euclaise/mathqa_programs huggingface dataset:
Problem: a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the share of a in profit of rs . 13600 after a year ?
Options: a ) 3630 , b ) 9232 , c ) 8828 , d ) 2387 , e ) 4080
Rationale: "6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 13600 = 4080 answer : e"
Answer: e
Python program:
a = 6300 + 4200 
b = a + 10500 
c = 6300 / b
d = c * 13600
Problem: two trains 120 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.16 , b ) 7.16 , c ) 7.07 , d ) 7.15 , e ) 7.11
Rationale: "t = ( 120 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.07 answer : c"
Answer: c
Python program:
a = 120 + 165 
b = 80 + 65 
c = b * const_0_2778
d = a / c
Problem: the average weight of 4 pigs is 15 kg . weight less than 16 kg is considered as under weight . what maximum no . of pig can be under weight .
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: sum of all four pigs weigh = 60 kg it is possible that all four pigs are underweight . because the average is 15 kg which itself underweight . answer e
Answer: e
Python program:
a = 16 - 15
b = a * 4
Problem: a can do a job in 30 days and b in 40 days . if they work on it together for 10 days , then the fraction of the work that is left is ?
Options: a ) 2 / 11 , b ) 3 / 13 , c ) 5 / 12 , d ) 7 / 10 , e ) 6 / 15
Rationale: "a ' s 1 day work = 1 / 30 b ' s 1 day work = 1 / 40 a + b 1 day work = 1 / 30 + 1 / 40 = 7 / 120 a + b 4 days work = 7 / 120 * 10 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 answer is c"
Answer: c
Python program:
a = 1 / 30
b = 1 / 40
c = a + b 
d = 10 * c
e = 1 - d
Problem: a retail appliance store priced a video recorder at 20 percent above the wholesale cost of $ 200 . if a store employee applied the 15 percent employee discount to the retail price to buy the recorder , how much did the employee pay for the recorder ?
Options: a ) $ 204 , b ) $ 216 , c ) $ 220 , d ) $ 230 , e ) $ 240
Rationale: "wholesale cost of video recorder = 200 $ video recorder was priced at 20 percent above 200 = 240 $ % discount given by store employee = 15 emlpoyee paid = . 85 * 240 = 204 $ answer a"
Answer: a
Python program:
a = 200 / 100
b = a * 20
c = 200 + b 
d = 200 / 100
e = d * 20
f = 200 + e 
g = f / 100
h = g * 15
i = c - h
Problem: the compound ratio of 1 : 4 , 2 : 5 and 1 : 6 ?
Options: a ) 1 : 3 , b ) 1 : 4 , c ) 1 : 10 , d ) 1 : 30 , e ) 1 : 60
Rationale: 1 / 4 * 2 / 5 * 1 / 6 = 1 / 60 1 : 60 answer : e
Answer: e
Python program:
a = 1 * 2
b = 4 * 5
c = a / b
d = 2 * 1
e = 5 * 6
f = d / e
g = c / f
Problem: the true discount on a bill due 9 months hence at 16 % per annum is rs . 189 . the amount of the bill is
Options: a ) rs . 1386 , b ) rs . 1764 , c ) rs . 1575 , d ) rs . 2268 , e ) none of these
Rationale: "solution 32.5 let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 189 . ∴ x 16 x 9 / 12 x 1 / 100 } = 189 or x = 1575 . ∴ p . w . = rs . 1575 . answer b"
Answer: b
Python program:
a = 4 * 3
b = 9 / a
c = b * 16
d = c / 100
e = 189 / d
f = e + 189
Problem: in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 35 as quotient . what is the correct quotient ?
Options: a ) 0 , b ) 12 , c ) 13 , d ) 20 , e ) 25
Rationale: 12 * 35 = 420 420 % 21 = 20 answer : d
Answer: d
Python program:
a = 12 * 35
b = a / 21
Problem: tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random . what is the probability that the ticket drawn bears a number which is a multiple of 3 ?
