euclaise/mathqa_programs huggingface dataset:
Problem: a can do a piece of work in 12 days and b alone can do it in 10 days . b works at it for 5 days and then leaves . a alone can finish the remaining work in
Options: a ) 5 days , b ) 6 days , c ) 7.5 days , d ) 8.5 days , e ) 9 days
Rationale: "explanation : b ' s 5 days work = 1 / 10 ∗ 5 = 1 / 2 remaining work = 1 − 1 / 2 = 1 / 2 a can finish work = 12 ∗ 1 / 2 = 6 days option b"
Answer: b
Python program:
a = 1 / 12
b = 1 / 10
c = a + b 
d = 1 / c
Problem: the average of 10 numbers was calculated as 20 . it is discovered later on that while calculating the average , one number , namely 86 , was incorrectly read as 26 . what is the correct average ?
Options: a ) 22 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: "10 * 20 - 26 + 86 = 260 260 / 10 = 26 the answer is e ."
Answer: e
Python program:
a = 10 * 20
b = 86 - 26
c = a + b 
d = c / 10
Problem: find the compound interest on $ 1200 for 3 years at 20 % p . a . if ci is component yearly ?
Options: a ) $ 120 , b ) $ 150 , c ) $ 874 , d ) $ 250 , e ) $ 300
Rationale: "a = p ( 1 + r / 100 ) ^ t = 1200 ( 1 + 20 / 100 ) ^ 3 = $ 2074 ci = $ 874 answer is c"
Answer: c
Python program:
a = 20 / 100
b = 1 + a 
c = b ** 3
d = 1200 * c
e = d - 1200
Problem: the cross - section of a cannel is a trapezium in shape . if the cannel is 12 m wide at the top and 8 m wide at the bottom and the area of cross - section is 690 sq m , the depth of cannel is ?
Options: a ) 39 , b ) 28 , c ) 27 , d ) 69 , e ) 71
Rationale: "1 / 2 * d ( 12 + 8 ) = 690 d = 69 answer : d"
Answer: d
Python program:
a = 12 + 8 
b = a / 2
c = 690 / b
d = c / 8
e = d / 2
Problem: a cistern which could be filled in 7 hours takes one hour more to be filled owing to a leak in its bottom . if the cistern is full in what time will the leak empty it ?
Options: a ) 76 hrs , b ) 70 / 3 hrs , c ) 55 hrs , d ) 90 hrs , e ) 11 hrs
Rationale: 1 / 7 - 1 / x = 1 / 10 = > 70 / 3 hrs answer : b
Answer: b
Python program:
a = 1 / 7
b = 1 / 10
c = a - b
d = 1/(c)
Problem: pooja travels from a to b a distance of 800 miles in 10 hours . he returns to a in 5 hours . find his average speed ?
Options: a ) 123.07 mph , b ) 100 mph , c ) 150.07 mph , d ) 200 mph , e ) 300 mph
Rationale: speed from a to b = 800 / 8 = 100 mph speed from b to a = 800 / 5 = 160 mph average speed = 2 * 100 * 160 / 260 = 123.07 mph answer is a
Answer: a
Python program:
a = 800 / 10
b = 800 / 5
c = a + b 
d = c / 2
Problem: find the simple interest on rs . 68,000 at 16 2 / 3 % per year for 9 months .
Options: a ) 7500 , b ) 6500 , c ) 8500 , d ) 9500 , e ) none of them
Rationale: "p = rs . 68000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 68,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8500 answer is c ."
Answer: c
Python program:
a = 2 * 3
b = a * 100
c = b * 100
d = 3 * 3
e = d * 100
f = 3 + 2 
g = f * 2
h = e * g
i = c + h 
j = 16 * 3
k = j + 2 
l = k / 3
m = i * l
n = 3 * 3
o = 2 * 3
p = 2 * o
q = n / p
r = m * q
s = 1 / 100
t = r * s
Problem: if y is the smallest positive integer such that 11,025 multiplied by y is the square of an integer , then y must be
Options: a ) 2 , b ) 4 , c ) 6 , d ) 7 , e ) 14
Rationale: "i just tried plugging in the numbers and found out that 4 * 11025 = 44 , 100 , which is a square of 210 b"
Answer: b
Python program:
a = 2 + 3 
b = a * 2
Problem: when jessica withdrew $ 400 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 1 / 4 of the remaining balance , what will be the final balance in her bank account ?
