euclaise/mathqa_programs huggingface dataset:
Problem: of all the students in a certain dormitory , 1 / 2 are first - year students and the rest are second - year students . if 4 / 5 of the first - year students have not declared a major and if the fraction of second - year students who have declared a major is 1 / 2 times the fraction of first - year students who have declared a major , what fraction of all the students in the dormitory are second - year students who have not declared a major ?
Options: a ) 1 / 15 , b ) 1 / 5 , c ) 9 / 20 , d ) 1 / 3 , e ) 2 / 5
Rationale: "tot students = x 1 st year student = x / 2 - - - - > non majaor = 4 / 5 ( x / 2 ) - - - - - > maj = 1 / 5 ( x / 2 ) 2 nd year student = x / 2 - - - - > maj = 1 / 2 ( 1 / 5 ( x / 2 ) ) = 1 / 20 ( x ) - - - > non major = x / 2 - 1 / 20 ( x ) = 9 / 20 ( x ) hence 9 / 20 c"
Answer: c
Python program:
a = 1 / 2
b = 2 * 10
c = 1 / b
d = a - c
Problem: a computer is programmed to multiply consecutive even integers 2 * 4 * 6 * 8 * … * n until the product is divisible by 1419 , what is the value of n ?
Options: a ) 86 , b ) 38 , c ) 62 , d ) 122 , e ) 672
Rationale: factorise 1419 . . 3 * 11 * 43 . . so n has to be a multiple of largest prime number , 61 . . so n = 2 * 43 = 86 . . ans : a
Answer: a
Python program:
a = 10 + 1 
b = 1419 / a
c = b / 3
d = 2 * c
Problem: what is the dividend ? the divisor is 17 , the quotient is 4 and the remainder is 8 .
Options: a ) 76 , b ) 67 , c ) 176 , d ) 671 , e ) 0
Rationale: "divided = divisor * quotient + remainder ? = 17 * 4 + 8 68 + 8 76 ( e . g . answer : a )"
Answer: a
Python program:
a = 17 * 4
b = a - 8
Problem: line m lies in the xy - plane . the y - intercept of line m is - 1 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 4 ) and ( 6 , - 8 ) . what is the slope of line m ?
Options: a ) - 3 , b ) - 1 , c ) - 1 / 3 , d ) 0 , e ) undefined
Rationale: ans : e solution : line m goes through midpoint of ( 2 , 4 ) and ( 6 , - 8 ) . midpoint is ( 4 , - 2 ) as we can see that the y axis of intercept point is ( 0 , - 1 ) means line m is parallel to x axis slope m = 0 ans : e
Answer: e
Python program:
a = 4 - 8
b = a / 2
c = b + 1 
d = 2 + 6 
e = d / 2
f = c / e
Problem: the average of first 10 prime numbers is ?
Options: a ) 12.6 , b ) 12.5 , c ) 12.9 , d ) 12.2 , e ) 12.1
Rationale: "sum of 10 prime no . = 129 average = 129 / 10 = 12.9 . answer : c"
Answer: c
Python program:
a = 10 + 1
Problem: if f ( x ) = 2 x ^ 2 + y , and f ( 2 ) = 50 , what is the value of f ( 5 ) ?
Options: a ) 104 , b ) 60 , c ) 92 , d ) 50 , e ) 25
Rationale: "f ( x ) = 2 x ^ 2 + y f ( 2 ) = 50 = > 2 * ( 2 ) ^ 2 + y = 50 = > 8 + y = 50 = > y = 42 f ( 5 ) = 2 * ( 5 ) ^ 2 + 42 = 92 answer c"
Answer: c
Python program:
a = 2 ** 2
b = a * 2
c = 50 - b
d = 5 ** 2
e = 2 * d
f = c + e
Problem: a man has an investment of $ 3000 which yields a fixed 305 for every $ 500 invested . if the man takes out $ 12.6 for every $ 500 how long will it take for him to double his investment assuming no compounding of interest .