Options: a ) 3 / 10 , b ) 1 / 2 , c ) 2 / 5 , d ) 3 / 7 , e ) 1 / 6
Rationale: "here , s = { 1 , 2,3 , . . . . . . , 19,20 } e = event getting a multiple of 3 = { 3,6 , 9,12 , 15,18 } probability = 6 / 20 = 3 / 10 correct option is a"
Answer: a
Python program:
a = 3 / 10
Problem: the sum of the digits of [ ( 10 ^ x ) ^ y ] - 64 = 279 . what is the value of xy ?
Options: a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 32
Rationale: 1000 − 64 = 936 . whatever xy is you finish with 36 = = > 3 + 6 = 9 therefore , 279 − 9 = 270 and 270 / 9 = 30 now you add the last two digits ( 3 and 6 ) answer is 30 + 2 = 32 answer : e
Answer: e
Python program:
a = 64 / 2
Problem: a corporation paid $ 7 million in federal taxes on its first $ 50 million of gross profits and then $ 30 million in federal taxes on the next $ 150 million in gross profits . by approximately what percent did the ratio of federal taxes to gross profits increase from the first $ 50 million in profits to the next $ 150 million in profits ?
Options: a ) 6 % , b ) 14 % , c ) 20 % , d ) 23 % , e ) 43 %
Rationale: "initial ratio of federal taxes to gross profits : 7 / 50 = 0.14 final ratio : 30 / 150 = 0.2 thus , the percentage change : ( 0.2 - 0.14 ) / 0.14 * 100 = 6 / 14 * 100 = 3 / 7 * 100 = just less than 50 % . answer : e"
Answer: e
Python program:
a = 30 + 7 
b = a / 150
c = 7 / 50
d = b - c
e = 7 / 50
f = d / e
g = f * 100
Problem: jack and jill are marathon runners . jack can finish a marathon ( 42 km ) in 5.5 hours and jill can run a marathon in 4.2 hours . what is the ratio of their average running speed ? ( jack : jill )
Options: a ) 14 / 15 , b ) 15 / 14 , c ) 4 / 5 , d ) 42 / 55 , e ) can not be determined
Rationale: "average speed of jack = distance / time = 42 / ( 11 / 2 ) = 84 / 11 average speed of jill = 42 / ( 4.2 ) = 10 ratio of average speed of jack to jill = ( 84 / 11 ) / 10 = 84 / 110 = 42 / 55 answer d"
Answer: d
Python program:
a = 42 / 5
b = 42 / 4
c = a / b
Problem: two trains a and b are 100 m and 150 m long and are moving at one another at 54 km / hr and 36 km / hr respectively . arun is sitting on coach b 1 of train a . calculate the time taken by arun to completely cross train b .
Options: a ) 10 s , b ) 6 s , c ) 4 s , d ) 8 s , e ) 12 s
Rationale: "detailed solution speed of a = 54 ∗ 1000 / 60 ∗ 60 = 15 m / s speed of b = 36 ∗ 1000 / 60 ∗ 60 = 10 m / s relative speed = s 1 + s 2 = 15 + 10 m / s = 25 m / s the length that needs to be crossed = length of train b = 150 m . therefore time taken = 150 / 25 = 6 s . what is the time taken for trains to completely cross each other ? the length that needs to be crossed = 100 + 150 = 250 m . time taken = 250 / 25 = 10 s . correct answer b ."
Answer: b
Python program:
a = 100 + 150 
b = 54 * 1000
c = b / 3600
d = 36 * 1000
e = d / 3600
f = c + e 
g = a / f
Problem: angelo and isabella are both salespersons . in any given week , angelo makes $ 550 in base salary plus 8 percent of the portion of his sales above $ 5,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 7,500 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: "official solution : the problem asks for the amount of weekly sales it takes for angelo and isabella to earn the same amount of money . you can write an equation that sets angelo ’ s and isabella ’ s weekly earnings equal to each other , with x representing weekly sales . weekly earnings for each salesperson equal base salary plus commission . so angelo ’ s earnings are 550 + ( 0.08 ) ( x – 5,000 ) , and isabella ’ s are 0.10 x . set up the equation and solve : 550 + ( 0.08 ) ( x – 5,000 ) = 0.10 x distribute the 0.08 : 550 + 0.08 x – 400 = 0.10 x combine terms and subtract 0.08 x from both sides : 150 = 0.02 x divide both sides by 0.02 : 7,500 = x your answer is a ."
