euclaise/mathqa_programs huggingface dataset:
Problem: if a car had traveled 35 kmh faster than it actually did , the trip would have lasted 30 minutes less . if the car went exactly 105 km , at what speed did it travel ?
Options: a ) 50 kmh , b ) 55 kmh , c ) 60 kmh , d ) 65 kmh , e ) 70 kmh
Rationale: "time = distance / speed difference in time = 1 / 2 hrs 105 / x - 105 / ( x + 35 ) = 1 / 2 substitute the value of x from the options . - - > x = 70 - - > 105 / 70 - 105 / 105 = 3 / 2 - 1 = 1 / 2 answer : e"
Answer: e
Python program:
a = 105 * 35
b = 2 * a
c = b * 4
d = 35 ** 2
e = c + d 
f = math.sqrt(e)
g = f - 35
h = g / 2
Problem: the base of pyramid p is an isosceles right triangle whose leg is 3 . if the height of p is 4 , what is the volume of p ?
Options: a ) 36
b ) 18
c ) 12
d ) 8
e ) 6
Rationale: volume of a pyramid is given by v = 1 / 3 ah , where a is the area of the triangular base and h is the height of the pyramid . area of triangular base = 1 / 2 * 3 * 3 = 9 / 2 so , v = 1 / 3 * 9 / 2 * 4 = 6 option e
Answer: e
Python program:
a = 3 ** 2
b = a / 2
c = b * 4
d = c / 3
Problem: 10 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 6514 , how much was it in the beginning ?
Options: a ) 8545 , b ) 8770 , c ) 8515 , d ) 7999 , e ) 7989
Rationale: "x * ( 90 / 100 ) * ( 85 / 100 ) = 6514 x = 8515 answer : c"
Answer: c
Python program:
a = 100 - 10
b = a / 100
c = 100 - 15
d = c / 100
e = b * d
f = 6514 / e
g = math.floor(f)
Problem: if each year the population of the country grows by 10 % , how many years will elapse before the population of the country doubles ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 7 , e ) 8
Rationale: till year 2000 , population is 100 . year 2001 : population becomes 110 . . . . . . . . . . . . . 1 year elapsed year 2002 : population becomes 121 . . . . . . . . . . . . . 2 year elapsed year 2003 : population becomes > 133 . . . . . . . . . . . . . 3 year elapsed year 2004 : population becomes > 146 . . . . . . . . . . . . . . . . . . 4 year elapsed year 2005 : population becomes > 160 . . . . . . . . . . . . . . . . . . 5 year elapsed year 2006 : population becomes > 176 . . . . . . . . . . . . . . . . . . 6 year elapsed year 2007 : population becomes > 193 . . . . . . . . . . . . . . . . . . 7 year elapsed year 2008 : population > 200 . . . . . . . . . . . . . . . . . . 8 year elapsed answer : e
Answer: e
Python program:
a = 4 + 4
Problem: 5 percent of a certain grass seed is timothy . if the amount of the mixture needed to plant one acre contains 2 pounds of timothy , how many acres can be planted with 600 pounds of the seed mixture ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 120
Rationale: if the mixture contains 2 pounds of timothy , the mixture must be 40 pounds . thus we need 40 pounds of mixture per acre . 600 / 40 = 15 acres the answer is b .
Answer: b
Python program:
a = 100 / 5
b = 2 * a
c = 600 / b
Problem: we invested a total of $ 1,000 . we invested one part of the money at 5 % and the rest of the money at 6 % . the total investment with interest at the end of the year was $ 1 , 054.50 . how much money did we invest at 5 % ?
Options: a ) $ 400 , b ) $ 450 , c ) $ 500 , d ) $ 550 , e ) $ 600
Rationale: "let x be the money invested at 5 % . 1.05 x + 1.06 ( 1000 - x ) = 1054.50 . 0.01 x = 1060 - 1054.50 . 0.01 x = 5.50 . x = 550 . the answer is d ."
