euclaise/mathqa_programs huggingface dataset:
Problem: due to construction , the speed limit along an 5 - mile section of highway is reduced from 52 miles per hour to 36 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 3.12 , b ) b ) 8 , c ) c ) 10 , d ) d ) 2.57 , e ) e ) 24
Rationale: "old time in minutes to cross 5 miles stretch = 5 * 60 / 52 = 5 * 15 / 13 = 5.76 new time in minutes to cross 5 miles stretch = 5 * 60 / 36 = 5 * 5 / 3 = 8.33 time difference = 2.57 ans : d"
Answer: d
Python program:
a = 52 + 5 
b = a - 1
c = 5 / 36
d = 5 / 52
e = c - d
f = b * e
g = max(f)
Problem: it is currently 7 : 16 pm . at what time in the morning was it exactly 19,443 minutes earlier ?
Options: a ) 7 : 11 , b ) 7 : 13 , c ) 7 : 17 , d ) 7 : 19 , e ) 7 : 21
Rationale: converting 19,443 minutes to hours , we get 19,443 / 60 = 324 r 3 ; that is 324 hours and 3 minutes . all of the answers are during the same hour of the morning , thus the hours can be assumed to bring us into the 7 am hour evenly from 7 : 16 pm . thus 324 hours ago was 7 : 16 am . take an extra 3 minutes off , and it was 7 : 13 am . b
Answer: b
Python program:
a = 16 - 3
b = 7 / a
Problem: 52 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780 . the bigger part is :
Options: a ) 30.33 , b ) 34.44 , c ) 26.1 , d ) 28.0 , e ) 21.0
Rationale: "explanation : let the two parts be ( 52 - x ) and x . then , 10 ( 52 - x ) + 22 x = 780 = > 12 x = 260 = > x = 21.66 . bigger part = ( 52 - x ) = 30.33 . answer : a ) 30.33"
Answer: a
Python program:
a = 52 * 10
b = 780 - a
c = 22 - 10
d = b / c
e = 52 - d
Problem: the price of 2 sarees and 4 shirts is $ 1600 . with the same money one can buy 1 saree and 6 shirts . if one wants to buy 12 shirts , how much shall he have to pay ?
Options: a ) 3800 , b ) 3300 , c ) 2400 , d ) 4200 , e ) 1400
Rationale: c $ 2400 let the price of a saree and a shirt be $ x and $ y respectively . then , 2 x + 4 y = 1600 . . . . ( i ) and x + 6 y = 1600 . . . . ( ii ) divide equation ( i ) by 2 , we get the below equation . = > x + 2 y = 800 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 6 y = 1600 ( - ) x + 2 y = 800 - - - - - - - - - - - - - - - - 4 y = 800 - - - - - - - - - - - - - - - - therefore , y = 200 . now apply value of y in ( iii ) = > x + 2 x 200 = 800 = > x + 400 = 800 therefore x = 400 solving ( i ) and ( ii ) we get x = 400 , y = 200 . cost of 12 shirts = $ ( 12 x 200 ) = $ 2400 .
Answer: c
Python program:
a = 2 * 1600
b = a - 1600
c = 2 * 6
d = c - 4
e = b / d
f = e * 12
Problem: on dividing 271 by a number , the quotient is 9 and the remainder is 1 . find the divisor ?
Options: a ) a ) 12 , b ) b ) 15 , c ) c ) 16 , d ) d ) 17 , e ) e ) 30
Rationale: "d = ( d - r ) / q = ( 271 - 1 ) / 9 = 270 / 9 = 30 e )"
Answer: e
Python program:
a = 271 / 9
b = math.floor(a)
Problem: working alone at their respective constant rates , a can complete a task in ‘ a ’ days and b in ‘ b ’ days . they take turns in doing the task with each working 2 days at a time . if a starts they finish the task in exactly 12 days . if b starts , they take half a day more . how long does it take to complete the task if they both work together ?