Answer: a
Python program:
a = 8 / 100
b = 5 * 0
c = 550 - b
d = 10 / 100
e = 8 / 100
f = d - e
g = c / f
h = g / 5
i = math.floor(h)
Problem: 15 % people of a village in sri lanka died by bombardment , 25 % of the remainder left the village on account of fear . if now the population is reduced to 4555 , how much was it in the beginning ?
Options: a ) 7400 , b ) 7145 , c ) 7200 , d ) 7323 , e ) 6030
Rationale: "x * ( 85 / 100 ) * ( 75 / 100 ) = 4555 x = 7145 answer : b"
Answer: b
Python program:
a = 100 - 15
b = a / 100
c = 100 - 25
d = c / 100
e = b * d
f = 4555 / e
g = math.floor(f)
Problem: in a group of cows and hens , the number of legs are 18 more than twice the number of heads . the number of cows is
Options: a ) 5 , b ) 7 , c ) 9 , d ) 12 , e ) 14
Rationale: "explanation : let the number of cows be x and the number of hens be y . then , 4 x + 2 y = 2 ( x + y ) + 18 4 x + 2 y = 2 x + 2 y + 18 2 x = 18 x = 9 . answer : c"
Answer: c
Python program:
a = 18 - 4
Problem: the area of rectangular field is 460 square metres . if the length is 15 per cent more than the breadth , what is the breadth of the rectangular field ?
Options: a ) 15 metres
b ) 26 metres
c ) 34.5 metres
d ) can not be determined
e ) none of these
Rationale: let the breadth of the rectangular field be ‘ x ’ m . then , length of the field will be x + x × 15 / 100 = 23 x / 20 now , x × 23 x / 20 = 460 or , 23 x 2 = 460 × 20 or , x 2 = 20 × 20 or , x = 20 m answer e
Answer: e
Python program:
a = 2 * 10
b = 460 * a
c = 2 * 10
d = 460 * c
e = d / 100
f = b / e
Problem: sum of the squares of 3 no . is 252 and the sum of their products taken two at a time is 116 . find the sum ?
Options: a ) 24 , b ) 33 , c ) 22 , d ) 20 , e ) 21
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 252 + 2 * 116 a + b + c = â ˆ š 484 = 22 answer c"
Answer: c
Python program:
a = 116 * 2
b = 252 + a 
c = math.sqrt(b)
Problem: a train 120 m long running at 72 kmph crosses a platform in 25 sec . what is the length of the platform ?
Options: a ) 443 m , b ) 354 m , c ) 450 m , d ) 380 m , e ) 250 m
Rationale: "d 350 d = 72 * 5 / 18 = 25 = 500 â € “ 120 = 380"
Answer: d
Python program:
a = 72 * const_0_2778
b = 25 * a
c = b - 120
Problem: an exam consists of 8 true / false questions . brian forgets to study , so he must guess blindly on each question . if any score above 60 % is a passing grade , what is the probability that brian passes ?
