euclaise/mathqa_programs huggingface dataset:
Problem: every student in a room is either a junior or a senior . there is at least one junior and at least one senior in the room . if 2 / 3 of the juniors is equal to 1 / 2 of the seniors , what fraction of the students in the room are juniors ?
Options: a ) 3 / 20 , b ) 1 / 3 , c ) 3 / 7 , d ) 2 / 7 , e ) 7 / 2
Rationale: "let total number of juniors = j total number of seniors = s ( 2 / 3 ) j = ( 1 / 2 ) s = > s = 4 / 3 j total number of students = j + s = ( 7 / 3 ) j fraction of the students in the room are juniors = j / ( j + s ) = j / [ ( 7 / 3 ) j ] = 3 / 7 answer c"
Answer: c
Python program:
a = 3 * 3
b = 3 * 3
c = 2 + b 
d = a / c
Problem: a meal cost $ 34.50 and there was no tax . if the tip was more than 10 pc but less than 15 pc of the price , then the total amount paid should be :
Options: a ) 40 - 42 , b ) 39 - 41 , c ) 38 - 40 , d ) 37 - 39 , e ) 36 - 37
Rationale: 10 % ( 34.5 ) = 3.45 15 % ( 34.5 ) = 5.175 total amount could have been 34.5 + 3.45 and 34.5 + 5.175 = > could have been between 37.95 and 39.675 = > approximately between 38 and 40 answer is c .
Answer: c
Python program:
a = 15 / 100
b = 34 * 5
c = b + 34
Problem: in an examination , questions were asked in 5 sections . out of the total students , 5 % candidates cleared the cut - off in all the sections and 5 % cleared none . of the rest , 25 % cleared only one section and 20 % cleared 4 sections . if 24.5 % of the entire candidates cleared two sections and 300 candidates cleared 3 sections . find out how many candidates appeared at the examination ?
Options: a ) 1000 , b ) 1200 , c ) 1500 , d ) 2000 , e ) 1800
Rationale: solution : passed in none = 5 % passed in all = 5 % passed in four = 20 % 0 f 90 % = 18 % passed in three = 24.5 % passed in three = ( 100 - 5 - 5 - 22.5 - 24.5 - 18 ) = 25 % . but given 300 students passed in three . hence , 25 % = 300 . so , 100 % = 1200 . 1200 students must have appeared . answer : option b
Answer: b
Python program:
a = 5 + 5 
b = 5 + 5 
c = 100 - b
d = c * 25
e = d / 100
f = a + e 
g = 5 + 5 
h = 100 - g
i = h * 20
j = i / 100
k = f + j 
l = k + 24 
m = 100 - l
n = 300 / m
o = n * 100
Problem: a carpenter worked alone for 1 day on a job that would take him 4 more days to finish . he and another carpenter completed the job in 2 more days . how many days would it have taken the second carpenter to do the complete job working alone ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 14 , e ) 24
Rationale: "a carpenter worked only 1 day on something that takes him 4 more days . means ; carpenter finishes his work in 5 days . let his buddy finish the same task in x days . respective rates per day : 1 / 5 and 1 / x to complete 1 work : first guy worked for 3 days @ rate = 1 / 5 per day . second one worked for 2 days @ rate = 1 / x per day expression : days * rate = work 3 * 1 / 5 + 2 * 1 / x = 1 3 x + 10 = 5 x 2 x = 10 x = 5 days . ans : a"
Answer: a
Python program:
a = 1 + 4 
b = 2 * a
c = b / 2
Problem: g ( x ) is defined as the product of all even integers k such that 0 < k ≤ x . for example , g ( 14 ) = 2 × 4 × 6 × 8 × 10 × 12 × 14 . if g ( z ) is divisible by 4 ^ 11 , what is the smallest possible value for z ?
Options: a ) 22 , b ) 24 , c ) 28 , d ) 32 , e ) 44
Rationale: g ( z ) = 4 ^ 11 = 2 ^ 22 . so we have to find a product with atleast 22 2 ' s in it . in option 1 22 the total no of 2 ' s = [ 22 / 2 ] + [ 22 / 4 ] + [ 22 / 8 ] + [ 22 / 16 ] = 11 + 5 + 2 + 1 = 19 in option 2 24 the total no of 2 ' s = [ 24 / 2 ] + [ 24 / 4 ] + [ 24 / 8 ] + [ 24 / 16 ] = 12 + 6 + 3 + 1 = 22 . hence b
Answer: b
Python program:
a = 2 * 12
Problem: if 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a 7 - percent vinegar solution , what was the concentration of the original solution ?