Answer: d
Python program:
a = 2 + 3 
b = a * 2
c = 100 * b
d = 6 / 100
e = d + 1 
f = c * e
g = 2 + 3 
h = g * 2
i = 100 * h
j = 2 + 3 
k = j * 2
l = k * 5
m = i + l 
n = 2 * 3
o = m + n 
p = f - o
q = 6 / 100
r = q + 1 
s = 4 / 0
t = s + 1 
u = r - t
v = p / u
Problem: the average of 1 st 3 of 4 numbers is 16 and of the last 3 are 15 . if the sum of the first and the last number is 19 . what is the last numbers ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 7
Rationale: "a + b + c = 48 b + c + d = 45 a + d = 19 a – d = 3 a + d = 19 2 d = 16 d = 8 answer d"
Answer: d
Python program:
a = 3 * 16
b = 19 - 16
c = b + 3 
d = a - c
e = d - 16
Problem: if two integers x , y ( x > y ) are selected from - 10 to 5 ( inclusive ) , how many possible cases are there ?
Options: a ) 105 , b ) 120 , c ) 190 , d ) 210 , e ) 240
Rationale: "if two integers x , y ( x > y ) are selected from - 10 to 5 ( inclusive ) , how many possible cases are there ? a . 150 b . 180 c . 190 d . 210 e . 240 - - > 16 c 2 = 16 * 15 / 2 = 120 . therefore , the answer is b ."
Answer: b
Python program:
a = 5 + 10 
b = 5 + 2 
c = a + b 
d = 5 + 1 
e = c + d 
f = e + 5 
g = f + 10 
h = g + 2 
i = h + 1
Problem: a cistern 8 m long and 6 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :
Options: a ) 80 m 2 , b ) 50 m 2 , c ) 83 m 2 , d ) 86 m 2 , e ) 55 m 2
Rationale: area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 6 x 1.25 + 8 x 1.25 ) + 8 x 6 ] m 2 = 83 m 2 . answer : c
Answer: c
Python program:
a = 25 / 100
b = a + 1 
c = b * 6
d = 25 / 100
e = d + 1 
f = e * 8
g = c + f 
h = 2 * g
i = 6 * 8
j = h + i
Problem: in a certain accounting class of 90 students , 70 % of the students took the final exam on the assigned day while the rest of the students took the exam on a make - up date . if the students on the assigned day had an average score of 60 % , and the students on the make - up date had an average score of 70 % , what was the average score for the entire class ?
Options: a ) 63 % , b ) 64 % , c ) 65 % , d ) 66 % , e ) 67 %
Rationale: "70 % of the class scored 60 % and 30 % of the class scored 70 % . the difference between 60 % and 70 % is 10 % . the average will be 60 % + 0.3 ( 10 % ) = 63 % . the answer is a ."
Answer: a
Python program:
a = 70 * 60
b = 90 - 70
c = 70 * b
d = a + c 
e = d / 90
Problem: a sum fetched a total simple interest of 4016.25 at the rate of 9 % . p . a . in 5 years . what is the sum ?
Options: a ) 4462.5 , b ) 8032.5 , c ) 8925 , d ) none of these , e ) can not be determined
Rationale: "explanation : principal = ( 100 x 4016.25 ) / ( 9 x 5 ) = 401625 / 45 = 8925 answer : option c"
Answer: c
Python program:
a = 4016 * 25
b = a / 9
c = b / 5
Problem: a bag consists of 20 marbles , of which 5 are blue , 9 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ?
Options: a ) 3 / 4 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
Rationale: "bag consists of 20 marbles , of which 5 are blue , 9 are red remainder are white . so , white = 20 - 5 - 9 = 6 . probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white probability that the marble will be red or white = 9 / 20 + 6 / 20 = 15 / 20 = 3 / 4 hence , answer will be a ."