Options: a ) 1 / 16 , b ) 37 / 256 , c ) 1 / 2 , d ) 35 / 256 , e ) 15 / 16
Rationale: "if you have 8 t or f and brian is going to guess then each question he has a 50 % chance of getting correct . if a passing score is 70 % it means brian needs to get 6 / 8 = 75 % , 7 / 8 = 87.5 % , or 8 / 8 = 100 % to pass . each is a possibility . if brian gets a 5 / 8 ( = 62.5 % ) or below he fails . so first figure out the number of ways that brian can get 6 out of 8 , 7 out of 8 , and 8 out of 8 questions correct . which is 8 choose 6 , equals is 28 , 8 choose 7 , equals 8 , and 8 choose 8 , equals 1 . this sums to 37 . the number of possible questions outcomes - the sum of 8 choose 8 , 7 choose 8 , 6 choose 8 … . 2 choose 8 , 1 choose 8 , and 0 choose 8 is 256 , so the chance of him passing is 35 / 256 . d"
Answer: d
Python program:
a = 1 / 2
b = a ** 8
c = 1 / 2
d = c ** 8
e = 8 * d
f = b + e 
g = 8 * 3
h = 1 / 2
i = h ** 8
j = g * i
k = f + j 
l = 1 - k
m = l / 10
n = 1 / 2
o = n ** 8
p = 1 / 2
q = p ** 8
r = 8 * q
s = o + r 
t = 8 * 3
u = 1 / 2
v = u ** 8
w = t * v
x = s + w 
y = 1 - x
z = m + y
Problem: the positive numbers w , x , y , and z are such that x is 35 percent greater than y , y is 20 percent greater than z , and w is 20 percent less than x . what percent greater than z is w ?
Options: a ) 15.2 % , b ) 16.0 % , c ) 20.0 % , d ) 23.2 % , e ) 24.8 %
Rationale: "my strategy is same as thedobermanbut instead take z = 100 , which makes life a bit easy . as : z = 100 y = 120 ( 20 % greater than z ) z = 144 ( 20 % greater than y ) now calculate w 20 % less than z = 144 * 80 / 100 = 115.2 now by just looking , relation between w and z : w - z / z * 100 = 20 - answer c"
Answer: c
Python program:
a = 35 + 100 
b = a / 100
c = 35 + 100 
d = c / 100
e = b * d
f = 100 - 35
g = f / 100
h = e * g
i = h - 1
j = 100 * i
Problem: evaluate : 22 + sqrt ( - 4 + 6 * 4 * 3 ) = ?
Options: a ) 4 , b ) 14 , c ) 24 , d ) 34 , e ) 44
Rationale: "according to order of operations , inner brackets first where 6 ? 4 ? 3 is first calculated since it has a multiplication and a division . 6 * 4 * 3 = 24 * 3 = 8 hence 22 + sqrt ( - 4 + 6 * 4 * 3 ) = 22 + sqrt ( - 4 + 8 ) = 22 + sqrt ( 4 ) = 22 + 2 = 24 correct answer c"
Answer: c
Python program:
a = 6 * 4
b = a / 3
c = b - 4
d = math.sqrt(c)
e = 22 + d
Problem: the width of a rectangle is 10 mtr and its area is 150 square meter . if length of the rectangle is increased , then its new area is 1 ( 1 / 3 ) times of the original area . what is the new perimeter of the rectangle ?
Options: a ) 45
b ) 54
c ) 67
d ) 60
e ) 69
Rationale: ans . ( d ) sol . length of original rectangle = 150 / 10 = 15 ( 10 * ( 15 + x ) ) / ( 10 * 15 ) = 4 / 3 x = 5 perimeter of new rectangle = 2 ( 10 + 20 ) = 60
Answer: d
Python program:
a = 150 * 4
b = a / 3
c = b / 10
d = 2 * c
e = 2 * 10
f = d + e
Problem: how long will a boy take to run round a square field of side 40 meters , if he runs at the rate of 9 km / hr ?
Options: a ) 64 sec , b ) 45 sec , c ) 1 min , d ) 32 sec , e ) 25 sec
Rationale: "speed = 9 km / hr = 9 * 5 / 18 = 5 / 2 m / sec distance = 40 * 4 = 160 m time taken = 160 * 2 / 5 = 64 sec answer is a"
Answer: a
Python program:
a = 40 * 4
b = 1000 / 3600
c = 9 * b
d = a / c
Problem: a runs twice as fast as b and gives b a start of 83 m . how long should the racecourse be so that a and b might reach in the same time ?
