euclaise/mathqa_programs huggingface dataset:
Problem: courtyard 3.78 meters long 5.95 meters wide is to be paved exactly with square tiles , all of the same size . what is the largest size of the tile which could be used for the purpose ?
Options: a ) 22 , b ) 77 , c ) 877 , d ) 99 , e ) 88
Rationale: 3.78 meters = 378 cm = 2 × 3 × 3 × 3 × 7 5.25 meters = 525 cm = 5 × 5 × 3 × 7 hence common factors are 3 and 7 hence lcm = 3 × 7 = 21 hence largest size of square tiles that can be paved exactly with square tiles is 77 cm . answer : b
Answer: b
Python program:
a = 5 * 95
b = a * 3
c = b + 10
Problem: in a college the ratio of the numbers of boys to the girls is 8 : 5 . if there are 160 girls , the total number of students in the college is ?
Options: a ) 562 , b ) 356 , c ) 452 , d ) 416 , e ) 512
Rationale: "let the number of boys and girls be 8 x and 5 x then , 5 x = 160 x = 32 total number of students = 13 x = 13 * 32 = 416 answer is d"
Answer: d
Python program:
a = 8 / 5
b = a * 160
c = b + 160
Problem: x is a positive integer less than 500 . when x is divided by 5 , the remainder is 1 ; when x is divided by 3 , the remainder is 2 . how many x are there ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "the nubmer which when divided by 5 leaves remainder 1 should be of the form 7 k + 1 this number when divided by 3 leaves remainder 2 . so , ( 7 k + 1 ) - 2 should be divisible by 3 or 7 k - 1 should be divisible by 3 . we now put the values of k starting from 0 to find first number divisible by 3 we find 1 st number at k = 1 thus smallest number will be 7 ( 1 ) + 1 = 8 now , next number will be = 8 + lcm of 37 i . e 29 now we will find number of all such values less than 500 by using the formula for last term of an a . p 8 + ( n - 1 ) 21 = 500 n = 24.42 or n = 24 answer : - d"
Answer: d
Python program:
a = reminder * (
b = a + 3 
c = b - reminder
Problem: john distributes his pencil among his 4 friends rose , mary , ranjan , and rohit in the ratio 1 / 4 : 1 / 3 : 1 / 4 : 1 / 5 . what is the minimum no . of pencils that the person should have ?
Options: a ) 45 , b ) 62 , c ) 70 , d ) 77 , e ) 98
Rationale: "rakesh : rahul : ranjan : rohit = 1 / 4 : 1 / 3 : 1 / 4 : 1 / 5 step 1 : at first we need to do is lcm of 2 , 3,4 and 5 is 60 . step 2 : then pencil are distributed in ratio among friends , rakesh = ( 1 / 4 x 60 ) = 15 . rahul = ( 1 / 3 x 60 ) = 20 . ranjan = ( 1 / 4 x 60 ) = 15 . rohit = ( 1 / 5 x 60 ) = 12 . step 3 : total number of pencils are ( 15 x + 20 x + 15 x + 12 x ) = 62 x . for minimum number of pencils x = 1 . the person should have at least 62 pencils . b )"
Answer: b
Python program:
a = math.lcm(4, 1)
b = math.lcm(a, 1)
c = math.lcm(b, 3)
d = c / 4
e = math.lcm(4, 1)
f = math.lcm(e, 1)
g = math.lcm(f, 3)
h = g / 1
i = d + h 
j = math.lcm(4, 1)
k = math.lcm(j, 1)
l = math.lcm(k, 3)
m = l / 1
n = i + m 
o = math.lcm(4, 1)
p = math.lcm(o, 1)
q = math.lcm(p, 3)
r = q / 3
s = n + r
Problem: tough and tricky questions : word problems . a salesman ' s income consists of commission and base salary . his weekly income totals over the past 5 weeks have been $ 406 , $ 413 , $ 420 , $ 436 and $ 395 . what must his average ( arithmetic mean ) income over the next 5 weeks be to increase his average weekly income to $ 500 over the 10 - week period ?