Answer: a
Python program:
a = 5 + 9 
b = 20 - a
c = b + 9 
d = c / 20
Problem: how many different positive integers exist between 10 ^ 6 and 10 ^ 7 , the sum of whose digits is equal to 2 ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 18
Rationale: "total cases = > 1000000 = > 6 cases for 1 being present at any of the 6 zero and last case 2000000 hence & cases answer : c"
Answer: c
Python program:
a = 4 + 3 
b = a + 1
Problem: john distributes his pencil among his 4 friends rose , mary , ranjan , and rohit in the ratio 1 / 1 : 1 / 3 : 1 / 4 : 1 / 5 . what is the minimum no . of pencils that the person should have ?
Options: a ) 45 , b ) 65 , c ) 98 , d ) 107 , e ) 198
Rationale: "rakesh : rahul : ranjan : rohit = 1 / 1 : 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 / 1 x 60 ) = 60 . 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 ( 60 x + 20 x + 15 x + 12 x ) = 107 x . for minimum number of pencils x = 1 . the person should have at least 107 pencils . d )"
Answer: d
Python program:
a = math.lcm(1, 1)
b = math.lcm(a, 1)
c = math.lcm(b, 3)
d = c / 1
e = math.lcm(1, 1)
f = math.lcm(e, 1)
g = math.lcm(f, 3)
h = g / 1
i = d + h 
j = math.lcm(1, 1)
k = math.lcm(j, 1)
l = math.lcm(k, 3)
m = l / 1
n = i + m 
o = math.lcm(1, 1)
p = math.lcm(o, 1)
q = math.lcm(p, 3)
r = q / 3
s = n + r
Problem: a sum of rs . 1550 was lent partly at 5 % and partly at 8 % p . a . simple interest . the total interest received after 3 years was rs . 300 . the ratio of the money lent at 5 % to that lent at 8 % is :
Options: a ) 16 : 15 , b ) 15 : 16 , c ) 15 : 8 , d ) 8 : 15 , e ) 8 : 17
Rationale: explanation : let the partial amount at 5 % be x and the partial amount at 8 % be ( 1550 - x ) interest on x at 5 % for 3 years + interest on ( 1550 - x ) at 8 % for 3 years = 300 x × 5 × 3 / 100 + ( 1550 - x ) × 8 × 3 / 100 = 300 x × 5 / 100 + ( 1550 - x ) × 8 / 100 = 100 5 x + 8 ( 1550 − x ) = 10000 5 x + 12400 − 8 x = 10000 3 x = 2400 x = 800 required ratio = x : ( 1550 - x ) = 800 : ( 1550 - 800 ) = 800 : 750 = 16 : 15 answer : option a
Answer: a
Python program:
a = 8 + 8 
b = 5 + 5 
c = 5 + b 
d = a / c
Problem: a certain library assesses fines for overdue books as follows . on the first day that a book is overdue , the total fine is $ 0.20 . for each additional day that the book is overdue , the total fine is either increased by $ 0.30 or doubled , whichever results in the lesser amount . what is the total for a book on the third day it is overdue ?
Options: a ) $ 0.60 , b ) $ 0.70 , c ) $ 0.80 , d ) $ 0.90 , e ) $ 1.00
Rationale: "1 st day fine - 0.2 2 nd day fine - 0.2 * 2 = 0.4 ( as doubling gives lower value ) 3 rd day fine - 0.4 + 3 = 0.7 ( as doubling gives higher value ) answer : b ."
Answer: b
Python program:
a = 0 * 20
b = a * 2
c = b * 2
d = c + 0
Problem: a part - time employee ’ s hourly wage was increased by 15 % . she decided to decrease the number of hours worked per week so that her total income did not change . by approximately what percent should the number of hours worked be decreased ?
Options: a ) 13 % , b ) 15 % , c ) 25 % , d ) 50 % , e ) 100 %
Rationale: "let ' s plug in somenicenumbers and see what ' s needed . let ' s say the employee used to make $ 1 / hour and worked 100 hours / week so , the total weekly income was $ 100 / week after the 15 % wage increase , the employee makes $ 1.15 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.15 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.15 to get : new # of hours = 100 / 1.15 ≈ 87 hours so , the number of hours decreases from 100 hours to ( approximately ) 87 hours . this represents a 13 % decrease ( approximately ) . answer : a"
Answer: a
Python program:
a = 15 / 100
b = 15 + 100 
c = b / 100
d = a / c
e = d * 100
Problem: if y is 60 % greater than x , than x is what % less than y ?