Options: a ) 19.3 % , b ) 17 % , c ) 36.17 % , d ) 15.5 % , e ) 12.5 %
Rationale: let x be the quantity of non - vinegar in the strong vinegar solution thus vinegar quantity will be 12 - x when 50 ounces of water were added the percentage of vinegar becomes 7 % , thus ( 12 - x ) / 62 = 7 / 100 from this equation x = 7.66 answer ( 12 - 7.66 ) / 12 = 36.17 % answer : c
Answer: c
Python program:
a = 50 + 12 
b = a * 7
c = b / 12
Problem: if ( a + b ) = 5 , ( b + c ) = 6 and ( c + d ) = 3 , what is the value of ( a + d ) ?
Options: a ) 16 . , b ) 8 . , c ) 7 . , d ) 2 . , e ) - 2 .
Rationale: "given a + b = 5 b + c = 6 c + d = 3 ( a + b ) - ( b + c ) + ( c + d ) = ( a + d ) = > 5 - 6 + 3 = 2 . option d . . ."
Answer: d
Python program:
a = 5 + 3 
b = a - 6
Problem: on a map the distance between two mountains is 312 inches . the actual distance between the mountains is 136 km . ram is camped at a location that on the map is 25 inch from the base of the mountain . how many km is he from the base of the mountain ?
Options: a ) 10.89 , b ) 14.81 , c ) 14.8 , d ) 14.82 , e ) 14.12
Rationale: "explanation : since 312 inch = 136 km so 1 inch = 136 / 312 km so 25 inch = ( 136 ã — 25 ) / 312 = 10.89 km answer : a"
Answer: a
Python program:
a = 25 * 136
b = a / 312
Problem: a garrison of 400 men had a provision for 31 days . after 27 days 200 persons re - enforcement leave the garrison . find the number of days for which the remaining ration will be sufficient ?
Options: a ) 65 days , b ) 45 days , c ) 8 days , d ) 16 days , e ) 18 days
Rationale: 400 - - - 31 400 - - - 4 200 - - - ? 400 * 4 = 200 * x = > x = 8 days . answer : c
Answer: c
Python program:
a = 31 - 27
b = a * 400
c = b / 200
Problem: a salesman commission is 10 % on all sales upto $ 5000 and 5 % on all sales exceeding this . he remits $ 15000 to his parent company after deducting his commission . find the total sales ?
Options: a ) 15456 , b ) 14758 , c ) 15789 , d ) 13250 , e ) 12450
Rationale: "let his total sales be x total sales - commission = $ 15000 x - [ ( 10 % of 5000 ) + 5 % of ( x - 5000 ) ] = 15000 95 x / 100 = 15000 x = 15789 approximately answer is c"
Answer: c
Python program:
a = 10 * 5000
b = a / 100
c = 4 * 0
d = c / 100
e = b - d
f = 15000 + e 
g = 5 / 100
h = 1 - g
i = f / h
Problem: ( 7.5 × 7.5 + 3.75 + 2.5 × 2.5 ) is equal to
Options: a ) 30 , b ) 60 , c ) 80 , d ) 100 , e ) 90
Rationale: "solution given expression = ( 7.5 x 7.5 + 2 × 7.5 × 2.5 + 2.5 × 2.5 ) ² = ( a ² + 2 ab + b ² ) = ( a + b ) ² = ( 7.5 + 2.5 ) ² = 10 ² = 100 . answer d"
Answer: d
Python program:
a = 7 * 5
b = 2 * 5
c = a + b 
d = c + 3
Problem: a merchant has selected two items to be placed on sale , one of which currently sells for 40 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 ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 30 % , e ) 20 %
Rationale: "expensive item = $ 100 ; cheap item = $ 60 ; we must increase $ 60 to $ 100 , so by $ 40 , which is approximately 60 % increase : ( 100 - 60 ) / 60 = 2 / 3 = ~ 0.66 . answer : c ."