Options: a ) $ 570 , b ) $ 586 , c ) $ 630 , d ) $ 686 , e ) $ 715
Rationale: official solution : ( b ) first , we need to add up the wages over the past 5 weeks : $ 406 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2070 . to average $ 500 over 10 weeks , the salesman would need to earn : $ 500 × 10 = $ 5000 . subtract $ 2070 from $ 5000 to determine how much he would need to earn , in total , over the next 5 weeks to average $ 500 for the 10 weeks : $ 5000 – $ 2070 = $ 2930 . dividing $ 2930 by 5 will give us the amount he needs to earn on average over the next 5 weeks : $ 2930 / 5 = $ 586 . the correct answer is choice ( b ) .
Answer: b
Python program:
a = 406 + 413 
b = a + 420 
c = b + 436 
d = c + 395 
e = d / 5
f = 500 - e
g = 500 + f
Problem: when a random experiment is conducted , the probability that event a occurs is 1 / 3 . if the random experiment is conducted 4 independent times , what is the probability that event a occurs exactly twice ?
Options: a ) 8 / 27 , b ) 10 / 31 , c ) 12 / 37 , d ) 14 / 41 , e ) 16 / 49
Rationale: "one case is : 1 / 3 * 1 / 3 * 2 / 3 * 2 / 3 = 4 / 81 the total number of possible cases is 4 c 2 = 6 p ( event a occurs exactly twice ) = 6 * ( 4 / 81 ) = 8 / 27 the answer is a ."
Answer: a
Python program:
a = 2 / 3
b = 1 - a
Problem: if 16 % of 40 % of a number is 6 , then the number is
Options: a ) 200 , b ) 225 , c ) 93.75 , d ) 320 , e ) none of these
Rationale: explanation : let 16 / 100 × 40 / 100 × a = 6 a = 6 × 100 × 100 / 16 × 40 = 93.75 correct option : c
Answer: c
Python program:
a = 16 / 100
b = 40 / 100
c = a * b
d = 6 / c
Problem: one day a car rental agency rented 2 / 3 of its cars , including 3 / 5 of its cars with cd players . if 3 / 5 of its cars have cd players , what percent of the cars that were not rented had cd players ?
Options: a ) 18 / 25 , b ) 17 / 20 , c ) 11 / 15 , d ) 7 / 10 , e ) 3 / 5
Rationale: "the cars with cd players which were not rented is ( 2 / 5 ) ( 3 / 5 ) = 6 / 25 of all the cars . the cars which were not rented is 1 / 3 of all the cars . the percent of non - rented cars which had cd players is ( 6 / 25 ) / ( 1 / 3 ) = 18 / 25 the answer is a ."
Answer: a
Python program:
a = 3 * 3
b = a * 5
c = 3 * b
d = c / 5
e = 3 * 3
f = e * 5
g = 3 * f
h = g / 5
i = h * 3
j = i / 3
k = d - j
l = 3 * 3
m = l * 5
n = 3 * 3
o = n * 5
p = 2 * o
q = p / 3
r = m - q
s = k / r
t = s * 100
Problem: if the price of gasoline increases by 20 % and a driver intends to spend only 8 % more on gasoline , by how much percent should the driver reduce the quantity of gasoline that he buys ?
Options: a ) 4 % , b ) 5 % , c ) 6 % , d ) 8 % , e ) 10 %
Rationale: "let x be the amount of gasoline the driver buys originally . let y be the new amount of gasoline the driver should buy . let p be the original price per liter . ( 1.2 * p ) y = 1.08 ( p * x ) y = ( 1.08 / 1.2 ) x = 0.9 x which is a reduction of 10 % . the answer is e ."
Answer: e
Python program:
a = 20 + 100 
b = 8 + 100 
c = a - b
d = 20 + 100 
e = c / d
f = e * 100
Problem: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg . what might be the weight of the new person ?