Options: a ) 300 , b ) 375 , c ) 400 , d ) 500 , e ) 750
Rationale: as per the question 400 = 2 a / 5 thus - a which is the total amount = 1000 the amount thus left = 600 she then deposited 1 / 4 of 600 = 150 total amount in her account = 750 answer e
Answer: e
Python program:
a = 3 / 5
b = 1 - a
c = 400 / b
d = c - 400
e = 1 / 4
f = 1 + e 
g = d * f
Problem: a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 290 m long ?
Options: a ) 38 sec , b ) 35 sec , c ) 44 sec , d ) 40 sec , e ) 52 sec
Rationale: "explanation : speed = 45 km / hr = 45 × ( 10 / 36 ) m / s = 150 / 12 = 50 / 4 = 25 / 2 m / s total distance = length of the train + length of the platform = 360 + 290 = 650 meter time taken to cross the platform = 650 / ( 25 / 2 ) = 650 × 2 / 25 = 52 seconds answer : option e"
Answer: e
Python program:
a = 290 / 1000
b = 360 / 1000
c = a + b 
d = c / 45
e = d * 3600
Problem: if x and y are integers such that ( x + 1 ) ^ 2 is less than or equal to 81 and ( y - 1 ) ^ 2 is less than 64 , what is the sum of the maximum possible value of xy and the minimum possible value of xy ?
Options: a ) - 16 , b ) - 20 , c ) 0 , d ) 14 , e ) 16
Rationale: "( x + 1 ) ^ 2 < = 81 x < = 8 x > = - 10 ( y - 1 ) ^ 2 < 64 y < 9 y > - 7 max possible value of xy is - 10 × - 6 = 60 minimum possible value of xy is - 10 × 8 = - 80 - 80 + 60 = - 20 answer : b"
Answer: b
Python program:
a = math.sqrt(81)
b = math.sqrt(64)
c = a + b
Problem: the simple interest on a sum of money will be rs . 900 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?
Options: a ) 1800 , b ) 2888 , c ) 1200 , d ) 2699 , e ) 2771
Rationale: "p - - - 10 - - - - 900 p - - - 5 - - - - - 450 3 p - - - 5 - - - - - 1350 - - - - - - = > 1800 answer : a"
Answer: a
Python program:
a = 900 / 10
b = a * 5
c = b * 3
d = 900 / 10
e = d * 5
f = c + e
Problem: a number when divided by 6 leaves a remainder 3 . when the square of the same number is divided by 6 , the remainder is :
Options: a ) 0
b ) 1
c ) 2
d ) 3
e ) 4
Rationale: let x = 6 q + 3 . then , x 2 = ( 6 q + 3 ) 2 = 36 q 2 + 36 q + 9 = 6 ( 6 q 2 + 6 q + 1 ) + 3 . so , when 2 n is divided by 4 , remainder = 3 . answer : d
Answer: d
Python program:
a = 6 * 3
b = a / 6
Problem: the present ratio of students to teachers at a certain school is 40 to 1 . if the student enrollment were to increase by 50 students and the number of teachers were to increase by 5 , the ratio of students to teachers would then be 25 to 1 . what is the present number of teachers ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: "we are given that the ratio of students to teacher is 40 to 1 . we can rewrite this using variable multipliers . students : teachers = 40 x : x we are next given that student enrollment increases by 50 and the number of teachers increases by 5 . with this change the new ratio becomes 25 to 1 . we can put all this into an equation : students / teachers  25 / 1 = ( 40 x + 50 ) / ( x + 5 ) if we cross multiply we have : 25 ( x + 5 ) = 40 x + 50 25 x + 125 = 40 x + 50 5 = x since x is the present number of teachers , currently there are 5 teachers . answer a ."