Options: a ) 4 , b ) 4.5 , c ) 6 , d ) 8 , e ) 6.5
Rationale: "work done by ab in a day = xy respectively . when a starts : no . of days when a works = 6 no . of days when b works = 6 → 6 x + 6 y = 1 when b starts : no . of days when a works = 6.5 no . of days when b works = 5.5 → 6.5 x + 5.5 y = 1 solving the above two equations for xy x = 1 / 12 y = 1 / 12 → total work done by ab in a day = 1 / 12 + 1 / 12 = 2 / 12 = 1 / 6 → no . of days to complete the work when both work together = 6 answer : c"
Answer: c
Python program:
a = 12 - 1
b = 1/(a)
c = 12 + 2 
d = 1/(c)
e = b + d 
f = 1/(e)
Problem: on dividing a number by 5 , we get 3 as remainder . what will the remainder when the square of the this number is divided by 5 ?
Options: a ) 0 , b ) 5 , c ) 8 , d ) 9 , e ) 4
Rationale: "explanation : let the number be x and on dividing x by 5 , we get k as quotient and 3 as remainder . x = 5 k + 3 x ^ 2 = ( 5 k + 3 ) ^ 2 = ( 25 k ^ 2 + 30 k + 9 ) = 5 ( 5 k ^ 2 + 6 k + 1 ) + 4 on dividing x 2 by 5 , we get 4 as remainder . e )"
Answer: e
Python program:
a = 3 ** 2
b = a / 5
c = 3 ** 2
d = c / 5
e = math.floor(d)
f = b - e
g = f * 5
Problem: find the area of a rhombus one side of which measures 20 cm and one diagonal is 24 cm .
Options: a ) 370 cm 2 , b ) 365 cm 2 , c ) 380 cm 2 , d ) 384 cm 2 , e ) 394 cm 2
Rationale: "explanation : let other diagonal = 2 x cm . since diagonals of a rhombus bisect each other at right angles , we have : ( 20 ) 2 = ( 12 ) 2 + ( x ) 2 = > x = √ ( 20 ) 2 – ( 12 ) 2 = √ 256 = 16 cm . _ i so , other diagonal = 32 cm . area of rhombus = ( 1 / 2 ) x ( product of diagonals ) = ( 1 / 2 × 24 x 32 ) cm 2 = 384 cm 2 answer : option d"
Answer: d
Python program:
a = 1 / 2
b = a * 24
c = 20 * 20
d = c * 4
e = 24 * 24
f = d - e
g = math.sqrt(f)
h = b * g
i = h + 24
Problem: a taxi leaves point a 4 hours after a bus left the same spot . the bus is traveling 30 mph slower than the taxi . find the speed of the taxi , if it overtakes the bus in two hours .
Options: a ) 40 , b ) 42 , c ) 45 , d ) 48 , e ) 49
Rationale: "let the speed of bus be v - 30 , speed of taxi be v the bus travelled a total of 6 hrs and taxi a total of 2 hrs . hence 6 * ( v - 30 ) = 2 v 6 v - 180 = 2 v 4 v = 180 v = 45 mph c"
Answer: c
Python program:
a = 4 * 30
b = 4 * 30
c = a + b 
d = 3 + 0 
e = d - 4
f = c / e
Problem: m and n are the x and y coordinates , respectively , of a point in the coordinate plane . if the points ( m , n ) and ( m + p , n + 15 ) both lie on the line defined by the equation x = ( y / 5 ) - ( 2 / 5 ) , what is the value of p ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "x = ( y / 5 ) - ( 2 / 5 ) , and so y = 5 x + 2 . the slope is 5 . ( n + 15 - n ) / ( m + p - m ) = 5 p = 3 the answer is c ."
Answer: c
Python program:
a = 15 / 5
Problem: in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 7 : 7 : 8 . if the shop carries 330 dogs and bunnies total in stock , how many dogs are there ?