Options: a ) 75 m . , b ) 80 m . , c ) 150 m . , d ) 100 m . , e ) none of the above
Rationale: "ratio of speeds of a and b is 2 : 1 b is 83 m away from a but we know that a covers 1 meter ( 2 - 1 ) more in every second than b the time taken for a to cover 83 m is 83 / 1 = 83 m so the total time taken by a and b to reach = 2 * 83 = 166 m answer : e"
Answer: e
Python program:
a = 83 * 2
Problem: two trains 190 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.7 , b ) 10.9 , c ) 10.6 , d ) 12.6 , e ) 18.8
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 190 + 160 = 350 m . required time = 350 * 9 / 250 = 12.6 sec . answer : d"
Answer: d
Python program:
a = 190 + 160 
b = 60 + 40 
c = b * const_0_2778
d = a / c
Problem: 10 litres of water are poured into an aquarium of dimensions 50 cm length , 20 cm breadth , and 40 cm height . how high ( in cm ) will the water rise ? ( 1 litre = 1000 cm ³ )
Options: a ) 6 , b ) 8 , c ) 10 , d ) 20 , e ) 40
Rationale: lxbxh = 10000 h = 10000 / 50 * 20 = 10 cm ' c ' is the answer .
Answer: c
Python program:
a = 50 * 20
b = a * 40
c = b / 1000
d = c / 10
e = 40 / d
Problem: a retailer sells 10 shirts . the first 3 he sells for $ 82 , $ 100 and $ 90 . if the retailer wishes to sell the 10 shirts for an overall average price of over $ 100 , what must be the minimum average price of the remaining 7 shirts ?
Options: a ) $ 100.00 , b ) $ 104.00 , c ) $ 110.00 , d ) $ 115.00 , e ) $ 119.00
Rationale: first 3 shirts are sold for $ 82 , $ 100 and $ 90 = $ 272 . to get average price of $ 100 , total sale should be 10 * $ 100 = $ 1000 so remaining 7 shirts to be sold for $ 1000 - $ 272 = $ 728 answer should be 728 / 7 = $ 104.00 that is b
Answer: b
Python program:
a = 10 * 100
b = 82 + 100 
c = b + 90 
d = a - c
e = d / 7
Problem: a train running at the speed of 90 km / hr crosses a pole in 9 seconds . find the length of the train .
Options: a ) 225 meter , b ) 200 meter , c ) 250 meter , d ) 210 meter , e ) 230 meter
Rationale: "speed = 90 * ( 5 / 18 ) m / sec = 25 m / sec length of train ( distance ) = speed * time ( 25 ) * 9 = 225 meter answer : a"
Answer: a
Python program:
a = 90 * 1000
b = a / 3600
c = b * 9
Problem: what is the total number of integers between 20 and 80 ( exclusive ) that are divisible by 10 ?
Options: a ) 5 , b ) 7 , c ) 4 , d ) 9 , e ) 3
Rationale: "30 , 40,50 , 60,70 total 5 answer is a"
Answer: a
Python program:
a = 80 - 20
b = a / 10
c = b + 1
Problem: a mixture of 85 kg contains milk and water in the ratio 27 : 7 . how much more water is to be added to get a new mixture containing milk and water in the ratio 3 : 1 ?
Options: a ) 5 kg , b ) 6.5 kg , c ) 7.5 kg , d ) 8 kg , e ) 9 kg
Rationale: explanation : expl : milk in 85 kg of mix = 85 * ( 27 / 34 ) = 135 / 2 kg . water in it = 85 - 135 / 2 = 35 / 2 kg . let x kg of water be added to it . then , ( 135 / 2 ) / ( 35 / 2 + x ) = 3 / 1 ; 135 / ( 35 + 2 x ) = 3 / 1 ; 105 + 6 x = 135 ; 6 x = 30 ; x = 5 the quantity of water to be added = 5 kg answer : a
Answer: a
Python program:
a = 27 + 7 
b = 27 / a
c = 85 * b
d = 27 + 7 
e = 7 / d
f = 85 * e
g = 3 * f
h = c - g
i = h / 3
Problem: what is the sum of all the multiples of 25 between 30 and 100 ?