Answer: a
Python program:
a = 40 + 25 
b = a / 25
Problem: what is the sum of all possible solutions to | x - 6 | ^ 2 + | x - 6 | = 20 ?
Options: a ) - 1 , b ) 6 , c ) 7 , d ) 12 , e ) 14
Rationale: denote | x - 6 | as y : y ^ 2 + y = 20 - - > y = - 5 or y = 4 . discard the first solution since y = | x - 6 | , so it ' s an absolute value and thus can not be negative . y = | x - 6 | = 4 - - > x = 10 or x = - 2 . the sum = 12 . answer : d .
Answer: d
Python program:
a = 4 + 6 
b = 6 - 4
c = a + b
Problem: how many diagonals does a polygon with 15 sides have , if one of its vertices does not connect to any diagonal ?
Options: a ) 80
b ) 90
c ) 77
d ) 88
e ) 99
Rationale: if i calculate it using the formulae , # diagonals = n ( n - 3 ) / 2 each vertex sends of n - 3 diagonals n = 15 - 1 then 14 * ( 14 - 3 ) / 2 = 77 correct option : c
Answer: c
Python program:
a = 15 - 1
b = 15 - 1
c = b - 3
d = a * c
e = d / 2
Problem: a and b undertake to do a piece of work for rs . 600 . a alone can do it in 6 days while b alone can do it in 8 days . with the help of c , they finish it in 3 days . find the share of a
Options: a ) 300 , b ) 450 , c ) 750 , d ) 800 , e ) none of them
Rationale: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 24 a : b : c = ratio of their 1 day ' s work = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . a ’ s share = rs . ( 600 * 4 / 8 ) = rs . 300 , b ' s share = rs . ( 600 * 3 / 8 ) = rs . 225 . c ' s share = rs . [ 600 - ( 300 + 225 » ) = rs . 75 . answer is a"
Answer: a
Python program:
a = 4 + 3 
b = a + 1 
c = 1 / b
d = c * 600
Problem: truck x is 13 miles ahead of truck y , which is traveling the same direction along the same route as truck x . if truck x is traveling at an average speed of 47 miles per hour and truck y is traveling at an average speed of 53 miles per hour , how long will it take truck y to overtake and drive 5 miles ahead of truck x ?
Options: a ) 2 hours , b ) 2 hours 20 minutes , c ) 2 hours 30 minutes , d ) 2 hours 45 minutes , e ) 3 hours
Rationale: relative speed = 53 - 47 = 6 miles per hour dist required = 13 + 5 = 18 miles time taken to overtake = 18 / 6 = 3 hours . e is the answer .
Answer: e
Python program:
a = 13 + 5 
b = 53 - 47
c = a / b
Problem: how many bricks , each measuring 125 cm x 11.25 cm x 6 cm , will be needed to build a wall of 8 m x 6 m x 22.5 cm ?
Options: a ) 1280 , b ) 2400 , c ) 5500 , d ) 7400 , e ) 3400
Rationale: "number of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 22.5 ) / ( 125 x 11.25 x 6 ) = 1280 answer : a"
Answer: a
Python program:
a = 8 * 100
b = 6 * 100
c = a * b
d = c * 22
e = 125 * 11
f = e * 6
g = d / f
Problem: the number of boxes in a warehouse can be divided evenly into 5 equal shipments by boat or 24 equal shipments by truck . what is the smallest number of boxes that could be in the warehouse ?
Options: a ) 27 , b ) 33 , c ) 54 , d ) 81 , e ) 120
Rationale: answer is the lcm of 5 and 24 = 120 answer e
Answer: e
Python program:
a = 2 * 2
b = a * 2
c = b * 3
d = c * 5
Problem: a sum of money amounts to rs . 6690 after 3 years and to rs . 10,035 after 6 years on compound interest . find the sum .