Options: a ) 42 , b ) 66 , c ) 98 , d ) 112 , e ) 154
Rationale: "let us assume the number of dogs , cats and bunnies to be 7 x , 7 x and 8 x total dogs and bunnies = 15 x . and we are given that 15 x = 330 . hence x = 22 . dogs = 7 x = 7 * 22 = 154 ( option e )"
Answer: e
Python program:
a = 7 + 8 
b = 330 / a
c = b * 7
Problem: of the 150 employees at company x , 80 are full - time , and 100 have worked at company x for at least a year . there are 10 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?
Options: a ) 10 , b ) 30 , c ) 50 , d ) 80 , e ) 100
Rationale: "full time employee who have not worked for at least one year = a full time employee who have worked for at least one year = b non full time employee who have worked for at least one year = c non full time employee who have not worked for at least one year = d a + b + c + d = 150 a + b = 80 i . e . c + d = 70 b + c = 100 i . e . a + d = 50 d = 20 i . e . c = 70 - 20 = 50 i . e . b = 100 - 50 = 50 i . e . a = 80 - 50 = 30 b = 10 answer : option a"
Answer: a
Python program:
a = 150 - 80
b = a - 10
Problem: if y is the smallest positive integer such that 7,700 multiplied by y is the square of an integer , then y must be
Options: a ) 29 , b ) 58 , c ) 63 , d ) 74 , e ) 77
Rationale: "7700 = 5 * 5 * 2 * 2 * 7 * 11 , so we need one 7 and one 11 to make it a square of a number . so 7 * 11 = 77 ans : e"
Answer: e
Python program:
a = 2 + 3 
b = a * 2
Problem: a bookstore has a shelf that contains biographies which normally sell for $ 20 each and mysteries that normally sell for $ 12 each . during a sale , the biographies and mysteries are discounted at different rates so that a customer saves a total of $ 19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries . if the sum of the discount rates for the two types of books is 38 percent , what is the discount rate on mysteries ?
Options: a ) 18 % , b ) 29.68 % , c ) 19.68 % , d ) 29 % , e ) 68 %
Rationale: "let b be the discount on biographies and m be the discount on mysteries so . , b + m = 0.38 - - - - - ( 1 ) and ( 20 * 5 + 12 * 3 ) - ( 20 * 5 * ( 1 - b ) + 12 * 3 * ( 1 - m ) ) = 19 - - > 100 ( 1 - ( 1 - b ) ) + 36 ( 1 - ( 1 - m ) = 19 100 b + 36 m = 19 - - - - - - ( 2 ) solving 12 . , we get m = 0.2968 = 29.68 % b"
Answer: b
Python program:
a = 20 * 2
b = 20 + 38 
c = b + 1 
d = a / c
e = 1 - d
f = e * 100
Problem: find the ones digit of 73 ^ 320
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "cyclicity of 3 is 3,9 , 7,1 after 4 multiplication again the cycle repeats . so divide 320 by 4 and we get 87 as quotient and 2 as remainder . so cycle will run for 87 times and then 2 times more . so pick up the 2 nd item from the cycle . hence answer d ."
Answer: d
Python program:
a = 3 + 4 
b = a * 10
c = 73 - b
d = 320 / 4
e = math.floor(d)
f = e * 4
g = 320 - f
h = c ** g
i = 2 * 10
j = h - i
Problem: the ratio of ducks and frogs in a pond is 37 : 39 respectively . the average number of ducks and frogs in the pond is 152 . what is the number of frogs in the pond ?