Options: a ) 4 , b ) 33.8 , c ) 10 , d ) 30 , e ) 37.3
Rationale: annual increase is ( 500 + 30.5 - 12.6 ) * 6 = 3107.4 hence every year there is an increase of 107.4 for his saving to double he needs additional $ 4000 therefore $ 4000 / 107.4 = 37.3 correct option is e ) 37.3
Answer: e
Python program:
a = 3000 / 305
b = a * 3
c = b + 3 
d = c + 1 
e = d + 4
Problem: each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , annie is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week annie worked a total of 47 hours . if harry and annie were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 40 , b ) 42 , c ) 44 , d ) 46 , e ) 48
Rationale: "annie earned 40 x + 7 ( 2 x ) = 54 x let h be the number of hours that harry worked . harry earned 30 x + 1.5 x ( h - 30 ) = 54 x ( 1.5 x ) ( h ) = 69 x h = 46 hours the answer is d ."
Answer: d
Python program:
a = 40 + 2 
b = a - 30
c = b / 1
d = c + 30
Problem: car a runs at the speed of 80 km / hr & reaches its destination in 5 hr . car b runs at the speed of 100 km / h & reaches its destination in 2 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 11 : 5 , b ) 11 : 8 , c ) 2 : 1 , d ) 15 : 7 , e ) 16 : 9
Rationale: "sol . distance travelled by car a = 80 × 5 = 400 km distance travelled by car b = 100 × 2 = 200 km ratio = 400 / 200 = 2 : 1 answer : c"
Answer: c
Python program:
a = 80 * 5
b = 100 * 2
c = a / b
Problem: the area of one square is x ^ 2 + 10 x + 25 and the area of another square is 4 x ^ 2 − 12 x + 9 . if the sum of the perimeters of both squares is 32 , what is the value of x ?
Options: a ) 0 , b ) 2 , c ) 2.5 , d ) 4.67 , e ) 10
Rationale: "spotting the pattern of equations both are in form of ( x + c ) ^ 2 so a 1 = ( x + 5 ) ^ 2 & a 2 = ( 2 x - 3 ) ^ 2 l 1 = x + 5 & l 2 = 2 x - 3 p 1 = 4 ( x + 5 ) & p 2 = 4 ( 2 x - 3 ) p 1 + p 2 = 32 4 ( x + 5 ) + 4 ( 2 x - 3 ) = 32 . . . . . . . . . . . . . . > x = 2 answer : b"
Answer: b
Python program:
a = 10 / 2
b = 4 * a
c = b - 10
d = 32 - c
e = d / 10
Problem: sandy had $ 217 left after spending 30 % of the money she took for shopping . how much money did sandy take along with her ?
Options: a ) $ 270 , b ) $ 290 , c ) $ 310 , d ) $ 330 , e ) $ 350
Rationale: "let the money sandy took for shopping be x . 0.7 x = 217 x = 310 the answer is c ."
Answer: c
Python program:
a = 100 - 30
b = a / 100
c = 217 / b
Problem: the cube root of . 000216 is :
Options: a ) 0.6
b ) 0.06
c ) 0.9
d ) 0.2
e ) 0.61
Rationale: answer : b ) . 06
Answer: b
Python program:
a = 216 / 1000
b = a / 1000
c = 1 / 3
d = b ** c
Problem: at a special sale , 12 tickets can be purchased for the price of 4 tickets . if 12 tickets are purchased at the sale , the amount saved will be what percent of the original price of the 12 tickets ?
Options: a ) 20 % , b ) 33.3 % , c ) 40 % , d ) 60 % , e ) 66.6 %
Rationale: "let the price of a ticket be rs . 100 , so 4 tickets cost 400 & 12 tickets cost 1200 12 tickets purchased at price of 4 tickets ie . , for 400 , so amount saved s rs . 800 , % of 5 tickets = ( 800 / 1200 ) * 100 = 66.6 % answer : e"
Answer: e
Python program:
a = 12 * 12
b = 4 * 12
c = a - b
d = c * 100
e = 12 * 12
f = d / e
Problem: a person can swim in still water at 12 km / h . if the speed of water 6 km / h , how many hours will the man take to swim back against the current for 6 km ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "m = 12 s = 6 us = 12 - 6 = 6 d = 36 t = 36 / 6 = 6 answer : d"
Answer: d
Python program:
a = 12 - 6
b = 6 / a
Problem: a train 320 m in length crosses a telegraph post in 12 seconds . the speed of the train is ?