Answer: c
Python program:
a = 40 / 100
b = 40 / 100
c = 1 - b
d = a / c
e = d * 100
Problem: a owes b rs . 50 . he agrees to pay b over a number of consecutive days on a monday , paying single note or rs . 10 or rs . 20 on each day . in how many different ways can a repay b .
Options: a ) 2 , b ) 8 , c ) 9 , d ) 6 , e ) 5
Rationale: he can pay by all 10 rupee notes = 1 way 3 ten rupee + 1 twenty rupee = 4 ! 3 ! × 1 ! 4 ! 3 ! × 1 ! = 4 ways 1 ten rupee + 2 twenty rupee notes = 3 ! 2 ! × 1 ! 3 ! 2 ! × 1 ! = 3 ways total ways = 1 + 4 + 3 = 8 answer : b
Answer: b
Python program:
a = math.factorial(3)
b = math.factorial(2)
c = a / b
d = math.factorial(4)
e = math.factorial(3)
f = d / e
g = c + f 
h = 50 / 10
i = math.factorial(h)
j = 50 / 10
k = math.factorial(j)
l = i / k
m = g + l
Problem: if two positive numbers are in the ratio 1 / 12 : 1 / 9 , then by what percent is the second number more than the first ?
Options: a ) 70 % , b ) 90 % , c ) 33.33 % , d ) 50 % , e ) 65 %
Rationale: "given ratio = 1 / 12 : 1 / 9 = 9 : 12 let first number be 9 x and the second number be 12 x . the second number is more than first number by 3 x . required percentage = 3 x / 9 x * 100 = 33.33 % . answer : c"
Answer: c
Python program:
a = 1 / 9
b = a * 100
Problem: a and b invests rs . 10000 each , a investing for 6 months and b investing for all the 12 months in the year . if the total profit at the end of the year is rs . 4500 , find their shares ?
Options: a ) 1500,6000 , b ) 4500,3000 , c ) 3500,3000 , d ) 1500,3000 , e ) 2500,3000
Rationale: "the ratio of their profits a : b = 6 : 12 = 1 : 2 share of a in the total profit = 1 / 3 * 4500 = rs . 1500 share of b in the total profit = 2 / 3 * 4500 = rs . 3000 answer : d"
Answer: d
Python program:
a = 10000 * 1
b = a / 3
Problem: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 32.49 , the number of the member is the group is :
Options: a ) 57 , b ) 67 , c ) 77 , d ) 87 , e ) 97
Rationale: "explanation : money collected = ( 32.49 x 100 ) paise = 3249 paise . ∴ number of members = √ ( 3249 ) = 57 . answer : a"
Answer: a
Python program:
a = 32 * 49
b = math.sqrt(a)
Problem: q ' = 3 q - 3 , what is the value of ( 6 ' ) ' ?
Options: a ) 120 , b ) 150 , c ) 180 , d ) 210 , e ) 240
Rationale: ( 6 ' ) ' = ( 3 * 6 - 3 ) ' = 15 ' = 15 * 15 - 15 = 210 answer d
Answer: d
Python program:
a = 3 * 6
b = a - 3
c = b * 3
d = c - 3
e = 6 - 1
f = d * e
Problem: in 1979 approximately 1 / 3 of the 38.3 million airline passengers traveling to or from the united states used kennedy airport . if the number of such passengers that used miami airport was 1 / 2 the number that used kennedy airport and 4 times the number that used logan airport , approximately how many millions of these passengers used logan airport that year ?
Options: a ) 18.6 , b ) 9.3 , c ) 6.2 , d ) 3.1 , e ) 1.6
Rationale: number of passengers using kennedy airport = 38 / 3 = ~ 12.67 passengers using miami airport = 12.67 / 2 = ~ 6.3 passengers using logan airport = 6.3 / 4 = ~ 1.58 so e
Answer: e
Python program:
a = 38 / 3
b = 4 * 2
c = a / b
Problem: when n is divided by 24 , the remainder is 3 . find thee difference between previous remainder and the remainder when 9 n is divided by 7 ?