Options: a ) 148 , b ) 152 , c ) 156 , d ) 144 , e ) none
Rationale: "solution : ratio of ducks and frogs in pond , = 37 : 39 . average of ducks and frogs in pond , = 152 . so , total number of ducks and frogs in the pond , = 2 * 152 = 304 . therefore , number of frogs , = ( 304 * 39 ) / 76 = 156 . answer : option c"
Answer: c
Python program:
a = 37 + 39 
b = a + 2 
c = b / 2
d = 152 / c
e = 39 * d
Problem: the “ connection ” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b . for instance , the smallest common multiple of 8 and 12 is 24 , and the product of 8 and 12 is 96 , so the connection between 8 and 12 is 24 / 96 = 1 / 4 the positive integer y is less than 20 and the connection between y and 6 is equal to 1 / 1 . how many possible values of y are there ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: since “ connection ” between y and 6 is 1 / 1 then lcm ( 6 , y ) = 6 y , which means that 6 and y are co - prime ( they do not share any common factor but 1 ) , because if the had any common factor but 1 then lcm ( 6 , y ) would be less than 6 y . so , we should check how many integers less than 20 are co - prime with 6 , which can be rephrased as how many integers less than 20 are not divisible by 2 or 3 ( 6 = 2 * 3 ) . there are ( 18 - 2 ) / 2 + 1 = 9 multiples of 2 in the range from 0 to 20 , not inclusive ; there are ( 18 - 3 ) / 3 + 1 = 6 multiples of 3 in the range from 0 to 20 , not inclusive ; there are 3 multiples of 6 in the range from 0 to 20 , not inclusive ( 6 , 12 , 18 ) - overlap of the above two sets ; total multiples of 2 or 6 in the range from 0 to 20 , not inclusive is 9 + 6 - 3 = 12 ; total integers in the range from 0 to 20 , not inclusive is 19 ; hence , there are total of 19 - 12 = 7 numbers which have no common factor with 6 other than 1 : 1 , 5 , 7 , 11 , 13 , 17 and 19 . answer : a .
Answer: a
Python program:
a = 20 - 1
b = a - 12
Problem: the probability of two events a and b are 0.15 and 0.40 respectively . the probability that both a and b occur is 0.15 . the probability that neither a nor b occur is _________
Options: a ) 0.45 , b ) 0.4 , c ) 0.5 , d ) 0.05 , e ) 0.6
Rationale: "we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 15 + . 40 - . 15 = . 40 but the probability of neither a nor b = 1 - . 40 = 0.60 answer : e"
Answer: e
Python program:
a = 0 + 15 
b = a - 0
c = 1 - b
Problem: ( 0.8 ) ( power 3 ) - ( 0.5 ) ( power 3 ) / ( 0.8 ) ( power 2 ) + 0.40 + ( 0.5 ) ( power 2 ) is :
Options: a ) 0.6 , b ) 0.5 , c ) 0.35 , d ) 0.3 , e ) none of them
Rationale: "given expression = ( 0.8 ) ( power 3 ) - ( 0.5 ) ( power 3 ) / ( 0.8 ) ( power 2 ) + ( 0.8 x 0.5 ) + ( 0.5 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.8 - 0.5 ) = 0.30 answer is d ."
Answer: d
Python program:
a = 0 ** 8
b = 0 ** 5
c = a - b
d = 0 ** 8
e = d + 0 
f = 0 ** 5
g = e + f 
h = c / g
Problem: if the length of the sides of two cubes are in the ratio 7 : 1 , what is the ratio of their total surface area ?
Options: a ) 7 : 1 , b ) 14 : 1 , c ) 21 : 1 , d ) 42 : 1 , e ) 49 : 1
Rationale: "let x be the length of the small cube ' s side . the total surface area of the small cube is 6 x ^ 2 . the total surface area of the large cube is 6 ( 7 x ) ^ 2 = 294 x ^ 2 . the ratio of surface areas is 49 : 1 . the answer is e ."
Answer: e
Python program:
a = 7 * 7
Problem: when a merchant imported a certain item , she paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 110.60 , what was the total value of the item ?
Options: a ) $ 2160 , b ) $ 2370 , c ) $ 2580 , d ) $ 2790 , e ) $ 2950
Rationale: "let x be the value of the item . 0.07 * ( x - 1000 ) = 110.60 x = 2580 the answer is c ."