Options: a ) 4360 , b ) 4460 , c ) 4560 , d ) 4660 , e ) 4760
Rationale: "let the sum be rs . p . then p ( 1 + r / 100 ) 3 = 6690 … ( i ) p ( 1 + r / 100 ) 6 = 10035 … ( ii ) on dividing , we get ( 1 + r / 100 ) 3 = 10025 / 6690 = 3 / 2 . substituting this value in ( i ) , we get : p * ( 3 / 2 ) = 6690 or p = ( 6690 * 2 / 3 ) = 4460 hence , the sum is rs . 4460 . answer : b"
Answer: b
Python program:
a = 10 - 35
b = 6690 * 6
c = 3 * 10
d = b - c
e = a / d
f = e * 100
Problem: a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 45 , what is the total amount ?
Options: a ) 166 , b ) 105 , c ) 175 , d ) 177 , e ) 169
Rationale: "x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 45 35 - - - ? = > 175 answer : c"
Answer: c
Python program:
a = 100 / 45
b = a * 45
c = 30 / 45
d = c * 45
e = b + d 
f = e + 45
Problem: without stoppages , a train travels certain distance with an average speed of 100 km / h , and with stoppages , it covers the same distance with an average speed of 95 km / h . how many minutes per hour the train stops ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: due to stoppages , it covers 5 km less . time taken to cover 5 km = 5 â  „ 100 h = 1 â  „ 20 h = 1 â  „ 20 ã — 60 min = 3 min answer c
Answer: c
Python program:
a = 95 / 100
b = a * const_60
c = const_60 - b
Problem: a tank is 25 m long , 12 m wide and 6 m deep . what is the cost of plastering its walls and bottom at the rate of 75 paise per sq . m ?
Options: a ) 558 , b ) 502 , c ) 516 , d ) 612 , e ) 700
Rationale: "total surface s = 2 lw + 2 lh + 2 wh = ( 25 * 12 ) + ( 2 * 25 * 6 ) + ( 2 * 12 * 6 ) = 300 + 300 + 144 = 744 m 2 therefore cost of plastering = 744 * 75 = 5800 paise = 558 answer a"
Answer: a
Python program:
a = 25 + 12 
b = a * 2
c = b * 6
d = 25 * 12
e = c + d 
f = 75 / 100
g = e * f
Problem: a man swims downstream 36 km and upstream 26 km taking 2 hours each time , what is the speed of the man in still water ?
Options: a ) 9 , b ) 18.4 , c ) 15.5 , d ) 16.7 , e ) 13.4
Rationale: "36 - - - 2 ds = 18 ? - - - - 1 26 - - - - 2 us = 13 ? - - - - 1 m = ? m = ( 18 + 13 ) / 2 = 15.5 answer : c"
Answer: c
Python program:
a = 26 / 2
b = 36 / 2
c = a + b 
d = c / 2
Problem: a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 19200 . a ' s share is ?
Options: a ) 8876 , b ) 2765 , c ) 6400 , d ) 1298 , e ) 1261
Rationale: "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 19200 = 6400 answer : c"
Answer: c
Python program:
a = 1 * 12
b = 1 * 12
c = 12 - 6
d = c * 2
e = b + d 
f = 12 - 8
g = f * 3
h = e + g 
i = 19200 / h
j = a * i
Problem: a student chose a number , multiplied it by 3 , then subtracted 220 from the result and got 110 . what was the number he chose ?
Options: a ) 90 , b ) 100 , c ) 110 , d ) 120 , e ) 130
Rationale: "let x be the number he chose , then 3 ⋅ x − 220 = 110 3 x = 330 x = 110 correct answer c"
Answer: c
Python program:
a = 110 + 220 
b = a / 3
Problem: 2 + 2 + 2 ² + 2 ³ . . . + 2 ^ 10
Options: a ) 2 ^ 9 , b ) 2 ^ 10 , c ) 2 ^ 11 , d ) 2 ^ 35 , e ) 2 ^ 37
Rationale: "2 + 2 = 2 ^ 2 2 ^ 2 + 2 ^ 2 = ( 2 ^ 2 ) * ( 1 + 1 ) = 2 ^ 3 2 ^ 3 + 2 ^ 3 = ( 2 ^ 3 ) * ( 1 + 1 ) = 2 ^ 4 so you can notice the pattern . . . in the end you will have 2 ^ 10 + 2 ^ 10 , which will give you 2 ^ 11 answer c"
Answer: c
Python program:
a = 2 + 2 
b = 2 * a
c = b / 2
Problem: a football field is 7200 square yards . if 1200 pounds of fertilizer are spread evenly across the entire field , how many pounds of fertilizer were spread over an area of the field totaling 3600 square yards ?