Options: a ) 70 kg , b ) 80 kg , c ) 85 kg , d ) 90 kg , e ) 95 kg
Rationale: "total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 50 + 20 ) kg = 70 kg . a )"
Answer: a
Python program:
a = 8 * 2
b = a + 50
Problem: machine a can finish a job in 4 hours , machine в can finish the job in 2 hours , and machine с can finish the job in 6 hours . how many hours will it take for a , b , and с together to finish the job ?
Options: a ) 4 / 3 , b ) 6 / 5 , c ) 8 / 7 , d ) 10 / 9 , e ) 12 / 11
Rationale: "the combined rate is 1 / 4 + 1 / 2 + 1 / 6 = 11 / 12 of the job per hour . the time to complete the job is 12 / 11 hours . the answer is e ."
Answer: e
Python program:
a = 1/(4)
b = 1/(2)
c = a + b 
d = 1/(6)
e = c + d 
f = 1/(e)
Problem: a cubical block of metal weighs 3 pounds . how much will another cube of the same metal weigh if its sides are twice as long ?
Options: a ) 48 , b ) 32 , c ) 24 , d ) 18 , e ) 12
Rationale: "for example our cube have a side 1 meter , so we have 1 cubical meter in this cube and this cubical meter weigth 3 pounds if we take cube with side 2 meters we will have 8 cubical meters in this cube 8 meters * 3 pounds = 24 pounds so answer is c and similar but more theoretical approach : if we have sides a and b than they have equal ration with their areas : a / b = a ^ 2 / b ^ 2 and they have equal ration with their volumes : a / b = a ^ 3 / b ^ 3 we have two sides 1 / 2 so their volume will be in ratio 1 / 8 weight of one cube * volume of another cube 3 * 8 = 24 so answer is c"
Answer: c
Python program:
a = 2 * 4
b = 3 * a
Problem: two coins are tossed . find the probability of at most 2 tails ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 3 , d ) 1 , e ) 3 / 4
Rationale: "n ( s ) = 2 ^ 2 = 4 . . . . ( 2 coins are tossed ) let e is the event of getting at most 2 tails n ( e ) = hh , tt , ht , th = 4 p ( e ) = n ( e ) / n ( s ) = 4 / 4 = 1 ans - d"
Answer: d
Python program:
a = 2 ** 2
b = 2 / a
Problem: a trader sells 85 meters of cloth for rs . 8925 at the profit of rs . 35 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 21 , b ) 28 , c ) 90 , d ) 26 , e ) 70
Rationale: "explanation : sp of 1 m of cloth = 8925 / 85 = rs . 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 105 - rs . 35 = rs . 70 . answer : e"
Answer: e
Python program:
a = 8925 / 85
b = a - 35
Problem: how many seconds will a train 200 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?
Options: a ) 22 sec , b ) 35 sec , c ) 25 sec , d ) 18 sec , e ) 17 sec
Rationale: "d = 200 + 150 = 350 s = 36 * 5 / 18 = 10 mps t = 350 / 10 = 35 sec answer : b"
Answer: b
Python program:
a = 150 + 200 
b = 36 * const_0_2778
c = a / b
Problem: a sum of rs . 427 is to be divided among a , b and c in such a way that 3 times a ’ s share , 4 times b ’ s share and 7 times c ’ s share are all equal . the share of c is
Options: a ) 82 , b ) 83 , c ) 84 , d ) 85 , e ) 86
Rationale: "a + b + c = 427 3 a = 4 b = 7 c = > ( 7 c / 3 ) + ( 7 c / 4 ) + c = 427 = > c = 84 answer : c"
Answer: c
Python program:
a = 7 / 7
b = 7 / 3
c = 7 / 4
d = b + c 
e = a + d 
f = 427 / e
Problem: find the average of first 4 multiples of 12 ?