Options: a ) 29.3 % , b ) 33.4 % , c ) 37.5 % , d ) 41.6 % , e ) 45.7 %
Rationale: "y = 1.6 x x = y / 1.6 = 10 y / 16 = 5 y / 8 x is 3 / 8 less which is 37.5 % less than y . the answer is c ."
Answer: c
Python program:
a = 60 + 100 
b = 60 / a
c = b * 100
Problem: a student gets 50 % in one subject , 70 % in the other . to get an overall of 70 % how much should get in third subject .
Options: a ) 90 % , b ) 25 % , c ) 45 % , d ) 55 % , e ) 65 %
Rationale: "let the 3 rd subject % = x 50 + 70 + x = 3 * 70 120 + x = 210 x = 210 - 120 = 90 answer : a"
Answer: a
Python program:
a = 70 * 3
b = 50 + 70 
c = a - b
Problem: the product of two successive numbers is 2652 . which is the smaller of the two numbers ?
Options: a ) 51 , b ) 68 , c ) 57 , d ) 55 , e ) 37
Rationale: "a 51 from the given alternatives , 51 × 52 = 2652 ∴ smaller number = 51"
Answer: a
Python program:
a = math.sqrt(2652)
Problem: a sum of money deposited at c . i . amounts to rs . 2560 in 3 years and to rs . 2989 in 4 years . find the rate percent ?
Options: a ) 30 % , b ) 10 % , c ) 20 % , d ) 16 % , e ) 50 %
Rationale: "2560 - - - 429 100 - - - ? = > 16 % answer : d"
Answer: d
Python program:
a = 2989 - 2560
b = a / 2560
c = b * 100
Problem: if k is a non - negative integer and 30 ^ k is a divisor of 929,260 then 3 ^ k - k ^ 3 =
Options: a ) 0 , b ) 1 , c ) 45 , d ) 130 , e ) 520
Rationale: 9 + 2 + 9 + 2 + 6 + 0 = 28 , so this number is not divisible by 3 and thus not divisible by 30 . therefore , k = 0 3 ^ k - k ^ 3 = 1 - 0 = 1 the answer is b .
Answer: b
Python program:
a = 1 - 1
b = 3 ** a
c = 1 - 1
d = c ** 3
e = b - d
Problem: a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 18 % . what was its profit on the items sold in february ?
Options: a ) 27.5 % , b ) 30 % , c ) 35 % , d ) 23 % , e ) 40 %
Rationale: "assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.82 * 150 x = 123 x hence total profit = 23 % option d"
Answer: d
Python program:
a = 100 - 18
b = a / 100
c = 100 + 20 
d = 100 + 25 
e = d / 100
f = c * e
g = b * f
h = g - 100
Problem: in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 5500 , the number of valid votes that the other candidate got , was :
Options: a ) 2800 , b ) 1980 , c ) 2900 , d ) 2200 , e ) 2300
Rationale: "b number of valid votes = 80 % of 5500 = 4400 . valid votes polled by other candidate = 45 % of 4400 = ( 45 / 100 x 4400 ) = 1980 ."
Answer: b
Python program:
a = 20 / 100
b = 1 - a
c = 55 / 100
d = 1 - c
e = b * d
f = e * 5500
Problem: there are 7 players in a bowling team with an average weight of 103 kg . if two new players join the team , one weighs 110 kg and the second weighs 60 kg , what will be the new average weight ?
Options: a ) 95 kg . , b ) 99 kg . , c ) 89 kg . , d ) 90 kg . , e ) 92 kg .