Options: a ) 2 , b ) 7 , c ) 5 , d ) 3 , e ) 6
Rationale: "let n = 3 ( leaves a remainder of 3 when divided by 24 ) 9 n = 9 ( 3 ) = 27 , which leaves a remainder of 6 when divided by 7 . difference = 6 - 3 = 3 . answer d"
Answer: d
Python program:
a = 3 - reminder
Problem: the initial price of an article is rs . 6000 which increases 40 % increse in its price in the first year , a 20 % decrease in the second year and a 20 % increase in the next year . what is the final price of the article ?
Options: a ) rs . 5392 , b ) rs . 6392 , c ) rs . 8392 , d ) rs . 7392 , e ) rs . 9392
Rationale: "the initial price of the article is rs . 6000 . in the 1 st year , price of the article = 6000 + 2400 = rs . 8400 . in the 2 nd year , price = 8400 - 20 % of 8400 = 8400 - 1680 = rs . 6720 . in the 3 rd year , price = 6720 + 10 % of 6720 = 6720 + 672 = rs . 7392 required price = = rs . 7392 . answer : d"
Answer: d
Python program:
a = 6000 * 20
b = a / 100
c = 6000 - b
d = 6000 * 20
e = d / 100
f = 6000 - e
g = f * 20
h = g / 100
i = c + h
Problem: a and b can finish a work in 16 days while a alone can do the same work in 20 days . in how many days b alone will complete the work ?
Options: a ) 76 days , b ) 48 days , c ) 80 days , d ) 31 days , e ) 22 days
Rationale: "b = 1 / 16 – 1 / 20 = 1 / 80 = > 80 days answer : c"
Answer: c
Python program:
a = 1/(16)
b = 1/(20)
c = a - b
d = 1/(c)
Problem: a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 16000 left with him . find salary . .
Options: a ) $ 10800 , b ) $ 18000 , c ) $ 160000 , d ) $ 1800 , e ) none
Rationale: "[ 1 / ( x 1 / y 1 + x 2 / y 2 + x 3 / y 3 ) ] * total amount = balance amount [ 1 - ( 1 / 5 + 1 / 10 + 3 / 5 ) } * total salary = $ 16000 , = [ 1 - 9 / 10 ] * total salary = $ 16000 , total salary = $ 16000 * 10 = $ 160000 , correct answer ( c )"
Answer: c
Python program:
a = 1 / 5
b = 1 / 10
c = a + b 
d = 3 / 5
e = c + d 
f = 1 - e
g = 16000 / f
Problem: a has 10000 chocolates . 20 % of the chocolates are eaten . what percentage of the uneaten chocolates must be eaten so that 3 / 2 of all chocolates are eaten ?
Options: a ) 39.25 , b ) 37.25 , c ) 37.26 , d ) 38.21 , e ) 38.32
Rationale: number of chocolates = 10,000 currently eaten = 10,000 * 20 / 100 = 2000 uneaten chocolates = 10000 - 2000 = 8000 2 / 3 of all chocolates = 5000 the number of chocolates to be eaten to make 2 / 3 of all chocolates eaten = 5000 - 2000 = 3000 so now the question remains - 3000 is how much percentage of uneaten chocolates ( 8000 ) = 3000 * 100 / 8000 = 37.5 answer ( b )
Answer: b
Python program:
a = 10000 / 2
b = 20 * 10000
c = b / 100
d = a - c
e = d * 100
f = 20 * 10000
g = f / 100
h = 10000 - g
i = e / h
Problem: a school has 4 section of chemistry in class x having 60 , 35 , 45 and 42 students . the mean marks obtained in chemistry test are 50 , 60 , 55 and 45 respectively for the 4 sections . determine the overall average of marks per student .