Options: a ) 450 , b ) 600 , c ) 750 , d ) 2400 , e ) 3200
Rationale: "answer a ) 9600 yards need 1200 lbs 1 yard will need 1200 / 7200 = 1 / 6 lbs 3600 yards will need 1 / 6 * 3600 yards = 600 lbs b"
Answer: b
Python program:
a = 1200 / 7200
b = 3600 * a
Problem: { ( 476 + 424 ) 2 - 4 x 476 x 424 } = ?
Options: a ) 2135 , b ) 6551 , c ) 2704 , d ) 6466 , e ) 1113
Rationale: given exp . = [ ( a + b ) 2 - 4 ab ] , where a = 476 and b = 424 = [ ( 476 + 424 ) 2 - 4 x 476 x 424 ] = [ ( 900 ) 2 - 807296 ] = 810000 - 807296 = 2704 . correct option is c
Answer: c
Python program:
a = 476 + 424 
b = a ** 2
c = 4 * 476
d = c * 424
e = b - d
Problem: an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 18 - meter platform and caught it after it had traveled 53.4 meters . how many times did the ball bounce ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "ans : 6 division of total diatance travelled will be 18 + 18 + 9 + 4.5 + 2.25 + 1.125 + 0.5 ans b"
Answer: b
Python program:
a = 18 / 2
b = a / 2
Problem: a certain telescope increases the visual range at a particular location from 90 kilometers to 150 kilometers . by what percent is the visual range increased by using the telescope ?
Options: a ) 30 % , b ) 33 1 / 2 % , c ) 40 % , d ) 60 % , e ) 66 2 / 3 %
Rationale: "original visual range = 90 km new visual range = 150 km percent increase in the visual range by using the telescope = ( 150 - 90 ) / 90 * 100 % = 2 / 3 * 100 % = 66.67 % answer e"
Answer: e
Python program:
a = 150 - 90
b = a / 90
c = b * 100
Problem: bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 35 more . what was his original selling price ?
Options: a ) $ 180 , b ) $ 280 , c ) $ 420 , d ) $ 550 , e ) $ 700
Rationale: "let p be the original purchase price of the product . bill originally sold the product for 1.1 * p . in the second scenario , the purchase price is 0.9 * p . a 30 % profit means the selling price would be 1.3 * 0.9 * p = 1.17 * p thus , according to the information in the question , 1.17 p - 1.1 p = 35 0.07 = 35 p = 500 the original selling price was 500 * 1.1 = 550 . the correct answer is d ."
Answer: d
Python program:
a = 10 / 100
b = 1 - a
c = 30 / 100
d = 1 + c 
e = b * d
f = 10 / 100
g = 1 + f 
h = e - g
i = 35 / h
j = 10 / 100
k = 1 + j 
l = i * k
Problem: a car left town a towards town b driving at a speed of v = 32 km / hr . after 3 hours on the road the driver stopped for 15 min in town c . because of a closed road he had to change his route , making the trip 28 km longer . he increased his speed to v = 40 km / hr but still he was 30 min late . find the distance the car has covered .
Options: a ) 114 , b ) 115 , c ) 116 , d ) 117 , e ) 118
Rationale: the driver did not plan the stop at c . suppose it took x hours for him to get from c to b . then the distance is s = 40 ⋅ x km . it took x − 3060 − 1560 = x − 4560 = x − 34 h to drive from c to b . the distance from c to b is 32 ( x − 34 ) km , which is 28 km shorter than 40 ⋅ x , i . e . 32 ( x − 34 ) + 28 = 40 x 32 x − 24 + 28 = 40 x 4 = 8 x x = 12 hr ⋅ x = 30 min . then the time of the trip from c to b was 30 min . the distance covered equals 3 ⋅ 32 + 12 ⋅ 40 = 96 + 20 = 116 km . so answer is c .