Rationale: "the new average will be = ( 103 * 7 + 110 + 60 ) / 9 = 99 kgs b is the answer"
Answer: b
Python program:
a = 7 * 103
b = 110 + 60 
c = a + b 
d = 7 + 2 
e = c / d
Problem: find the average of all numbers between 3 and 86 which are divisible by 5
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 45
Rationale: "explanation : average = ( 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50 + 55 + 60 + 65 + 70 + 75 + 80 + 85 ) / 17 = 765 / 17 = 45 answer : option e"
Answer: e
Python program:
a = 5 * 3
b = 5 * 2
c = 5 + b 
d = a + c 
e = 5 * 4
f = d + e 
g = 4 + 1 
h = g * 5
i = f + h 
j = i / 5
Problem: if the annual increase in the population of a town is 10 % and the present number of people is 14000 , what will the population be in 2 years ?
Options: a ) 12100 , b ) 15240 , c ) 12456 , d ) 16940 , e ) 10002
Rationale: "the required population is = 14000 ( 1 + 10 / 100 ) ^ 2 = 14000 * 11 / 10 * 11 / 10 = 16940 answer is d"
Answer: d
Python program:
a = 10 + 100 
b = a / 100
c = b * 14000
d = 10 + 100 
e = d / 100
f = c * e
Problem: the average of 21 numbers is 44 . average of the first 11 of them is 48 and that of the last 11 is 41 . find the 11 th number ?
Options: a ) 48 , b ) 51 , c ) 47 , d ) 49 , e ) 55
Rationale: sum of all the 21 numbers = 21 * 44 = 924 sum of the first 11 of them = 11 * 48 = 528 sum of the last 11 of them = 11 * 41 = 451 so , the 11 th number = 528 + 451 - 924 = 55 . answer : e
Answer: e
Python program:
a = 11 * 41
b = 21 * 44
c = 48 * 11
d = b - c
e = a - d
Problem: a train running at the speed of 30 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 75 m , b ) 180 m , c ) 324 m , d ) can not be determined , e ) none of these
Rationale: "speed = 30 * 5 / 18 = 25 / 3 m / sec length of the train = speed * time = 25 / 3 * 9 = 75 m answer : a"
Answer: a
Python program:
a = 30 * 1000
b = a / 3600
c = b * 9
Problem: in the next cricket world cup t - 20 , team t has decided to score 200 runs only through 4 s and 6 s . in how many ways can the team t score these 200 runs ?
Options: a ) 13 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: team t can score a maximum of 50 fours and a minimum of 2 fours with an interval or spacing of 3 units to accommodate the 6 ' s . so the number of fours scored forms an ap 2 , 5 , 8 , . . . 50 with a common difference of 3 . number of ways of scoring 200 only through 4 ' s and 6 ' s = ( 50 - 2 ) / 3 + 1 = 17 answer : d alternate solution : 4 x + 6 y = 200 - - > 2 x + 3 y = 100 x = ( 100 - 3 y ) / 2 - - > 100 - 3 y should be even . this is possible when 3 y is even . there are 17 even multiples of 3 between 0 and 100 . answer : d
Answer: d
Python program:
a = 200 / 4
b = 200 / 6
c = a - b
Problem: for each 6 - month period during a light bulb ' s life span , the odds of it not burning out from over - use are half what they were in the previous 6 - month period . if the odds of a light bulb burning out during the first 6 - month period following its purchase are 1 / 5 , what are the odds of it burning out during the period from 6 months to 1 year following its purchase ?
Options: a ) 5 / 27 , b ) 2 / 9 , c ) 1 / 2 , d ) 4 / 9 , e ) 2 / 3
Rationale: "p ( of not burning out in a six mnth period ) = 1 / 2 of p ( of not burning out in prev 6 mnth period ) p ( of burning out in 1 st 6 mnth ) = 1 / 5 - - - > p ( of not burning out in 1 st 6 mnth ) = 1 - 1 / 5 = 4 / 5 - - - - > p ( of not burning out in a six mnth period ) = 1 / 2 * 4 / 5 = 4 / 10 = 2 / 5 - - - > p ( of burning out in a six mnth period ) = 1 - 2 / 5 = 3 / 5 now p ( of burning out in 2 nd six mnth period ) = p ( of not burning out in 1 st six mnth ) * p ( of burning out in a six mnth ) = 4 / 5 * 3 / 5 = 1 / 2 ans c"
Answer: c
Python program:
a = 1 / 5
b = 1 - a
c = 2 / 0
d = 1 - c
e = d / 1
f = 1 - e
g = b * f
Problem: the perimeter of an isosceles right triangle is 8 + 8 sq rt 2 . what is the length of the hypotenuse of the triangle ?