Options: a ) 10 , b ) 12.6 , c ) 22.5 , d ) 30 , e ) 40.8
Rationale: "average = ( 12 + 24 + 36 + 48 ) / 4 = 30 answer is d"
Answer: d
Python program:
a = 4 + 1 
b = 4 + 1 
c = b + 2 
d = a + c 
e = 12 - 4
f = 12 - 2
g = e + f 
h = d + g 
i = h / 4
Problem: there is a rectangular prism made of 1 in cubes that has been covered in tin foil . there are exactly 128 cubes that are not touching any tin foil on any of their sides . if the width of the figure created by these 128 cubes is twice the length and twice the height , what is the p measure in inches of the width of the foil covered prism ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 10
Rationale: "if the width is w , then length and height would be w / 2 . so , w * w / 2 * w / 2 = 128 = > w ^ 3 = ( 2 ^ 3 ) * 64 = ( 2 ^ 3 ) * ( 4 ^ 3 ) = > w = 2 * 4 = 8 in . along the width of the cuboid , 8 cubes do n ' t touch the tin foil . so the actual width will be non - touching cubes + touching cubes = 8 + 2 = p = 10 ans e ."
Answer: e
Python program:
a = 1 * 2
b = 1 * a
c = 128 / b
d = 1/(3)
e = c ** d
f = 1 * 2
g = e * f
h = 1 * 2
i = g + h
Problem: if 15 students in a class average 80 % on an english exam and 10 students average 90 % on the same exam , what is the average in percent for all 25 students ?
Options: a ) 83 % , b ) 83 1 ⁄ 2 % , c ) 84 % , d ) 85 % , e ) 86 2 ⁄ 3 %
Rationale: the average percentage = ( 15 x 80 % + 10 x 90 % ) / 25 = ( 15 x 80 % + 10 x 80 % + 10 x 10 % ) / 25 . . . . . . ( as 90 % = 10 % + 80 % ) = ( 25 x 80 % + 10 x 10 % ) / 25 = 80 % + 10 x 10 % / 25 = 80 % + 4 % = 84 % answer : c
Answer: c
Python program:
a = 15 * 80
b = 10 * 90
c = a + b 
d = c / 25
Problem: a man sitting in a train which is traveling at 50 kmph observes that a goods train , traveling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed
Options: a ) 52 kmph , b ) 56 kmph , c ) 58 kmph , d ) 62 kmph , e ) 72 kmph
Rationale: "explanation : relative speed = 280 / 9 m / sec = ( ( 280 / 9 ) × ( 18 / 5 ) ) kmph = 112 kmph . speed of goods train = ( 112 - 50 ) kmph = 62 kmph answer : option d"
Answer: d
Python program:
a = 280 / 9
b = a * const_3_6
c = b - 50
Problem: how many positive factors do 160 and 96 have in common ?
Options: a ) 6 , b ) 12 , c ) 16 , d ) 18 , e ) 24
Rationale: "the number of common factors will be same as number of factors of the highest common factor ( hcf ) hcf of 160 and 96 is 32 number of factors of 32 = 6 answer : a"
Answer: a
Python program:
a = 96 - 10
b = a / 10
Problem: how many odd prime numbers are there less than 50 ?
Options: a ) 15 , b ) 1 , c ) 2 , d ) 14 , e ) 17
Rationale: "odd prime number less than 50 : 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 there is 14 the odd prime number answer is d"
Answer: d
Python program:
a = 50 - 100
b = a + 4
Problem: at a local appliance manufacturing facility , the workers received a 15 % hourly pay raise due to extraordinary performance . if one worker decided to reduce the number of hours that he worked so that his overall pay would remain unchanged , by approximately what percent would he reduce the number of hours that he worked ?
Options: a ) 13 % , b ) 80 % , c ) 20 % , d ) 17 % , e ) 12 %
Rationale: "let ' s say he works usually 10 hours and earns 100 per hour . 10 * 100 = 1000 10 * 115 = 1150 ( this are the new earnings after the raise ) to figure out how much he needs to work with the new salary in order to earn the original 1000 : 1000 / 115 = 8.7 so he can reduce his work by 1.3 hours . which is > 13 % . answer a"
Answer: a
Python program:
a = 15 - 1
Problem: if the simple interest on $ 2000 increase by $ 40 , when the time increase by 4 years . find the rate percent per annum .