Options: a ) 50 , b ) 52 , c ) 51 , d ) 53 , e ) none of the above
Rationale: "required average marks = 60 ã — 50 + 35 ã — 60 + 45 ã — 55 + 42 ã — 45 / 60 + 35 + 45 + 42 = 3000 + 2100 + 2475 + 1890 / 182 = 9465 â  „ 182 = 52 answer b"
Answer: b
Python program:
a = 60 * 50
b = 35 * 60
c = a + b 
d = 45 * 55
e = c + d 
f = 42 * 45
g = e + f 
h = 60 + 35 
i = h + 45 
j = i + 42 
k = g / j
Problem: the number of employees in obelix menhir co . is a prime number and is less than 300 . the ratio of the number of employees who are graduates and above , to that of employees who are not , can possibly be : -
Options: a ) 101 : 88 , b ) 87 : 100 , c ) 110 : 111 , d ) 85 : 98 , e ) 97 : 84
Rationale: explanation : going through the given options , option 1 : - 101 : 88 = > 189 . [ divisible by 3 ] option 2 : - 87 : 100 = > 187 . [ divisible by 11 ] option 3 : - 85 : 98 = > 183 . [ divisible by 3 ] option 4 : - 97 : 84 = > 181 . [ prime number ] hence , only 181 is the prime number i . e the total number of employee in the company and the required ratio is 97 : 84 . answer : e
Answer: e
Python program:
a = 300 / 100
b = 100 - a
c = 300 / 100
d = 100 - c
e = 300 / 100
f = 10 + e 
g = d - f
h = b / g
Problem: rs . 825 becomes rs . 956 in 3 years at a certain rate of simple interest . if the rate of interest is increased by 4 % , what amount will rs . 825 become in 3 years ?
Options: a ) rs . 1020.80 , b ) rs . 1025 , c ) rs . 1055 , d ) data inadequate , e ) none of these
Rationale: "solution s . i . = rs . ( 956 - 825 ) = rs . 131 rate = ( 100 x 131 / 825 x 3 ) = 524 / 99 % new rate = ( 524 / 99 + 4 ) % = 920 / 99 % new s . i . = rs . ( 825 x 920 / 99 x 3 / 100 ) rs . 230 . ∴ new amount = rs . ( 825 + 230 ) = rs . 1055 . answer c"
Answer: c
Python program:
a = 956 - 825
b = a * 100
c = 825 * 3
d = b / c
e = d + 4 
f = 825 * e
g = f * 3
h = g / 100
i = 825 + h
Problem: mahesh marks an article 15 % above the cost price of rs . 540 . what must be his discount percentage if he sells it at rs . 496.80 ?
Options: a ) 22 , b ) 27 , c ) 20 , d ) 21 , e ) 12
Rationale: "cp = rs . 540 , mp = 540 + 15 % of 540 = rs . 621 sp = rs . 496.80 , discount = 621 - 496.80 = 124.20 discount % = 124.2 / 621 * 100 = 20 % . answer : c"
Answer: c
Python program:
a = 100 + 15 
b = a / 100
c = 540 * b
d = c - 496
e = d * 100
f = 100 + 15 
g = f / 100
h = 540 * g
i = e / h
Problem: a 45 ° - 45 ° - 90 ° right triangle has hypotenuse of length h . what is the area of the triangle t in terms of h ?
Options: a ) h / √ 2
b ) h / 2
c ) h / 4
d ) ( h ) ^ 2
e ) ( h ) ^ 2 / 4
Rationale: if . . . each of the two shorter sides = 3 , then the hypotenuse = h = 3 ( root 2 ) . the area t = ( 1 / 2 ) ( base ) ( height ) = ( 1 / 2 ) ( 3 ) ( 3 ) = 9 / 2 . so we ' re looking for an answer that = 9 / 2 when h = 3 ( root 2 ) . there ' s only one answer that matches . . . e
Answer: e
Python program:
a = 45 / 90
b = a ** 2
Problem: a man swims downstream 54 km and upstream 18 km taking 3 hours each time , what is the speed of the man in still water ?
Options: a ) 2 , b ) 8 , c ) 9 , d ) 10 , e ) 12
Rationale: "54 - - - 3 ds = 18 ? - - - - 1 18 - - - - 3 us = 6 ? - - - - 1 m = ? m = ( 18 + 6 ) / 2 = 12 answer : e"
Answer: e
Python program:
a = 18 / 3
b = 54 / 3
c = a + b 
d = c / 2
Problem: the average of 11 results is 52 , if the average of first 6 results is 49 and that of the last 6 is 52 . find the sixth result ?