Options: a ) 77 kmph , b ) 95 kmph , c ) 94 kmph , d ) 98 kmph , e ) 96 kmph
Rationale: "s = 320 / 12 * 18 / 5 = 96 kmph answer : e"
Answer: e
Python program:
a = 320 / 12
b = const_3_6 * a
Problem: 12 + 13 + 14 + . . . 51 + 52 + 53 + 54 = ?
Options: a ) 1419 , b ) 1362 , c ) 1363 , d ) 1364 , e ) 1365
Rationale: "sum = 12 + 13 + 14 + . . . 51 + 52 + 53 + 54 sum of n consecutive positive integers starting from 1 is given as n ( n + 1 ) / 2 sum of first 54 positive integers = 55 * 54 / 2 sum of first 11 positive integers = 11 * 12 / 2 sum = 12 + 13 + 14 + . . . 51 + 52 + 53 + 54 = 55 * 54 / 2 - 11 * 12 / 2 = 1419 answer : a"
Answer: a
Python program:
a = 51 + 12 
b = 51 * a
c = b / 13
Problem: 2 x + y = 13 | y | < = 13 for how many ordered pairs ( x , y ) that are solutions of the system above are x and y both integers ?
Options: a ) 7 , b ) 10 , c ) 12 , d ) 13 , e ) 14
Rationale: hi - the questions says | y | < = 13 so the values of y will range from 0 to 13 . so the values of y will be 0,1 , 2,3 , 4,5 , 6,7 , 8,9 , 10,11 , 12,13 . so 14 ( e ) is the answer . remember sign does n ' t matter for y as y will always be positive .
Answer: e
Python program:
a = 13 + 13 
b = a / 2
c = b + 1
Problem: mary decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month . if mary ' s savings by the end of the year from these monthly savings were 7 times the amount she spent per month , what should be the fraction of her salary that she spent each month ?
Options: a ) 1 / 4 , b ) 3 / 4 , c ) 10 / 19 , d ) 11 / 19 , e ) 12 / 19
Rationale: saving = s , expenditure = e , income = i at the end of 12 months ; 12 s = 7 e = 7 ( i - s ) = > 19 s = 7 i = > savings = 7 / 19 i hence expenditure = 1 - ( 7 / 19 ) = 12 / 19 answer ( e )
Answer: e
Python program:
a = 12 / 7
b = 12 / 7
c = b + 1 
d = a / c
Problem: what is the total number of integers between 20 and 70 that are divisible by 2 ?
Options: a ) 19 , b ) 25 , c ) 24 , d ) 26 , e ) 20
Rationale: "22 , 24 , 26 , . . . , 56,58 this is an equally spaced list ; you can use the formula : n = ( largest - smallest ) / ( ' space ' ) + 1 = ( 70 - 22 ) / ( 2 ) + 1 = 48 / 2 + 1 = 24 + 1 = 25 answer is b"
Answer: b
Python program:
a = 70 - 20
b = a / 2
c = b + 1
Problem: 9 men went to a hotel . 8 of them spent 3 each over their meals and the ninth spent 5 more than the average expenditure of all the 9 . the total money spent by all of them was
Options: a ) 26 , b ) 40 , c ) 29.25 , d ) 32.625 , e ) none of the above
Rationale: let the average expenditure of all the ninte be x then , 3 × 8 + x + 5 = 9 x ⇒ x = 3.625 ∴ total money spent = 9 x = 9 × 3.625 = 32.625 answer d
Answer: d
Python program:
a = 8 * 3
b = a + 5 
c = b / 8
d = c * 9
Problem: when a certain tree was first planted , it was 4 feet tall , and the height of the tree increased by a constant amount each year for the next 6 years . at the end of the 6 th year , the tree was 1 / 4 taller than it was at the end of the 4 th year . by how many feet did the height of the tree increase each year ?