Options: a ) 1.2 % , b ) 0.5 % , c ) 0.7 % , d ) 0.9 % , e ) 0.3 %
Rationale: "applying the above formula , we have 40 = 2000 * r * 4 / 100 r = 40 * 100 / 2000 * 4 = 0.5 % . answer is b"
Answer: b
Python program:
a = 40 / 4
b = a / 2000
c = b * 100
Problem: in a room filled with 7 people , 4 people have exactly 1 sibling in the room and 3 people have exactly 2 siblings in the room . if two individuals are selected from the room at random , what is the probability that those two individuals are not siblings ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 7 , e ) 16 / 21
Rationale: "# of selections of 2 out of 7 - c 27 = 21 c 72 = 21 ; # of selections of 2 people which are not siblings - c 12 ∗ c 12 c 21 ∗ c 21 ( one from first pair of siblings * one from second pair of siblings ) + c 12 ∗ c 13 c 21 ∗ c 31 ( one from first pair of siblings * one from triple ) + c 1 ^ _ 2 * c ^ 1 _ 3 ( one from second pair of siblings * one from triple ) = 4 + 6 + 6 = 16 = 4 + 6 + 6 = 16 . p = 16 / 21 answer : e"
Answer: e
Python program:
a = 4 / 7
b = 7 - 2
c = 7 - 1
d = b / c
e = a * d
f = 4 / 7
g = 7 - 4
h = 7 - 1
i = g / h
j = f * i
k = e + j
Problem: working at their respective constant rates , machine a makes 100 copies in 12 minutes and machine b makes 150 copies in 15 minutes . if these machines work simultaneously at their respective rates for 30 minutes , what is the total number of copies that they will produce ?
Options: a ) 250 , b ) 425 , c ) 550 , d ) 700 , e ) 750
Rationale: machine a can produce 100 * 30 / 12 = 250 copies and , machine b can produce 150 * 30 / 15 = 300 copies total producing 550 copies . c is the answer
Answer: c
Python program:
a = 100 / 12
b = 150 / 15
c = a + b 
d = c * 30
Problem: which number can we add to 897326 to get a number exactly divisible by 456 ?
Options: a ) 58 , b ) 66 , c ) 74 , d ) 82 , e ) 90
Rationale: 897326 / 456 = 1967 with a remainder of 374 . we need to add 456 - 374 = 82 the answer is d .
Answer: d
Python program:
a = 456 - reminder
Problem: when two dice are rolled , what is the probability that the sum is either 7 or 11 ?
Options: a ) 1 / 4 , b ) 1 / 9 , c ) 4 / 3 , d ) 3 / 9 , e ) 2 / 9
Rationale: total number of outcomes possible = 36 probability of getting sum of 7 = 6 / 36 probability of getting sum of 11 = 2 / 36 probability that the sum is either 7 or 11 = 6 / 36 + 2 / 36 = 2 / 9 answer : e
Answer: e
Python program:
a = 7 + 1 
b = 6 * 6
c = a / b
Problem: the radius of a wheel is 24.2 cm . what is the distance covered by the wheel in making 500 resolutions ?
Options: a ) 708 m , b ) 704 m , c ) 774 m , d ) 760.57 m , e ) 744 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 500 * 2 * 22 / 7 * 24.2 = 76057 cm = 760.57 m answer : d"
Answer: d
Python program:
a = 3 + 4 
b = a * 3
c = b + 1 
d = 3 + 4 
e = c / d
f = e * 24
g = f * 2
h = g * 500
i = h / 100
Problem: after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 3940 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ?
Options: a ) 2160 , b ) 2350 , c ) 2000 , d ) 2300 , e ) none of these
Rationale: "explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 3940 = 19440 exp in % = 100 - 10 = 90 % , 19440 = 90 % saving = 10 % = 19440 x 10 / 90 = rs . 2160 answer : a"
Answer: a
Python program:
a = 5000 + 1500 
b = a + 4500 
c = b + 2500 
d = c + 2000 
e = d + 3940 
f = e * 100
g = 100 - 10
h = f / g
i = 5000 + 1500 
j = i + 4500 
k = j + 2500 
l = k + 2000 
m = l + 3940 
n = h - m
Problem: the standard deviation of a normal distribution of data is 2 , and 3 standard deviations below the mean is greater than 44 . what is a possible value for the mean of the distribution ?