Options: a ) 4 , b ) 5.656 , c ) 5 , d ) 6 , e ) 7
Rationale: "side of triangle is a then perimeter = a + a + a . sqrt 2 ( right angle and pythagorus ) = 2 a + a . sqrt 2 = 8 + 8 sqrt 2 or , a . ( 2 + sqrt 2 ) = 8 ( 1 + sqrt 2 ) , a = 8 * ( 1 + sqrt 2 ) / 2 + sqrt 2 = 8 * 2.414 / 3.414 = 0.707 * 8 then hypotenuse = 5.656 b"
Answer: b
Python program:
a = math.sqrt(2)
b = 8 * a
c = b / 2
Problem: when x is multiplied by 3 , the result is 18 more than the result of subtracting x from 26 . what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 11 , d ) 13 , e ) 22
Rationale: "the equation that can be formed is : 3 x - 18 = 26 - x or , 4 x = 44 or , x = 11 . c answer ."
Answer: c
Python program:
a = 26 + 18 
b = 3 + 1 
c = a / b
Problem: a bag contains 5 red , 6 blue and 2 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 1 / 13 , b ) 2 / 23 , c ) 5 / 39 , d ) 4 / 27 , e ) 3 / 23
Rationale: "p ( both are red ) , 5 c 213 c 2 = 6 c 213 c 2 = 10 / 78 = 5 / 39 c"
Answer: c
Python program:
a = math.comb(5, 2)
b = 5 + 6 
c = b + 2 
d = math.comb(c, 2)
e = a / d
Problem: find the value of x . ( 47 % of 1442 - 36 % of 1412 ) + 61 = x ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: b ) 2
Answer: b
Python program:
a = 47 / 100
b = a * 1442
c = 36 / 100
d = c * 1412
e = b - d
f = e + 61 
g = reminder + ( 
h = math.floor(g, 1)
Problem: the maximum number of students among them 100 pens and 50 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?
Options: a ) 50 , b ) 75 , c ) 69 , d ) 79 , e ) 82
Rationale: "number of pens = 100 number of pencils = 50 required number of students = h . c . f . of 100 and 50 = 50 answer is a"
Answer: a
Python program:
a = math.gcd(100, 50)
Problem: the average age of 35 students in a class is 16 years . the average age of 21 students is 14 . what is the average age of remaining 95 students ?
Options: a ) 14 years , b ) 1.7 years , c ) 1.9 years , d ) 2.8 years , e ) none
Rationale: "solution sum of the ages of 14 students = ( 16 x 35 ) - ( 14 x 21 ) = 560 - 294 . = 266 . ∴ required average = 266 / 95 = 2.8 years . answer d"
Answer: d
Python program:
a = 35 * 16
b = a + 21 
c = b + 35 
d = 35 * 16
e = c - d
Problem: rahul travels from a to b a distance of 200 miles in 5 hours . he returns to a in 4 hours . find his average speed ?
Options: a ) 52.2 mph , b ) 61.9 mph , c ) 44.4 mph , d ) 35.7 mph , e ) 65.6 mph
Rationale: speed from a to b = 200 / 5 = 40 mph speed from b to a = 200 / 4 = 50 mph average speed = 2 * 40 * 50 / 90 = 44.4 mph answer is c
Answer: c
Python program:
a = 200 / 5
b = 200 / 4
c = a + b 
d = c / 2
Problem: if 5 x * x + 14 * x + k = 0 having two reciprocal roots find the value of k .
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: product of reciprocal roots = 1 product of roots of quadratic eqn ax ^ 2 + bx + c = 0 is c / a . hence k / 5 = 1 k = 5 answer : e
Answer: e
Python program:
a = 14 - 5
b = 14 - a
Problem: a watch was sold at a loss of 15 % . if it was sold for rs . 400 more , there would have been a gain of 5 % . what is the cost price ?