Options: a ) 1 , b ) 2 / 5 , c ) 1 / 2 , d ) 2 / 3 , e ) 6 / 5
Rationale: "say , the tree grows by x feet every year . then , 4 + 6 x = ( 1 + 1 / 4 ) ( 4 + 4 x ) or , x = 1 answer a"
Answer: a
Python program:
a = 6 - 4
b = a * 4
c = b - 4
d = 4 / c
Problem: find the value of 72519 x 9999 = m .
Options: a ) 233243413 , b ) 354545451 , c ) 343435451 , d ) 565656767 , e ) 725117481
Rationale: "72519 x 9999 = 72519 x ( 10000 - 1 ) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 e"
Answer: e
Python program:
a = 9999 - 4
b = a * 72519
Problem: john bought 9.25 m of cloth for $ 444 . find the cost price per metre .
Options: a ) 48 , b ) 47 , c ) 58 , d ) 56 , e ) 54
Rationale: "cloth bought by john = 9.25 m cost of 9.25 m = $ 444 cost per metre = 444 ÷ 9.25 the cost of the cloth per metre = $ 48 answers : a"
Answer: a
Python program:
a = 444 / 9
Problem: an woman swims downstream 81 km and upstream 36 km taking 9 hours each time ; what is the speed of the current ?
Options: a ) 0.5 , b ) 1.5 , c ) 2.5 , d ) 3.5 , e ) 4.5
Rationale: 81 - - - 9 ds = 9 ? - - - - 1 36 - - - - 9 us = 4 ? - - - - 1 s = ? s = ( 9 - 4 ) / 2 = 2.5 answer : c
Answer: c
Python program:
a = 81 / 9
b = 36 / 9
c = a - b
d = c / 2
Problem: an escalator moves towards the top level at the rate of 11 ft . sec and its length is 126 feet . if a person walks on the moving escalator at the rate of 3 feet per second towards the top level , how much time does he take to cover the entire length .
Options: a ) 14 sec , b ) 10 sec , c ) 12 sec , d ) 8 sec , e ) 9 sec
Rationale: "time taken to cover the entire length = tot . dist / resultant speed = 126 / ( 11 + 3 ) = 9 sec answer : e"
Answer: e
Python program:
a = 11 + 3 
b = 126 / a
Problem: one - third of rahul ' s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 1 , 80,000 as total savings , how much has he saved in public provident fund ?
Options: a ) 81000 , b ) 85000 , c ) 75000 , d ) 72000 , e ) 77000
Rationale: let savings in national savings certificate = x and savings in public provident fund = ( 180000 - x ) 1 / 3 x = 1 / 2 ( 180000 − x ) ⇒ 2 x = 3 ( 180000 − x ) ⇒ 2 x = 540000 − 3 x ⇒ 5 x = 540000 ⇒ x = 540000 / 5 = 108000 savings in public provident fund = ( 180000 - 108000 ) = 72000 answer is d .
Answer: d
Python program:
a = 100 * 10
b = a * 100
c = 100 * 10
d = c * 100
e = 2 * 100
f = e * 100
g = d - f
h = b + g 
i = 3 / 2
j = i + 1 
k = 1 / j
l = h * k
Problem: what will be the cost of building a fence around a square plot with area equal to 49 sq ft , if the price per foot of building the fence is rs . 58 ?
Options: a ) 3944 , b ) 1624 , c ) 2999 , d ) 2667 , e ) 2121
Rationale: "let the side of the square plot be a ft . a 2 = 49 = > a = 7 length of the fence = perimeter of the plot = 4 a = 28 ft . cost of building the fence = 28 * 58 = rs . 1624 . answer : b"
Answer: b
Python program:
a = math.sqrt(49)
b = square_perimeter * (
Problem: in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 11 years older than b , the present age of b is
Options: a ) 35 , b ) 37 , c ) 39 , d ) 41 , e ) 42
Rationale: "explanation : let b ' s age = x years . then , as age = ( x + 11 ) years . ( x + 11 + 10 ) = 2 ( x — 10 ) hence x = 41 . present age of b = 41 years answer : option d"
Answer: d
Python program:
a = 2 * 10
b = 11 + 10 
c = a + b
Problem: the area of a parallelogram is 200 sq m and its altitude is twice the corresponding base . then the length of the base is ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 10 , e ) 5
Rationale: "2 x * x = 200 = > x = 10 answer : d"
Answer: d
Python program:
a = 200 / 2
b = math.sqrt(a)
Problem: mr . karan borrowed a certain amount at 6 % per annum simple interest for 9 years . after 9 years , he returned rs . 8210 / - . find out the amount that he borrowed .