Answer: c
Python program:
a = 7 / 100
b = 110 / 60
c = 1 + 0
Problem: eighteen years ago , a father was 3 times as old as his son . now the father is only twice as old his son . then the sum of the present ages of the son and the father is :
Options: a ) 53 , b ) 108 , c ) 77 , d ) 107 , e ) 109
Rationale: explanation : let the present ages of the father and son be 2 x and x years respectively . then , ( 2 x - 18 ) = 3 ( x - 18 ) = > x = 36 required sum = ( 2 x + x ) = 108 years . answer : option d
Answer: d
Python program:
a = 3 + 3 
b = a * 3
c = b * 3
d = 3 + 3 
e = d * 3
f = c - e
g = 3 + 3 
h = g * 3
i = h * 3
j = 3 + 3 
k = j * 3
l = i - k
m = l * 2
n = f + m
Problem: how many pieces can a square pizza be cut into by making 5 linear cuts ?
Options: a ) 16 , b ) 17 , c ) 13 , d ) 14 , e ) 15
Rationale: "1 cut can make 2 pieces a second cut can make 4 pieces by cutting through 2 pieces a third cut can make 7 pieces by cutting through 3 of the pieces a fourth cut can make 11 pieces by cutting through 4 of the pieces a fifth cut can make 16 pieces by cutting through 5 of the pieces a"
Answer: a
Python program:
a = 5 * 3
b = a - 1
Problem: the area of a parallelogram is 128 sq m . then the area of a triangle formed by its diagonal is - - - - - - - - - - ?
Options: a ) 128 m
b ) 64 m
c ) 64 m ^ 2
d ) 128 m ^ 2
e ) none
Rationale: b * h / 2 = 128 / 2 = 64 m . ans : ( b )
Answer: b
Python program:
a = 128 / 2
Problem: a person crosses a 1080 m long street in 14 minutes . what is his speed in km per hour ?
Options: a ) 4.1 , b ) 4.5 , c ) 4.6 , d ) 5.4 , e ) 5.5
Rationale: "speed = 1080 / ( 12 x 60 ) m / sec = 1.3 m / sec . converting m / sec to km / hr = 1.3 x ( 18 / 5 ) km / hr = 4.6 km / hr . answer : c"
Answer: c
Python program:
a = 1080 / 1000
b = 14 * const_60
c = b / 3600
d = a / c
Problem: if x is a prime number , and x - 1 is the median of the set { x - 1 , 3 x + 3 , 2 x - 4 } , then what is the average ( arithmetic mean ) of the set ?
Options: a ) 2 , b ) 5 / 3 , c ) 3 , d ) 10 / 3 , e ) 14 / 3
Rationale: if x is a prime number , and x - 1 is the median of the set { x - 1 , 3 x + 3 , 2 x - 4 } , then what is the average ( arithmetic mean ) of the set ? a . 2 b . 5 / 3 c . 3 d . 10 / 3 e . 14 / 3 solution : x - 1 is the median of the set , implies if we arrange the set in ascending order , the set would be [ 2 x - 4 , x - 1 , 3 x + 3 ] . this means that : 2 x - 4 < x - 2 < 3 x + 3 solving inequality gives x > - 2 and x < 3 . since x is prime number and the only prime number < 3 is 2 , so put x = 2 . hence set becomes : [ 0 , 1 , 9 ] and avg = 10 / 3 . d
Answer: d
Python program:
a = 3 * 2
b = a + 3 
c = 2 - 1
d = b + c 
e = d / 3
Problem: the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score .
Options: a ) 179 , b ) 208 , c ) 210 , d ) 223 , e ) 229
Rationale: "explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 – 2552 = 208 runs . let the highest score be x , hence the lowest score = x – 150 x + ( x - 150 ) = 208 2 x = 358 x = 179 runs answer a"
Answer: a
Python program:
a = 60 * 46
b = 46 - 2
c = 58 * b
d = a - c
e = 150 + d 
f = e / 2
Problem: the sector of a circle has radius of 21 cm and central angle 135 o . find its perimeter ?