Answer: c
Python program:
a = 3 * 32
b = 40 / 2
c = a + b
Problem: total num of pupiles in 3 grades of scholl is 333 . the no of pupiles in grades 1 and 2 are un 3 : 5 ratio and 2 and 3 grades are 7 : 11 ratio . what is the strength of class that has highest no of pupils
Options: a ) 145 , b ) 155 , c ) 165 , d ) 175 , e ) 185
Rationale: ratio g 1 : g 2 = 3 : 5 and g 2 : g 3 = 7 : 11 so g 1 : g 2 : g 3 = 21 : 35 : 55 let the strength of three classes are 21 x , 35 x and 55 x respectively , then 21 x + 35 x + 55 x = 333 = > 111 x = 333 or x = 3 so strength of the class with highest number of pupils = 55 x = 55 * 3 = 165 answer : c
Answer: c
Python program:
a = 3 / 5
b = 7 / 11
c = a * b
d = 7 / 11
e = c + d 
f = e + 1 
g = 333 / f
Problem: a train 150 metres long is moving at a speed of 25 kmph . it will cross a man coming from the opposite direction at a speed of 2 km per hour in :
Options: a ) 20 sec , b ) 32 sec , c ) 36 sec , d ) 38 sec , e ) 40 sec
Rationale: relative speed = ( 25 + 2 ) km / hr = 27 km / hr = ( 27 × 5 / 18 ) m / sec = 15 / 2 m / sec . time taken by the train to pass the man = ( 150 × 2 / 15 ) sec = 20 sec answer : a
Answer: a
Python program:
a = 150 / 1000
b = 25 + 2 
c = a / b
d = 3600 * c
Problem: initially , the men and women in a room were in the ratio of 4 : 5 . then , 2 men entered the room and 3 women left the room . then , the number of women doubled . now there are 14 men in the room . how many d women are currently in the room ?
Options: a ) 12 , b ) 14 , c ) 15 , d ) 24 , e ) 36
Rationale: the number of women doubled means that they have become 24 from 12 . . and we have to tell the current strength so 24 is the answer . . let the number be 4 x and 5 x . . given 4 x + 2 = 14 . . so x = 3 . . women number = 5 * 3 - 3 = 12 , then doubled = 24 . . ans d
Answer: d
Python program:
a = 14 - 2
b = 5 * a
c = b / 4
d = c - 3
e = 2 * d
Problem: twenty four meters of wire is available to fence off a flower bed in the form of a circular sector . what must the radius of the circle in meters be , if we wish to have a flower bed with the greatest possible surface area ?
Options: a ) 2 √ 2 , b ) 2 √ 5 , c ) 6 , d ) 4 √ 2 , e ) none of these
Rationale: "area of sector , a = x / 360 * pi * r ^ 2 circumference of the sector = 24 = > x / 360 * 2 * pi * r + 2 r = 24 = > 2 a / r + 2 r = 24 = > a = r 12 - r ^ 2 = r 12 - r ^ 2 we will now max using derivations max value of a will found at a = 0 i . e 12 - 2 r = 0 r = 6 c"
Answer: c
Python program:
a = 10 + 4 
b = a * 2
c = b / 2
d = c / 2
Problem: the profit earned by selling an article for rs . 832 is equal to the loss incurred when the same article is sold for rs . 448 . what should be the sale price for making 20 % profit ?
Options: a ) 277 , b ) 960 , c ) 277 , d ) 266 , e ) 768
Rationale: "let c . p . = rs . x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 120 % of rs . 640 = 120 / 100 * 640 = rs . 768 . answer : e"
Answer: e
Python program:
a = 832 - 448
b = a / 2
c = 832 - b
d = 20 / 100
e = 1 + d 
f = c * e
Problem: how many positive integers , from 2 to 100 , inclusive , are not divisible by odd integers greater than 1 ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 10 , e ) 50
Rationale: the no will be of the form 2 ^ n to achieve this . since any other form will have odd no in the prime factorization . hence we need to find solution of n for equation - 1 < 2 ^ n < 101 . 2 ^ 6 = 64 , 2 ^ 7 - 128 hence n can take values from 1 to 6 . hence answer : b
Answer: b
Python program:
a = 2 * 2
b = 2 * a
c = 2 * b
d = 2 * c
e = d * 2
f = e - 4
g = f / 10
Problem: a and b finish the job in 15 days . while a , b and c can finish it in 6 days . c alone will finish the job in
Options: a ) 10 days , b ) 30 days , c ) 60 days , d ) 70 days , e ) 50 days
Rationale: "explanation : 6 = ( 15 * x ) / ( 15 + x ) 90 + 6 x = 15 x 9 x = 90 x = 10 answer : option a"
Answer: a
Python program:
a = 6 * 15
b = 15 - 6
c = a / b
Problem: in x game of billiards , x can give y 10 points in 60 and he can give z 30 points in 60 . how many points can y give z in x game of 100 ?