Options: a ) s . 5331 , b ) s . 5269 , c ) s . 5228 , d ) s . 5218 , e ) s . 52192
Rationale: "explanation : let us assume mr . karan borrowed amount is rs . a . ( the principal ) by formula of simple interest , s . i . = prt / 100 where p = the principal , r = rate of interest as a % , t = time in years s . i . = ( p * 6 * 9 ) / 100 = 54 p / 100 amount = principal + s . i . 8210 = p + ( 54 p / 100 ) 8210 = ( 100 p + 54 p ) / 100 8210 = 154 p / 100 p = ( 8210 * 100 ) / 154 = rs . 5331.169 answer : a"
Answer: a
Python program:
a = 6 * 9
b = a / 100
c = 1 + b 
d = 8210 / c
Problem: in a 200 meters race a beats b by 56 m or 7 seconds . a ' s time over the course is :
Options: a ) 22 seconds , b ) 12 seconds , c ) 10 seconds , d ) 18 seconds , e ) 28 seconds
Rationale: "b runs 56 m in 7 sec . = > b runs 200 m in 7 / 56 * 200 = 25 seconds since a beats b by 7 seconds , a runs 200 m in ( 25 - 7 ) = 18 seconds hence , a ' s time over the course = 18 seconds answer : d"
Answer: d
Python program:
a = 7 / 56
b = a * 200
c = b - 7
Problem: find the l . c . m of 2 / 15 , 3 / 10 , 6 / 5
Options: a ) 6 / 5 , b ) 2 / 3 , c ) 7 / 5 , d ) 8 / 5 , e ) 9 / 5
Rationale: "explanation : lcm of fractions = lcm of numerators / hcf of denominators ( lcm of 2 , 3 , 6 ) / ( hcf of 15 , 10 , 5 ) = 6 / 5 answer : option a"
Answer: a
Python program:
a = 10 * 3
Problem: a horse chases a pony 3 hours after the pony runs . horse takes 4 hours to reach the pony . if the average speed of the horse is 35 kmph , what s the average speed of the pony ?
Options: a ) 20 kmph , b ) 22 kmph , c ) 24 kmph , d ) 26 kmph , e ) 28 kmph
Rationale: "pony take 7 hours and horse take 4 hours . . . then distance chased by them is 35 * 4 . so speed of pony is ( 35 * 4 ) / 7 = 20 kmph . answer : a"
Answer: a
Python program:
a = 4 * 35
b = 4 + 3 
c = a / b
Problem: in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 60 questions and secures 150 marks , the no of questions he attempts correctly is :
Options: a ) 35 , b ) 38 , c ) 40 , d ) 42 , e ) 44
Rationale: "explanation : let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 4 x – ( 60 – x ) = 150 = > 5 x = 210 = > x = 42 answer : d"
Answer: d
Python program:
a = 150 + 60 
b = 4 + 1 
c = a / b
Problem: the area of a square field is 900 km 2 . how long will it take for a horse to run around at the speed of 12 km / h ?
Options: a ) 12 h
b ) 10 h
c ) 8 h
d ) 6 h
e ) none of these
Rationale: explanation area of field = 900 km 2 . then , each side of field = √ 900 = 30 km distance covered by the horse = perimeter of square field = 30 × 4 = 120 km ∴ time taken by horse = distances / peed = 120 / 12 = 10 h answer b
Answer: b
Python program:
a = math.sqrt(900)
b = 4 * a
c = b / 12
Problem: if a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster , he would have covered 60 more miles than he actually did . how many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day ?