Options: a ) 46 , b ) 47 , c ) 48 , d ) 49 , e ) 51
Rationale: "the standard deviation ( { sd } ) = 2 ; 3 standard deviations below the mean is greater than 44 : { mean } - 3 * { sd } > 44 ; { mean } - 6 > 44 ; { mean } > 50 . answer : e ."
Answer: e
Python program:
a = 3 * 2
b = 44 + a 
c = b + 1
Problem: the set x = { 78 , 910 } . the set y = { 23 , 45 } . we will randomly choose one element x from set x and one element y from set y . what is the probability that x / y will be an integer ?
Options: a ) 7 / 16 , b ) 5 / 16 , c ) 3 / 16 , d ) 7 / 8 , e ) 5 / 8
Rationale: the total number of x and y pairs is 4 * 4 = 16 . there are five pairs such that x / y is an integer . the probability that x / y is an integer is 5 / 16 . the answer is b .
Answer: b
Python program:
a = 78 / 23
b = math.floor(a)
c = b + 2 
d = 910 / 45
e = math.floor(d)
f = 78 / 23
g = math.floor(f)
h = e - g
i = h - 1
j = c / i
Problem: what is the value of 4 ^ 5 + 4 ^ 8 ?
Options: a ) 4 ^ 12 , b ) 4 ^ 35 , c ) 17 ( 4 ^ 5 ) , d ) 8 ^ 12 , e ) 65 ( 4 ^ 5 )
Rationale: "4 ^ 5 + 4 ^ 8 = 4 ^ 5 ( 1 + 4 ^ 3 ) = 4 ^ 5 * 65 answer e"
Answer: e
Python program:
a = 100 + const_60 
b = a + 1 
c = b * 4
d = c / 100
Problem: john bought a total of 12 mangoes and oranges . each mango costs 80 cents and each orange costs 50 cents . if the average price of the 12 mangoes and oranges that john originally purchased was 65 cents , then how many oranges needs to return to raise the average price of his purchase to 72 cents ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "let number of mangoes be x , number of oranges be 12 - x 0.80 x + ( 12 - x ) 0.50 / 12 = 0.65 solving for x , we get x = 6 - - > mangoes 6 , oranges 6 now , number of oranges to be returned be y [ 0.80 * 6 + ( 6 - y ) * 0.50 ] / 12 - y = 0.72 solving for y , y = 4 ans : a"
Answer: a
Python program:
a = 65 / 100
b = a * 12
Problem: two vessels contains equal number of mixtures milk and water in the ratio 4 : 2 and 5 : 1 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ?
Options: a ) 3 : 1 , b ) 9 : 13 , c ) 5 : 11 , d ) 11 : 3 , e ) 15 : 4
Rationale: "the ratio of milk and water in the new vessel is = ( 4 / 6 + 5 / 6 ) : ( 2 / 6 + 1 / 6 ) = 9 / 6 : 3 / 6 = 3 : 1 answer is a"
Answer: a
Python program:
a = 5 + 1 
b = 4 + 2 
c = a / b
d = 4 * c
e = d + 5 
f = 5 + 1 
g = 4 + 2 
h = f / g
i = 2 * h
j = i + 1 
k = e / j
Problem: for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of all the even integers between 99 and 201 ?
Options: a ) 7650 , b ) 9250 , c ) 12,650 , d ) 14,250 , e ) 15,150
Rationale: "100 + 102 + . . . + 200 = 100 * 51 + ( 2 + 4 + . . . + 100 ) = 100 * 51 + 2 * ( 1 + 2 + . . . + 50 ) = 100 * 51 + 2 ( 50 ) ( 51 ) / 2 = 100 * 51 + 50 * 51 = 150 ( 51 ) = 7650 the answer is a ."
Answer: a
Python program:
a = 201 - 1
b = 99 + 1 
c = a - b
d = c / 2
e = d + 1
Problem: in what time will a train 90 m long cross an electric pole , it its speed be 72 km / hr ?