Options: a ) 91.5 cm , b ) 92.2 cm , c ) 28.9 cm , d ) 29.2 cm , e ) 98.2 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 49.5 + 42 = 91.5 cm answer : a"
Answer: a
Python program:
a = 21 - 3
b = a * 2
c = 4 + 3 
d = b / c
e = 2 * d
f = e * 21
Problem: 8.008 / 1.001
Options: a ) 0.008 , b ) 8 , c ) 0.8 , d ) 80 , e ) 800
Rationale: "answer is 8 , move the decimal forward three places for both numerator and denominator or just multiply both by a thousand . the result is 8008 / 1001 = 8 answer b"
Answer: b
Python program:
a = 8 / 8
b = a * 100
Problem: the radius of a semicircle is 7 . what is the approximate perimeter of the semicircle ?
Options: a ) 36
b ) 25
c ) 15
d ) 28
e ) 37
Rationale: perimeter of a circle = 2 pi * r perimeter of a semicircle = pi * r + 2 r aprox perimiter = 3.14 * 7 + 2 * 7 = 35.98 approximately 36 answer a
Answer: a
Python program:
a = circumface / (
b = a + 2
Problem: a train consists of 12 boggies , each boggy 15 metres long . the train crosses a telegraph post in 18 seconds . due to some problem , one boggies were detached . the train now crosses a telegraph post in
Options: a ) 16.5 sec , b ) 12 sec , c ) 15 sec , d ) 20 sec , e ) none of these
Rationale: length of train = 12 ã — 15 = 180 m . then , speed of train = 180 â  „ 18 = 10 m / s now , length of train = 11 ã — 15 = 165 m â ˆ ´ required time = 165 â  „ 10 = 16.5 sec . answer a
Answer: a
Python program:
a = 12 * 15
b = a - 15
c = 12 * 15
d = c / 18
e = b / d
Problem: if a sum of money doubles itself in 8 years at simple interest , the ratepercent per annum is
Options: a ) 12 , b ) 12.5 , c ) 13 , d ) 13.5 , e ) 14
Rationale: explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 8 ) = 12.5 option b
Answer: b
Python program:
a = 8 / 100
b = 2 / a
c = b / 2
Problem: natasha climbs up a hill , and descends along the same way she went up . it takes her 4 hours to reach the top and 2 hours to come back down . if her average speed along the whole journey is 2 kilometers per hour , what was her average speed ( in kilometers per hour ) while climbing to the top ?
Options: a ) 1.5 , b ) 2.5 , c ) 3.75 , d ) 5 , e ) 7.5
Rationale: "let the distance to the top be x , so the total distance traveled by natasha is 2 x . the total time is 4 + 2 = 6 hours the average speed = total distance / total time taken = 2 x / 6 = x / 3 the average speed of the complete journey is 2 km / hour x / 3 = 2 x = 6 km the average speed while climbing = distance / time = 6 / 4 = 1.5 km / h the answer is a ."
Answer: a
Python program:
a = 4 + 2 
b = a * 2
c = b / 2
d = c / 4
Problem: the average ( arithmetic mean ) of 4 positive integers is 30 . if the average of 2 of these integers is 15 , what is the greatest possible value that one of the other 2 integers can have ?
Options: a ) 55 , b ) 89 , c ) 100 , d ) 109 , e ) 115
Rationale: "a + b + c + d = 120 a + b = 30 c + d = 90 greatest possible = 89 ( just less than 1 ) answer = b"
Answer: b
Python program:
a = 30 * 4
b = 15 * 2
c = a - b
Problem: carol spends 1 / 4 of her savings on a stereo and 1 / 3 less than she spent on the stereo for a television . what fraction of her savings did she spend on the stereo and television ?
Options: a ) 1 / 4 , b ) 2 / 7 , c ) 5 / 12 , d ) 1 / 2 , e ) 7 / 12
Rationale: "total savings = s amount spent on stereo = ( 1 / 4 ) s amount spent on television = ( 1 - 1 / 3 ) ( 1 / 4 ) s = ( 2 / 3 ) * ( 1 / 4 ) * s = ( 1 / 6 ) s ( stereo + tv ) / total savings = s ( 1 / 4 + 1 / 6 ) / s = 5 / 12 answer : c"
Answer: c
Python program:
a = 1 / 4
Problem: jancy had 100 currency notes in all , some of which are of rs 70 denomination and the remaining of rs 50 denomination . the total amount of all these currency notes was rs . 5000 . how much amount ( in rs ) did she have in the denomination of rs 50 ?