Options: a ) 100 , b ) 120 , c ) 140 , d ) 150 , e ) 160
Rationale: "case 1 : let rate = r , time = t , and distance = d so d = rt case 2 : ( d + 60 ) = ( r + 5 ) ( t + 1 ) case 3 : ( d + x ) = ( r + 10 ) ( t + 2 ) x = 120 ans b"
Answer: b
Python program:
a = 60 - 5
b = a * 2
c = 2 * 10
d = b + c
Problem: 98 students represent x percent of the boys at a school . if the boys at the school make up 50 % of the total school population of x students , what is x ?
Options: a ) 110 , b ) 140 , c ) 220 , d ) 250 , e ) 500
Rationale: "let b be the number of boys in the school . 98 = xb / 100 b = 0.5 x 9800 = 0.5 x ^ 2 x ^ 2 = 19600 x = 140 the answer is b ."
Answer: b
Python program:
a = 98 * 100
b = 50 / 100
c = a / b
d = math.sqrt(c)
Problem: two numbers are respectively 17 % and 30 % more than a third number . the percentage that is first of the second is ?
Options: a ) 75 % , b ) 80 % , c ) 85 % , d ) 70 % , e ) 90 %
Rationale: "i ii iii 117 130 100 130 - - - - - - - - - - 117 100 - - - - - - - - - - - ? = > 90 % answer : e"
Answer: e
Python program:
a = 17 + 100 
b = 30 + 100 
c = a / b
d = c * 100
e = 100 - d
Problem: 16 boys or 24 girls can construct the wall in 6 days . the number of days that 8 boys and 12 girls will take to construct ?
Options: a ) 7 days , b ) 14 days , c ) 6 days , d ) 8 days , e ) 9 days
Rationale: "explanation : 16 boys = 24 girls , 1 boy = 24 / 16 girls 1 boy = 6 / 4 girls 8 boys + 12 girls = 8 × 6 / 4 + 12 = 12 + 12 = 24 girls 6 days to complete the work answer : option c"
Answer: c
Python program:
a = 1 / 6
b = a / 24
c = 12 * b
d = 1 / 6
e = d / 16
f = 8 * e
g = c + f 
h = 1 / g
Problem: tea worth rs . 126 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 153 per kg , the price of the third variety per kg will be ?
Options: a ) 122.50 per kg , b ) 266.50 per kg , c ) 175.50 per kg , d ) 172.50 per kg , e ) 176.50 per kg
Rationale: "since first second varieties are mixed in equal proportions , so their average price = rs . ( 126 + 135 / 2 ) = rs . 130.50 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . cost of 1 kg tea of 1 st kind cost of 1 kg tea of 2 nd kind x - 153 / 22.50 = 1 = > x - 153 = 22.50 = > x = 175.50 . hence , price of the third variety = rs . 175.50 per kg . answer : c"
Answer: c
Python program:
a = 1 + 1 
b = a + 2 
c = 153 * b
d = 126 + 126 
e = c - d
f = e / 2
Problem: one - third of 1206 is what percent of 400 ?
Options: a ) 3 , b ) 30 , c ) 300 , d ) 100.5 , e ) 201.2
Rationale: "answer let one - third of 1206 is n % of 400 . ∵ 1206 / 3 = ( n x 400 ) / 100 ∴ n = ( 402 x 100 ) / 400 = 100.5 correct option : d"
Answer: d
Python program:
a = 1206 / 3
b = a / 400
c = 100 * b
Problem: if the population of a certain country increases at the rate of one person every 15 seconds , by how many persons does the population increase in 60 minutes ?
Options: a ) 80 , b ) 100 , c ) 150 , d ) 240 , e ) 300
Rationale: "since the population increases at the rate of 1 person every 15 seconds , it increases by 4 people every 60 seconds , that is , by 4 people every minute . thus , in 60 minutes the population increases by 60 x 4 = 240 people . answer . d ."
Answer: d
Python program:
a = const_60 / 15
b = a * 60
Problem: 1 / 3 rd of work is completed by kiran in 6 days . in how many days he can finish the remaining work ?
Options: a ) 6 days , b ) 10 days , c ) 12 days , d ) 15 days , e ) 20 days
Rationale: 1 / 3 rd work finished in 6 days 2 / 3 rd work = 2 / 3 * 3 * 6 = 12 days answer is c
Answer: c
Python program:
a = 6 * 3
b = a * 2
c = b / 3
Problem: find the middle one when the sum of 3 consecutive even numbers is 57 ?