Options: a ) 800 , b ) 625 , c ) 600 , d ) 250 , e ) 200
Rationale: "you first have to know all the multiples of 25 between 30 and 100 . they are 25 , 50,75 and 100 . if you add all these numbers together , you get 250 . final answer : d"
Answer: d
Python program:
a = 12 + 2 
b = a + 1 
c = 12 + 2 
d = 2 + 4 
e = d + 4 
f = 10 - 1
g = e + f 
h = 2 + 4 
i = h + 4 
j = g + i 
k = 10 + 2 
l = j + k 
m = c + l 
n = b + m 
o = 12 + 2 
p = o + 1 
q = p + 1 
r = n + q 
s = r + 25 
t = 2 + 4 
u = s + t
Problem: the product of a and b is equal to 12 more than twice the sum of a and b . if b = 10 , what is the value of b - a ?
Options: a ) 2 , b ) 5 , c ) 7 , d ) 6 , e ) 35
Rationale: ab = 12 + 2 ( a + b ) 10 a = 12 + 2 a + 20 8 a = 32 a = 4 b - a = 10 - 4 = 6 d is the answer
Answer: d
Python program:
a = 10 * 2
b = a + 12 
c = 10 - 2
d = b / c
e = 10 - d
Problem: there are 7 stores in town that had a total of 21 visitors on a particular day . however , only 11 people went shopping that day ; some people visited more than one store . if 7 people visited exactly two stores each , and everyone visited at least one store , what is the largest number of stores anyone could have visited ?
Options: a ) 6 , b ) 8 , c ) 4 , d ) 9 , e ) 2
Rationale: "7 people visited 2 stores each for 14 visits . to maximize the number of stores that one person visited , let ' s assume that 3 people visited 1 store each . the number of remaining visits is 21 - 14 - 3 = 4 , which is the maximum that one person could have visited . the answer is c ."
Answer: c
Python program:
a = 7 * 2
b = 21 - a
c = 11 - 7
d = c - 1
e = b - d
Problem: what is the largest 4 digit number exactly divisible by 12 ?
Options: a ) 4676 , b ) 4678 , c ) 8888 , d ) 9504 , e ) 9996
Rationale: "largest 4 digit number = 9999 9999 ÷ 12 = 833 , remainder = 3 hence largest 4 digit number exactly divisible by 12 = 9999 - 3 = 9996 answer : e"
Answer: e
Python program:
a = 10 ** 4
b = a / 12
c = math.floor(b)
d = c * 12
Problem: the length of a rectangulat plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 5300 , what is the length of the plot in metres ?
Options: a ) 40 , b ) 50 , c ) 200 , d ) 120 , e ) none
Rationale: solution let breadth = x metres then , length = ( x + 20 ) metres . perimeter = ( 5300 / 26.50 ) m = 200 m answer c
Answer: c
Python program:
a = 5300 / 26
Problem: if two positive numbers are in the ratio 1 / 8 : 1 / 7 , then by what percent is the second number more than the first ?
Options: a ) 14.3 % . , b ) 70 % . , c ) 60 % . , d ) 68 % . , e ) 80 % .
Rationale: given ratio = 1 / 8 : 1 / 7 = 7 : 8 let first number be 7 x and the second number be 8 x . the second number is more than first number by 1 x . required percentage = 1 x / 7 x * 100 = 14.3 % . answer : a
Answer: a
Python program:
a = 1 / 7
b = a * 100
Problem: ashok secured average of 79 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?
Options: a ) 104 , b ) 27 , c ) 99 , d ) 17 , e ) 80
Rationale: "explanation : number of subjects = 6 average of marks in 6 subjects = 79 therefore total marks in 6 subjects = 79 * 6 = 474 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 474 – 370 = 104 answer : a"
Answer: a
Python program:
a = 79 * 6
b = 74 * 5
c = a - b
Problem: johnny makes $ 4.75 per hour at his work . if he works 6 hours , how much money will he earn ?
Options: a ) $ 30 , b ) $ 54 , c ) $ 28.50 , d ) $ 12 , e ) $ 9.60
Rationale: 4.75 * 6 = 28.50 . answer is c .
Answer: c
Python program:
a = 4 * 75
Problem: the sale price sarees listed for rs . 150 after successive discount is 20 % and 10 % is ?