Options: a ) 103 , b ) 102 , c ) 100 , d ) 105 , e ) 106
Rationale: let the number of 50 - rupee notes = x then , the number of 70 - rupee notes = ( 100 – x ) 50 x + 70 ( 100 – x ) = 5000 : x = 100 answer : c
Answer: c
Python program:
a = 5000 / 50
Problem: a line that passes through ( – 1 , – 4 ) and ( 4 , k ) has a slope = k . what is the value of k ?
Options: a ) 3 / 4 , b ) 1 , c ) 4 / 3 , d ) 2 , e ) 7 / 2
Rationale: "slope = ( y 2 - y 1 ) / ( x 2 - x 1 ) = > k = ( k + 4 ) / ( 4 + 1 ) = > 5 k = k + 4 = > k = 1 ans b it is !"
Answer: b
Python program:
a = 4 / 4
Problem: a man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses . next year his income increases by 25 % but his savings increase by 100 % . if his total expenditure in 2 years is double his expenditure in 1 st year , what % age of his income in the first year did he save ?
Options: a ) 20 % , b ) 25 % , c ) 28.5 % , d ) 30 % , e ) 32 %
Rationale: "1 st year income = i 1 st year savings = s 1 st year expense = e 1 2 nd year income = 1.25 i 2 nd year savings = 2 s ( 100 % increase ) 2 nd year expense = e 2 e 1 + e 2 = 2 e 1 e 2 = e 1 that means expenses are same during both years . with increase of 25 % income the savings increased by 100 % . or s = . 25 i or s = 25 % of income b is the answer"
Answer: b
Python program:
a = 100 + 25 
b = a + 100 
c = 2 * 100
d = b - c
e = d / 100
f = e * 100
Problem: the contents of a certain box consist of 24 apples and 30 kiwis . how many kiwis must be added to the box so that exactly 30 % of the pieces of fruit in the box will be apples ?
Options: a ) 24 , b ) 26 , c ) 30 , d ) 46 , e ) 50
Rationale: "apples = ( apples + kiwi + x ) * 0.3 24 = ( 30 + 24 + x ) * 0.3 x = 26 . answer : b ."
Answer: b
Python program:
a = 24 + 30 
b = 30 / 100
c = 24 / b
d = a - c
Problem: p and q can complete a work in 80 days and 48 days respectively . p alone started the work and q joined him after 16 days till the completion of the work . how long did the work last ?
Options: a ) 5 days , b ) 10 days , c ) 14 days , d ) 22 days , e ) 40 days
Rationale: explanation : work done by p in 1 day = 1 / 80 work done by q in 1 day = 1 / 48 work done by p in 16 days = 16 ã — ( 1 / 80 ) = 1 / 5 remaining work = 1 â € “ 1 / 5 = 4 / 5 work done by p and q in 1 day = 1 / 80 + 1 / 48 = 1 / 30 number of days p and q take to complete the remaining work = ( 4 / 5 ) / ( 1 / 30 ) = 24 total days = 16 + 24 = 40 answer : option e
Answer: e
Python program:
a = 16 / 80
b = 1 - a
c = 1/(80)
d = 1/(48)
e = c + d 
f = b / e
g = 16 + f
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 16 hours respectively . the ratio of their speeds is
Options: a ) 4 : 9 , b ) 4 : 3 , c ) 4 : 12 , d ) 4 : 8 , e ) 4 : 5
Rationale: "let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = b : a = 16 : 9 = 4 : 3 . answer : b"
Answer: b
Python program:
a = math.sqrt(16)
b = math.sqrt(9)
c = a / b