is approximately .
Options: a ) 10.2 kmph , b ) 10.4 kmph , c ) 10.8 kmph , d ) 11.8 kmph , e ) none
Rationale: sol . total distance travelled = ( 10 + 12 ) km / hr = 22 km / hr . total time taken = [ 10 / 12 + 12 / 10 ] hrs = 61 / 30 hrs ∴ average speed = [ 22 * 30 / 61 ] km / hr = 10.8 km / hr . answer c
Answer: c
Python program:
a = 10 + 12 
b = 10 / 12
c = 12 / 10
d = b + c 
e = a / d
Problem: ( a / 2 ) / ( b / c ) in the expression above , a , b , and c are different numbers and each is one of the numbers 1 , 2 , or 4 . what is the largest possible value of the expression ?
Options: a ) 8 / 2 , b ) 2 / 4 , c ) 1 / 8 , d ) 2 / 4 , e ) 4 / 6
Rationale: ( a / 2 ) / ( b / c ) = ( a * c ) / 2 b the expression will have the largest value when numerator ( a * c ) is the largest . = ( 2 * 4 ) / 2 * 1 = 8 / 2 answer a
Answer: a
Python program:
a = 4 * 2
b = a / 2
Problem: in a college the ratio of the numbers of boys to the girls is 8 : 5 . if there are 190 girls , the total number of students in the college is ?
Options: a ) 562 , b ) 356 , c ) 452 , d ) 494 , e ) 512
Rationale: "let the number of boys and girls be 8 x and 5 x then , 5 x = 190 x = 38 total number of students = 13 x = 13 * 38 = 494 answer is d"
Answer: d
Python program:
a = 8 / 5
b = a * 190
c = b + 190
Problem: if the numerator of a fraction be increased by 15 % and its denominator be diminished by 8 % , the value of the fraction is 15 / 16 . find the original fraction ?
Options: a ) 1 / 2 , b ) 3 / 5 , c ) 5 / 7 , d ) 9 / 11 , e ) 3 / 4
Rationale: "let the original fraction be x / y then , 115 % of x / 92 % of y = 15 / 16 115 x / 92 y = 15 / 16 x / y = 3 / 4 answer is e"
Answer: e
Python program:
a = 100 - 8
b = a * 15
c = 100 + 15 
d = c * 16
e = b / d
Problem: simplify : 32 ÷ 8 × 24 + 16 =
Options: a ) 130 , b ) 124 , c ) 120 , d ) 115 , e ) 112
Rationale: "32 ÷ 8 × × 24 + 16 = > 4 × × 24 + 16 = 96 + 16 = 112 option e"
Answer: e
Python program:
a = 32 * 8
b = 24 * 16
c = a + b
Problem: a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 5 gallons of water and 10 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ?
Options: a ) 37.5 , b ) 75 , c ) 100 , d ) 150 , e ) 175
Rationale: "nope , 150 . i can only get it by following pr ' s backsolving explanation . i hate that . original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 10 gallons salt is added and 5 gallons of water is added . so salt now becomes - > ( 0.2 x + 10 ) and water - - > ( 0.6 x + 5 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 10 ) = ( 0.6 x + 5 ) / 2 = 0.4 x + 20 = 0.6 x + 5 = > 0.2 x = 15 solving , x = 75 answer : b"
Answer: b
Python program:
a = 10 * 2
b = a - 5
c = 20 / 100
d = 1 - c
e = 20 / 100
f = 1 - e
g = 1 / 4
h = f * g
i = d - h
j = 20 / 100
k = 2 * j
l = i - k
m = b / l
Problem: the tax on a commodity is diminished by 32 % but its consumption is increased by 12 % . find the decrease percent in the revenue derived from it ?