Options: a ) a ) 46 , b ) b ) 34 , c ) c ) 66 , d ) d ) 76 , e ) e ) 74
Rationale: 1 to 11 = 11 * 52 = 572 1 to 6 = 6 * 49 = 294 6 to 11 = 6 * 52 = 312 6 th = 294 + 312 – 572 = 34 answer : b
Answer: b
Python program:
a = 52 * 6
b = 49 * 6
c = a + b 
d = 52 * 11
e = c - d
Problem: sum of the squares of 3 no . is 138 and the sum of their products taken two at a time is 131 . find the sum ?
Options: a ) 20 , b ) 21 , c ) 25 , d ) 26 , e ) 27
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 138 + 2 * 131 a + b + c = √ 400 = 20 a"
Answer: a
Python program:
a = 131 * 2
b = 138 + a 
c = math.sqrt(b)
Problem: the total of 324 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is :
Options: a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250
Rationale: "explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 324 - x ) . 0.20 × ( x ) + 0.25 ( 324 - x ) = 71 = > x = 200 . answer : d"
Answer: d
Python program:
a = 324 * 25
b = 71 * 100
c = a - b
d = 25 - 20
e = c / d
Problem: 120 liters of a mixture contains milk and water in the ratio 4 : 2 . if 10 liters of this mixture be replaced by 10 liters of milk , the ratio of milk to water in the new mixture would be ?
Options: a ) 8 : 6 , b ) 9 : 3 , c ) 9 : 4 , d ) 9 : 6 , e ) 8 : 2
Rationale: quantity of milk in 120 liters if mix = 120 * 4 / 6 = 80 liters quantity of milk in 130 liters of new mix = 80 + 10 = 90 liters quantity of water in it = 130 - 90 = 40 liters ratio of milk and water in new mix = 90 : 40 = 9 : 4 answer is c
Answer: c
Python program:
a = 10 - 1
b = a * 2
c = 4 * 2
d = b / c
Problem: 170 kg of an alloy a is mixed with 250 kg of alloy b . if alloy a has lead and tin in the ratio 1 : 3 and alloy b has tin and copper in the ratio 3 : 5 , then the amount of tin in the new alloy is ?
Options: a ) 210.6 kg , b ) 221.3 kg , c ) 229.5 kg , d ) 110.8 kg , e ) 114 kg
Rationale: "quantity of tin in 170 kg of a = 170 * 3 / 4 = 127.5 kg quantity of tin in 250 kg of b = 250 * 3 / 8 = 93.75 kg quantity of tin in the new alloy = 127.5 + 93.75 = 221.25 kg answer is b"
Answer: b
Python program:
a = 1 + 3 
b = 170 / a
c = b * 3
d = 3 + 5 
e = 250 / d
f = e * 3
g = c + f
Problem: a train 360 m long can cross an electric pole in 30 sec and then find the speed of the train ?
Options: a ) 88 kmph , b ) 43 kmph , c ) 72 kmph , d ) 16 kmph , e ) 18 kmph
Rationale: "length = speed * time speed = l / t s = 360 / 30 s = 12 m / sec speed = 12 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 43 kmph answer : b"
Answer: b
Python program:
a = 360 / 1000
b = 30 / 3600
c = a / b
Problem: a can do a piece of work in 4 hours ; b and c together can do it in 2 hours , which a and c together can do it in 2 hours . how long will b alone take to do it ?
Options: a ) 2 hours , b ) 3 hours , c ) 4 hours , d ) 5 hours , e ) 6 hours
Rationale: "a ' s 1 hour work = 1 / 4 ; ( b + c ) ' s 1 hour work = 1 / 2 ; ( a + c ) ' s 1 hour work = 1 / 2 ( a + b + c ) ' s 1 hour work = ( 1 / 4 + 1 / 2 ) = 3 / 4 b ' s 1 hour work = ( 3 / 4 - 1 / 2 ) = 1 / 4 b alone will take 4 hours to do the work . answer : c"
Answer: c
Python program:
a = 1 / 2
b = 1 / 2
c = 1 / 4
d = b - c
e = a - d
f = 1 / e
Problem: the maximum number of student amoung them 1204 pens and 840 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Options: a ) 91 , b ) 28 , c ) 56 , d ) 89 , e ) none of these
Rationale: "solution required number of student = h . c . f of 1204 and 840 = 28 . answer b"
Answer: b
Python program:
a = math.gcd(1204, 840)
Problem: in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 7 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 105
Rationale: "f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 7 * 180 / 12 = 105 ounces of water e"
Answer: e
Python program:
a = 1 / 12
b = a * 3
c = 1 / 30
d = c / 2
e = b / d
f = e * 7
Problem: the product of three consecutive numbers is 120 . then the sum of the smallest two numbers is ?