Options: a ) 30 , b ) 20 , c ) 25 , d ) 40 , e ) 50
Rationale: "x scores 60 while y score 50 and z scores 30 . the number of points that z scores when y scores 100 = ( 100 * 30 ) / 50 = 60 . in x game of 100 points , y gives ( 100 - 60 ) = 40 points to c . d"
Answer: d
Python program:
a = 60 - 10
b = a * 3
c = 60 - 30
d = c * 3
e = b - d
Problem: find avrg speed if a man travels at speed of 16 km / hr up and 30 km / hr dawn at an altitude of 200 m .
Options: a ) 22.8 , b ) 21.8 , c ) 20.8 , d ) 28.8 , e ) 29.8
Rationale: "avg speed = 2 * x * y / ( x + y ) = 2 * 16 * 30 / ( 16 + 30 ) = 20.8 answer : c"
Answer: c
Python program:
a = 2 * 16
b = a * 30
c = 16 + 30 
d = b / c
Problem: a can do a work in 16 days and b can do it in 8 days . in how many days a and b can do the work ?
Options: a ) 20 days , b ) 5 1 / 3 days , c ) 6 days , d ) 8 days , e ) 7 days
Rationale: "explanation : a ' s 1 day ' s work = 1 / 16 b ' s 1 day ' s work = 1 / 8 they work together = 1 / 16 + 1 / 8 = 3 / 16 = 16 / 3 = 5 1 / 3 days answer : option b"
Answer: b
Python program:
a = 1 / 8
b = 1 / 16
c = a - b
d = 1 / c
Problem: in a forest 100 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 5 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ?
Options: a ) 150 , b ) 750 , c ) 1,250 , d ) 1,000 , e ) 2,500
Rationale: "the percentage of tagged deer in the second sample = 5 / 50 * 100 = 10 % . so , 100 tagged deers comprise 10 % of total # of deers - - > total # of deers = 100 * 10 = 1,000 . answer : d ."
Answer: d
Python program:
a = 50 * 5
Problem: find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 20 of money ?
Options: a ) 1500 , b ) 1992 , c ) 9921 , d ) 2798 , e ) 2000
Rationale: "p = 20 ( 100 / 10 ) 2 = > p = 2000 answer : e"
Answer: e
Python program:
a = 10 * 2
b = 20 / a
c = b * 100
d = 10 * 2
e = c * d
Problem: a man sold 20 articles for $ 50 and gained 20 % . how many articles should he sell for $ 90 to incur a loss 20 % ?
Options: a ) 45 , b ) 36 , c ) 40 , d ) 54 , e ) 48
Rationale: "production cost per article : $ 50 * ( 100 % - 20 % ) / 20 = $ 2.0 required production costs for a loss of 20 % : $ 90 * ( 100 % + 20 % ) = $ 108 number of articles to be sold for $ 108 to incur a 20 % loss : $ 108 / $ 2.0 = 54 thus , solution d is correct ."
Answer: d
Python program:
a = original_price_before_loss / (
Problem: find the least number must be added to 433124 so that remaining no . is divisible by 17 ?
Options: a ) 3 , b ) 2 , c ) 5 , d ) 6 , e ) 1
Rationale: "on dividing 433124 by 17 we get the remainder 15 , so 2 should be added b"
Answer: b
Python program:
a = 17 - reminder