Options: a ) 20 % , b ) 18 % , c ) 15 % , d ) 12 % , e ) 24 %
Rationale: "100 * 100 = 10000 68 * 112 = 7616 10000 - - - - - - - 2384 100 - - - - - - - ? = 24 % answer : e"
Answer: e
Python program:
a = 100 + 12 
b = 100 - 32
c = a * b
d = c / 100
e = 100 - d
Problem: 106 x 106 - 94 x 94 = ?
Options: a ) 2400 , b ) 2000 , c ) 1904 , d ) 1906 , e ) none of them
Rationale: "= ( 106 ) ^ 2 - ( 94 ) ^ 2 = ( 106 + 94 ) ( 106 - 94 ) = ( 200 x 12 ) = 2400 answer is a"
Answer: a
Python program:
a = 106 ** 94
b = 106 * a
Problem: of the 90 house in a development , 50 have a two - car garage , 40 have an in - the - ground swimming pool , and 35 have both a two - car garage and an in - the - ground swimming pool . how many houses in the development have neither a two - car garage nor an in - the - ground swimming pool ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 35
Rationale: "neither car nor garage = total - garage - ( swim - common ) = 90 - 50 - ( 40 - 35 ) = 90 - 55 = 35 answer e"
Answer: e
Python program:
a = 50 - 35
b = 40 - 35
c = a + b 
d = c + 35 
e = 90 - d
Problem: how many cuboids of length 5 m , width 6 m and height 3 m can be farmed from a cuboid of 18 m length , 15 m width and 2 m height .
Options: a ) 4 , b ) 6 , c ) 10 , d ) 8 , e ) 11
Rationale: "( 18 ã — 15 ã — 12 ) / ( 5 ã — 3 ã — 2 ) = 6 answer is b ."
Answer: b
Python program:
a = 18 * 15
b = a * 2
c = 5 * 6
d = c * 3
e = b / d
Problem: when x is multiplied by 3 , the result is 26 more than the result of subtracting x from 26 . what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 11 , d ) 13 , e ) 22
Rationale: "the equation that can be formed is : 3 x - 26 = 26 - x or , 4 x = 52 or , x = 13 . d answer ."
Answer: d
Python program:
a = 26 + 26 
b = 3 + 1 
c = a / b
Problem: the sum of digits of a two digit number is 11 , the difference between the digits is 5 . find the number
Options: a ) 85 , b ) 94 , c ) 83 , d ) 72 , e ) none
Rationale: "description : = > x + y = 11 , x - y = 5 adding these 2 x = 16 = > x = 8 , y = 3 . thus the number is 83 answer c"
Answer: c
Python program:
a = 11 + 5 
b = a / 2
c = b * 11
d = 11 + 5 
e = d / 2
f = 11 - e
g = c + f
Problem: if x , y , and z are positive integers and 3 x = 7 y = 5 z , then the least possible value of x + y + z is
Options: a ) 15 , b ) 25 , c ) 71 , d ) 35 , e ) 45
Rationale: "given 3 x = 7 y = 5 z x + y + z in terms of x = x + ( 3 x / 7 ) + ( 3 x / 5 ) = 71 x / 35 now checking with each of the answers and see which value gives a minimum integer value . a x = 35 / 71 * 15 , not an integer b , d , e can be ruled out similarly . c is minimum value as x = 71 * 35 / 71 = 35 answer is c"
Answer: c
Python program:
a = 3 * 7
b = a * 5
c = b / 3
d = 3 * 7
e = d * 5
f = e / 7
g = c - f
h = 3 * 7
i = h * 5
j = i / 5
k = g + j
Problem: a sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 90 extra yellow balls and making ratio of white balls to yellow balls 8 / 13 . how many tennis balls did the retailer order originally .
Options: a ) 180 , b ) 130 , c ) 140 , d ) 160 , e ) 288
Rationale: "white : yellow = x : ( x + 90 ) = 8 : 13 - - > 13 x = 8 x + 720 - - > x = 144 . the total # of balls originally x + x = 144 + 144 = 288 . answer : e ."