Options: a ) 187 , b ) 120 , c ) 108 , d ) 178 , e ) 175
Rationale: "150 * ( 80 / 100 ) * ( 90 / 100 ) = 108 answer : c"
Answer: c
Python program:
a = 150 * 20
b = a / 100
c = 150 - b
d = 150 * 20
e = d / 100
f = 150 - e
g = f * 10
h = g / 100
i = c - h
Problem: the difference between a number and its three fifth is 50 . what is the number ?
Options: a ) 75 , b ) 100 , c ) 125 , d ) 180 , e ) none
Rationale: "solution let the number be x . then , x - 3 / 5 x = 50 ‹ = › 2 / 5 x = 50 ‹ = › x = ( 50 x 5 / 2 ) ‹ = › 125 . answer c"
Answer: c
Python program:
a = 50 + 4 
b = a ** 4
Problem: a rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing . if the poles of the fence are kept 20 metres apart , how many poles will be needed ?
Options: a ) 55 , b ) 56 , c ) 14 , d ) 58 , e ) none of these
Rationale: "solution perimeter of the plot = 2 ( 90 + 50 ) = 280 m . ∴ number of poles = [ 280 / 20 ] = 14 m answer c"
Answer: c
Python program:
a = rectangle_perimeter / (
Problem: how many liters of water must be added to 14 liters of milk and water containing 10 % water to make it 30 % water ?
Options: a ) 1 liter , b ) 2 liters , c ) 3 liters , d ) 4 liters , e ) 5 liters
Rationale: by rule of alligation : 30 % - 10 % = 20 % 100 % - 30 % = 70 % quantity of pure water : quantity of the mixture = 2 : 7 there are 14 liters of mixture , so we need to add 4 liters of pure water . the answer is d .
Answer: d
Python program:
a = 14 / 10
b = 30 / 10
c = a * b
Problem: in the x - y plane , there are 4 points ( 0,0 ) , ( 0,4 ) , ( 4,4 ) , and ( 4,0 ) . if these 4 points makes a rectangle , what is the probability that x + y < 4 ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: "if x + y < 4 , then y < - x + 4 . the line y = - x + 4 intersects the rectangle and these three points of intersection ( 0,0 ) , ( 0,4 ) and ( 4,0 ) form a triangle . the points below the line y = - x + 4 satisfy x + y < 4 . the area of this triangle is ( 1 / 2 ) ( 4 ) ( 4 ) = 8 the area of the rectangle is 16 . p ( x + y < 4 ) = 8 / 16 = 1 / 2 the answer is a ."
Answer: a
Python program:
a = 4 * 4
b = a / 2
c = 1 + 4 
d = 4 * c
e = b / d
Problem: the population of a town is 10000 . it increases annually at the rate of 20 % p . a . what will be its population after 6 years ?
Options: a ) 14300 , b ) 29859 , c ) 14500 , d ) 14600 , e ) 15400
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 10000 × 120 / 100 ^ 6 = 29859 b )"
Answer: b
Python program:
a = 10000 * 20
b = a / 100
c = b * 6
d = 10000 + c
Problem: john and ingrid pay 30 % and 40 % tax annually , respectively . if john makes $ 58000 and ingrid makes $ 72000 , what is their combined tax rate ?
Options: a ) 32 % , b ) 34.4 % , c ) 35 % , d ) 35.6 % , e ) 37.4 %
Rationale: ( 1 ) when 30 and 40 has equal weight or weight = 1 / 2 , the answer would be 35 . ( 2 ) when 40 has larger weight than 30 , the answer would be in between 35 and 40 . unfortunately , we have 2 answer choices d and e that fit that condition so we need to narrow down our range . ( 3 ) get 72000 / 130000 = 36 / 65 . 36 / 65 is a little above 36 / 72 = 1 / 2 . thus , our answer is just a little above 35 . answer : d
Answer: d
Python program:
a = 30 / 100
b = a * 58000
c = 40 / 100
d = c * 72000
e = b + d 
f = 72000 + 58000 
g = e / f
h = g * 100