Options: a ) 9 , b ) 15 , c ) 20 , d ) 38 , e ) 56
Rationale: "product of three numbers = 120 120 = 2 * 2 * 5 * 6 = 4 * 5 * 6 so , the three numbers are 4,5 and 6 . and sum of smallest of these two = 4 + 5 = 9 . answer : option a"
Answer: a
Python program:
a = 2 ** 120
b = math.factorial(120)
c = a * b
Problem: a company pays 12.5 % dividend to its investors . if an investor buys rs . 40 shares and gets 25 % on investment , at what price did the investor buy the shares ?
Options: a ) 20 , b ) 66 , c ) 18 , d ) 19 , e ) 01
Rationale: "explanation : dividend on 1 share = ( 12.5 * 40 ) / 100 = rs . 5 rs . 25 is income on an investment of rs . 100 rs . 5 is income on an investment of rs . ( 5 * 100 ) / 25 = rs . 20 answer : a"
Answer: a
Python program:
a = 12 * 5
b = a / 100
c = b * 100
d = c / 25
Problem: how many even number in the range between 10 to 140 inclusive are not divisible by 3
Options: a ) 15 , b ) 30 , c ) 31 , d ) 33 , e ) 44
Rationale: we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 10 , 12,14 . . . 140 using ap formula , we can say 140 = 10 + ( n - 1 ) * 2 or n = 66 . for 6 , 12,18 , . . . 138 using ap formula , we can say 138 = 12 + ( n - 1 ) * 6 or n = 22 . hence , only divisible by 2 but not 3 = 66 - 22 = 44 . hence , answer e
Answer: e
Python program:
a = 140 - 10
b = a - 2
c = b / 2
d = 140 - 2
e = 3 * 4
f = d - e
g = f - 3
h = g - 3
i = h / 3
j = i / 2
k = c - j
Problem: the average of 15 result is 55 . average of the first 7 of them is 57 and that of the last 7 is 61 . find the 8 th result ?
Options: a ) 760 , b ) 720 , c ) 700 , d ) 786 , e ) 797
Rationale: "sum of all the 13 results = 15 * 55 = 825 sum of the first 7 of them = 7 * 57 = 399 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 825 + 399 - 427 = 797 . e"
Answer: e
Python program:
a = 7 * 57
b = 7 * 61
c = a + b 
d = 15 * 55
e = c - d
Problem: a train of length 250 m crosses a bridge of length 150 m in 32 seconds . what is the speed of train ?
Options: a ) 33 , b ) 27 , c ) 25 , d ) 22 , e ) 45
Rationale: "sol : ( length of train + length of bridge ) = speed of train x time ( 250 + 150 ) = 32 x speed speed = 400 / 32 = 12.5 m / s = 45 km / h answer = e"
Answer: e
Python program:
a = 250 + 150 
b = a / 32
c = const_3_6 * b
Problem: a cricketer scored 142 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 57.75 % , b ) 54.54 % , c ) 63 % , d ) 70 % , e ) none of these
Rationale: "explanation : number of runs made by running = 142 - ( 12 x 4 + 2 x 6 ) = 142 - ( 60 ) = 82 now , we need to calculate 82 is what percent of 142 . = > 82 / 142 * 100 = 57.75 % answer : a"
Answer: a
Python program:
a = 12 * 4
b = 2 * 3
c = 2 * b
d = a + c 
e = 142 - d
f = e / 142
g = f * 100
Problem: a train running at the speed of 54 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 288 , b ) 279 , c ) 135 , d ) 272 , e ) 150
Rationale: "speed = 54 * 5 / 18 = 15 m / sec length of the train = speed * time = 15 * 9 = 135 m answer : c"
Answer: c
Python program:
a = 54 * 1000
b = a / 3600
c = b * 9