Answer: e
Python program:
a = 8 * 90
b = 13 - 8
c = a / b
d = c * 2
Problem: a combustion reaction forms carbon dioxide . a carbon dioxide molecule contains one carbon and two oxygen atoms . if , over a period of 10 minutes , a combustion reaction creates 10000 molecules of carbon dioxide then approximately how many more atoms of oxygen than carbon are created on average per minute ?
Options: a ) 1,000 , b ) 500 , c ) 250 , d ) 50 , e ) 0
Rationale: solution : 10,000 carbon dioxide molecules are created over a period of 10 minutes . therefore 10,000 / 10 = 1,000 carbon dioxide molecules are created on average per minute each carbon dioxide molecule contains one carbon atom and two oxygen atoms . so 1,000 carbon dioxide molecules contain 1 × 1,000 = 1,000 carbon atoms and 2 × 1,000 = 2,000 oxygen atoms . the difference is 2,000 – 1,000 = 1,000 . the correct answer is a .
Answer: a
Python program:
a = 10000 / 10
b = 10000 / 10
c = a / b
Problem: if two girls starting from same point , walking in the opposite directions with 5 km / hr and 10 km / hr as average speeds respectively . then the distance between them after 5 hours is ?
Options: a ) 45 , b ) 55 , c ) 65 , d ) 75 , e ) 85
Rationale: "explanation : total distance = distance traveled by person a + distance traveled by person b = ( 5 ã — 5 ) + ( 10 ã — 5 ) = 25 + 50 = 75 km answer : d"
Answer: d
Python program:
a = 5 + 10 
b = a * 5
Problem: in the junior basketball league there are 15 teams , 1 / 3 of them are bad and ½ are rich . what ca n ' t be the number of teams that are rich and bad ?
Options: a ) 4 . , b ) 6 . , c ) 7 . , d ) 8 . , e ) 9 .
Rationale: "total teams = 15 bad teams = ( 1 / 3 ) * 15 = 5 rich teams = 8 so maximum value that the both rich and bad can take will be 8 . so e = 9 can not be that value . ans e ."
Answer: e
Python program:
a = 1 / 1
b = 15 * a
c = b + 1
Problem: the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 2028 sq m , then what is the breadth of the rectangular plot ?
Options: a ) 11 , b ) 17 , c ) 26 , d ) 101 , e ) 1322
Rationale: "let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 2028 3 b 2 = 2028 b 2 = 676 = 26 ( b > 0 ) b = 26 m . answer : c"
Answer: c
Python program:
a = 2028 / 3
b = math.sqrt(a)
Problem: find the least number which when divided by 5 , 67 , and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder
Options: a ) 1683 , b ) 1684 , c ) 1685 , d ) 1582 , e ) 1584
Rationale: explanation : l . c . m . of 5,6 , 7,8 = 840 . 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 . required number = ( 840 x 2 + 3 ) = 1683 answer is a
Answer: a
Python program:
a = 2 * 3
b = math.lcm(5, a)
c = 3 + 4 
d = math.lcm(b, c)
e = math.lcm(d, 8)
f = e * 2
g = f + 3
Problem: xavier , yvonne , and zelda each try independently to solve a problem . if their individual probabilities for success are 1 / 6 , 1 / 2 and 5 / 8 , respectively , what is the probability that xavier and yvonne , but not zelda , will solve the problem ?
Options: a ) 1 / 32 , b ) 7 / 8 , c ) 9 / 64 , d ) 5 / 64 , e ) 3 / 64
Rationale: "p ( xavier will solve ) = 1 / 6 p ( yvonne will solve ) = 1 / 2 p ( zelda will not solve ) = 1 - 5 / 8 = 3 / 8 . now , we need to multiply all this ps to find an answer : p = ( 1 / 6 ) * ( 1 / 2 ) * ( 3 / 8 ) = 1 / 32 . ans . a ."
Answer: a
Python program:
a = 1 / 6
b = 1 / 2
c = a * b
d = 5 / 8
e = 1 - d
f = c * e