Options: a ) 10 , b ) 12 , c ) 19 , d ) 15 , e ) 16
Rationale: 3 consecutive numbers can be a - 1 , a , a + 1 so sum of numbers = 3 a = 57 . hence a = 19 . c
Answer: c
Python program:
a = 3 + 3 
b = 57 - a
c = b / 3
d = c + 2
Problem: a number is increased by 20 % and then decreased by 20 % , the final value of the number is ?
Options: a ) does not change , b ) decreases by 2 % , c ) increases by 4 % , d ) decreases by 4 % , e ) none of these
Rationale: "here , x = 20 and y = - 20 therefore , the net % change in value = ( x + y + xy / 100 ) % = [ 20 - 20 + ( 20 x - 20 ) / 100 ] % or - 4 % since the sign is negative , there is a decrease in value by 4 % . answer : d"
Answer: d
Python program:
a = 20 + 100 
b = 100 - 20
c = a * b
d = c / 100
Problem: circular gears p and q start rotating at the same time at constant speeds . gear p makes 10 revolutions per minute and gear q makes 40 revolutions per minute . how many seconds after the gears start rotating will gear q have made exactly 10 more revolutions than gear p ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 20 , e ) 25
Rationale: "gear q makes 30 more revolutions each 60 seconds . the time to make 10 = 30 / 3 more revolutions is 60 / 3 = 20 seconds . the answer is d ."
Answer: d
Python program:
a = 40 / const_60
b = 10 / const_60
c = a - b
d = 10 / c
Problem: find 18 / 6 * 4
Options: a ) 1.25 , b ) 4.53 , c ) 2.69 , d ) 0.89 , e ) 0.75
Rationale: "answer = 18 / 6 * 4 = 18 / 24 = 0.75 option e is correct"
Answer: e
Python program:
a = 18 / 6
Problem: if 2 x = 3 y = 10 , then 9 xy = ?
Options: a ) 1,200 , b ) 200 , c ) 150 , d ) 40 , e ) 20
Rationale: "2 x = 10 ; x = 5 3 y = 10 ; y = 10 / 3 multiply : 9 xy = 9 * 5 * 10 / 3 = 150 answer : c ."
Answer: c
Python program:
a = 2 * 100
b = a / 2
c = b - 2
d = 2 * 100
e = d / 2
f = e + 2 
g = c / f
Problem: the average of first 16 even numbers is ?
Options: a ) 19 , b ) 18 , c ) 16 , d ) 11 , e ) 17
Rationale: "sum of 16 even numbers = 16 * 17 = 272 average = 272 / 16 = 17 answer : e"
Answer: e
Python program:
a = 16 + 1
Problem: if 5 a + 7 b = g , where a and b are positive integers , what is the largest possible value of g for which exactly one pair of integers ( a , b ) makes the equation true ?
Options: a ) 35 , b ) 48 , c ) 69 , d ) 70 , e ) 74
Rationale: 5 * a 1 + 7 * b 1 = g 5 * a 2 + 7 * b 2 = g 5 * ( a 1 - a 2 ) = 7 * ( b 2 - b 1 ) since we are dealing with integers we can assume that a 1 - a 2 = 7 * q and b 2 - b 1 = 5 * q where q is integer , so whenever we get a pair for ( a ; b ) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa , subtracting 7 from a and adding 5 to b . lets check how it works for our numbers , starting from the largest : e ) 74 = 5 * 12 + 7 * 2 ( a 1 = 12 , b 1 = 2 ) , subtract 7 from a and add 5 to b respectively , so a 2 = 5 and b 2 = 7 , second pair - bad d ) 70 = 5 * 7 + 7 * 5 ( a 1 = 7 , b 1 = 5 ) , if we add 7 to a we will have to subtract 5 from b but b ca n ' t be 0 , so - no pair , if we subtract 7 from a , we ' ll get a = 0 which also is n ' t allowed - no pair , thus this is the only pair for ( a ; b ) that works , good ! , thus d is the answer
Answer: d
Python program:
a = 5 * 7
b = 7 * 5
c = a + b