Options: a ) 1.5 , b ) 2.5 , c ) 3.5 , d ) 4.5 , e ) 5.5
Rationale: "speed = 72 * 5 / 18 = 20 m / sec time taken = 90 / 20 = 4.5 sec . answer : d"
Answer: d
Python program:
a = 72 * const_0_2778
b = 90 / a
Problem: a can give b 200 meters start and c 400 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 111.12 , b ) 250 , c ) 111.64 , d ) 111.11 , e ) 101.12
Rationale: "a runs 1000 m while b runs 800 m and c runs 600 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 600 ) / 800 = 750 m . b can give c = 1000 - 750 = 250 m . answer : b"
Answer: b
Python program:
a = 100 * 10
b = 100 * 10
c = 100 * 10
d = c - 400
e = b * d
f = 100 * 10
g = f - 200
h = e / g
i = a - h
Problem: a reduction of 40 % in the price of bananas would enable a man to obtain 65 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 1.95 , b ) 2.95 , c ) 4.95 , d ) 3.95 , e ) 5.95
Rationale: "40 * ( 40 / 100 ) = 16 - - - 65 ? - - - 12 = > rs . 2.95 answer : b"
Answer: b
Python program:
a = 40 / 100
b = 40 * a
c = b / 65
d = 12 * c
Problem: a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 20 % while buying and by 10 % while selling . what is his percentage profit ?
Options: a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 20 % , e ) ca n ' t be calculated
Rationale: "the owner buys 100 kg but actually gets 120 kg ; the owner sells 100 kg but actually gives 90 kg ; profit : ( 120 - 90 ) / 90 * 100 = 20 % answer : d ."
Answer: d
Python program:
a = 100 + 20 
b = 100 - 10
c = a - b
d = c * 100
e = 100 - 10
f = d / e
Problem: for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 115 units raises the average to 55 units per day , what is the value of n ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: the daily production was raised by 5 units for n days , which has a weighting of 5 n . 5 n = 115 - 55 = 60 n = 12 the answer is c .
Answer: c
Python program:
a = 115 - 50
b = 55 - 50
c = a / b
d = c - 1
Problem: the h . c . f . of two numbers is 11 and their l . c . m . is 7700 . if one of the numbers is 275 , then the other is :
Options: a ) 279 , b ) 283 , c ) 308 , d ) 318 , e ) 338
Rationale: other number = ( 11 x 7700 ) / 275 = 308 . answer : c
Answer: c
Python program:
a = 11 * 275
Problem: excluding stoppages , the speed of a bus is 54 kmph and including stoppages , it is 41 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 7 min , b ) 8 min , c ) 14.4 min , d ) 10 min , e ) 11 min
Rationale: due to stoppages , it covers 13 km less . time taken to cover 13 km = ( 13 / 54 ) x 60 = 14.4 min answer : c
Answer: c
Python program:
a = 54 - 41
b = a / 54
c = const_60 * b
Problem: a train length 100 m going with speed 10 m / sec another train 150 m long going with speed 15 m / sec . the distance between two train is 50 m . then how much time second train will take to cross the first train ?
Options: a ) 60 sec , b ) 40 sec , c ) 30 sec , d ) 45 sec , e ) 1 min 10 sec
Rationale: net speed = 15 - 10 = 5 m / sec net distance = 100 + 150 + 50 = 300 total time = 300 / 5 = 60 sec answer a
Answer: a
Python program:
a = 100 + 150 
b = a + 50 
c = 15 - 10
d = b / c
Problem: one copy machine can make 15 copies a minute , and a second copy machine makes 10 copies a minute . if the two copiers work together , how long would it take them to make 1,000 copies ?
Options: a ) 20 minutes , b ) 30 minutes , c ) 40 minutes , d ) 50 minutes , e ) 60 minutes
Rationale: total work done by both machines in a minute = 15 + 10 = 25 copies total number of copies required = 1000 time = 1000 / 25 = 40 mins answer c
Answer: c
Python program:
a = 10 ** 3
b = 15 + 10 
c = a / b