Options: a ) 1600 , b ) 2998 , c ) 2778 , d ) 2788 , e ) 2991
Rationale: "85 % 120 % - - - - - - - - 25 % - - - - 400 100 % - - - - ? = > rs . 1600 answer : a"
Answer: a
Python program:
a = 400 * 100
b = 100 + 5 
c = 100 - 15
d = b - c
e = a / d
Problem: meena wrote all the numbers from 1 to 49,999 inclusive . how many digits did she write in total ?
Options: a ) 154,889 , b ) 196,889 , c ) 238,889 , d ) 250,889 , e ) 264,889
Rationale: "1 - 9 = > 1 * 9 digits 10 - 99 = > 2 * 90 = 180 ( numbers between 10 - 99 is 90 where each has 2 digits ) 100 - 999 = > 3 * 900 = 2700 1000 - 9999 = > 4 * 9000 = 36,000 10000 - 49999 = > 5 * 40,000 = 200,000 the answer is 238,889 the answer is c ."
Answer: c
Python program:
a = 10 - 1
b = 100 - 10
c = b * 2
d = a + c 
e = 100 - 10
f = e * 3
g = d + f 
h = 100 - 10
i = h * 4
j = g + i
Problem: the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 12 . if p invested the money for 5 months , find for how much time did q invest the money ?
Options: a ) 19 , b ) 17 , c ) 13 , d ) 10 , e ) 12
Rationale: "7 * 5 : 5 * x = 7 : 12 x = 12 answer : e"
Answer: e
Python program:
a = 7 / 5
b = 12 / 7
c = a * b
d = c * 5
Problem: two employees x and y are paid a total of rs . 770 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 150 , b ) s . 200 , c ) s . 250 , d ) s . 350 , e ) s . 400
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 770 but x = 120 % of y = 120 y / 100 = 12 y / 10 â ˆ ´ 12 y / 10 + y = 770 â ‡ ’ y [ 12 / 10 + 1 ] = 770 â ‡ ’ 22 y / 10 = 770 â ‡ ’ 22 y = 7700 â ‡ ’ y = 700 / 22 = 700 / 2 = rs . 350 d )"
Answer: d
Python program:
a = 1 + 4 
b = a * 2
c = 770 * b
d = 1 + 4 
e = d * 2
f = e + 1 
g = f * 2
h = c / g
Problem: how many positive integers less than 300 can be formed using the numbers 1 , 2 , 3 and 5 for the digits ?
Options: a ) 48 , b ) 52 , c ) 66 , d ) 68 , e ) 84
Rationale: "notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero : 0 1 1 1 2 2 2 3 3 2 5 5 number of possibilities = 3 * 4 * 4 = 48 . then , just add up the number of 1 digits numbers = 4 , so total is 48 + 4 = 52 . answer : b"
Answer: b
Python program:
a = 4 + 1 
b = a - 1
c = math.factorial(b)
d = math.factorial(1)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: if 3 is one solution of the equation x ^ 2 + 3 x + k = 10 , where k is a constant , what is the other solution ?
Options: a ) - 7 , b ) - 6 , c ) - 3 , d ) 1 , e ) 6
Rationale: "the phrase “ 3 is one solution of the equation ” means that one value of x is 3 . thus , we first must plug 3 for x into the given equation to determine the value of k . so we have 3 ^ 2 + ( 3 ) ( 3 ) + k = 10 9 + 9 + k = 10 18 + k = 10 k = - 8 next we plug - 8 into the given equation for k and then solve for x . x ^ 2 + 3 x – 8 = 10 x ^ 2 + 3 x – 18 = 0 ( x + 6 ) ( x - 3 ) = 0 x = - 6 or x = 3 thus , - 6 is the other solution . answer b ."
Answer: b
Python program:
a = 3 ** 2
b = 3 * 3
c = a + b 
d = 10 - c
e = d / 3