euclaise/mathqa_programs huggingface dataset:
Problem: the rate of interest on a sum of money is 8 % p . a . for the first 3 years , 4 % p . a . for the next 4 years , and 5 % for the period beyond 7 years . if the s . i , occured on the sum for the total period of 8 years is rs . 540 / - , the sum is
Options: a ) 1,200 , b ) 2,000 , c ) 2,100 , d ) 2,250 , e ) 2,540
Rationale: explanation : i 1 = ( p x 3 x 8 ) / 100 = 6 p / 25 i 2 = ( p x 4 x 4 ) / 100 = 4 p / 25 i 3 = ( p x 1 x 5 ) / 100 = p / 20 6 p / 25 + 4 p / 25 + p / 20 = 540 9 p / 20 = 540 p = 1200 answer : option a
Answer: a
Python program:
a = 540 / 540
Problem: a team of 8 persons joins in a shooting competition . the best marksman scored 85 points . if he had scored 92 points , the average score for the team would have been 84 . the number of points , the team scored was
Options: a ) 665 , b ) 127 , c ) 272 , d ) 287 , e ) 227
Rationale: "let the total score be x . ( x + 92 - 85 ) / 8 = 84 . so , x + 7 = 672 = > x = 665 . answer : a"
Answer: a
Python program:
a = 84 * 8
b = a + 85 
c = b - 92
Problem: if tim had lunch at $ 50.50 and he gave 15 % tip , how much did he spend ?
Options: a ) $ 58 , b ) $ 60.60 , c ) $ 70.60 , d ) $ 40.60 , e ) $ 50.60
Rationale: "the tip is 20 % of what he paid for lunch . hence tip = 15 % of 50.50 = ( 15 / 100 ) * 50.50 = $ 7.575 total spent 50.50 + 7.575 = $ 58 correct answer a"
Answer: a
Python program:
a = 50 * 50
b = a / 100
c = 50 + 50
Problem: if the numbers 1 to 98 are written on 98 pieces of paper , ( one on each ) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ?
Options: a ) 1 / 50 , b ) 1 / 25 , c ) 1 / 98 , d ) 1 , e ) 2
Rationale: "there are 25 primes , 72 composite numbers from 1 to 98 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 98 . answer : c"
Answer: c
Python program:
a = 1 / 98
Problem: if ( x + 3 ) ^ 2 / ( 3 x + 65 ) = 2 , then the difference between the two possible values of x is :
Options: a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "( x + 3 ) ^ 2 / ( 3 x + 65 ) = 2 ( x + 3 ) ^ 2 = 2 ( 3 x + 65 ) x ^ 2 + 6 x + 9 = 6 x + 130 x ^ 2 - 121 = 0 ( x - 11 ) ( x + 11 ) = 0 x = 11 or x = - 11 the answer is d ."
Answer: d
Python program:
a = 65 * 3
b = 3 * 3
c = a - b
d = math.sqrt(c)
e = d * 2
Problem: if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 70 ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 17
Rationale: "four wheeler = 17 * 4 = 68 ( max ) 2 wheel = 1 so no of 4 wheeler = 17 answer : e"
Answer: e
Python program:
a = 70 - 2
b = a / 4
Problem: on a purchase of $ 112 , a store offered a payment plan consisting of a $ 12 down payment and 12 monthly payments of $ 10 each . what percent of the purchase price , to the nearest tenth of a percent , did the customer pay in interest by using this plan ?
Options: a ) 10.7 % , b ) 11.7 % , c ) 12.7 % , d ) 13.7 % , e ) 14.7 %
Rationale: "12 * 10 + 12 = 132 ( 12 / 112 ) * 100 = 10.7 answer : a"
Answer: a
Python program:
a = 10 * 12
b = a + 12 
c = 10 * 12
d = b - c
e = d / 112
f = e * 100
Problem: john bought 9.25 m of cloth for $ 425.50 . find the cost price per metre .
Options: a ) 46 , b ) 47 , c ) 58 , d ) 56 , e ) 54
Rationale: cloth bought by john = 9.25 m cost of 9.25 m = $ 425.50 cost per metre = 425.50 ÷ 9.25 the cost of the cloth per metre = $ 46 answers : a
Answer: a
Python program:
a = 425 / 5
Problem: a dog is tied to a tree by a long nylon cord . if the dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all items , and the dog ran approximately 30 feet , what was the approximate length of the nylon cord e , in feet ?
Options: a ) 30 , b ) 25 , c ) 15 , d ) 10 , e ) 5
Rationale: "because the cord was extended to its full length at all items , the dog ran along a semi - circular path , from north to south . the circumference of a full circle is 2 * pi * r , but since we only care about the length of half the circle , the semi - circle path is pi * r . e = pi * r = 30 . round pi = 3 , then r = 10 . chord is about 10 feet long . d"
Answer: d
Python program:
a = 30 / 3
Problem: a can go round a circular path 8 times in 40 minutes . if the diameter of the circle is increased to 10 times the original diameter , then the time required by a to go round the new path once , travelling at the same speed as before is
Options: a ) 20 min , b ) 35 min , c ) 50 min , d ) 70 min , e ) none
Rationale: solution let original diameter be d metres . then , its circumference = ( π d ) metres . time taken to cover ( 8 π d ) m = 40 min . new diameter = ( 10 d ) m . then , its circumference = ( π x 10 d ) m . time taken to go round it once ‹ = › [ 40 / 8 π d x 10 π d ] m ‹ = › 50 min . answer c
Answer: c
Python program:
a = 40 * 10
b = a / 8
Problem: find compound interest on rs . 8000 at 15 % per annum for 2 years 4 months , compounded annually .
Options: a ) rs 400 , b ) rs 300 , c ) rs 3109 , d ) rs 250 , e ) rs 400
Rationale: "time = 2 years 4 months = 2 ( 4 / 12 ) years = 2 ( 1 / 3 ) years . amount = rs ' . [ 8000 x ( 1 + ¬ ( 15 / 100 ) ) 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = rs . [ 8000 * ( 23 / 20 ) * ( 23 / 20 ) * ( 21 / 20 ) ] = rs . 11109 . . : . c . i . = rs . ( 11109 - 8000 ) = rs . 3109 . answer c rs 3109"
Answer: c
Python program:
a = 8000 * 15
b = a / 100
c = 8000 + b 
d = 8000 * 15
e = d / 100
f = 8000 + e 
g = f * 15
h = g / 100
i = c + h 
j = i - 8000
Problem: x is the product of each integer from 1 to 75 , inclusive and y = 100 ^ k , where k is an integer . what is the greatest value of k for which y is a factor of x ?
Options: a ) 8 , b ) 7 , c ) 6 , d ) 9 , e ) 10
Rationale: "the number of trailing zeros in the decimal representation of n ! , the factorial of a non - negative integer n , can be determined with this formula : n 5 + n 52 + n 53 + . . . + n 5 k , where k must be chosen such that 5 k ≤ n x = 1 * 2 * 3 . . . . * 75 = 50 ! no . of trailing zeros in 75 ! = 75 / 5 + 75 / 5 ^ 2 = 15 + 3 = 18 100 ^ k = 10 ^ 2 k → k = 18 / 2 = 9 d"
Answer: d
Python program:
a = 75 / 10
b = a + 1
Problem: a will was written such that an estate would be divided among 3 guys with the remainder donated to charity . one stipulation in the will is that no one from the guys can receive an amount within 30 % of another ' s amount . if one of the guys received $ 20000 , what is the smallest possible range between the highest and lowest amounts ( rounded to the nearest dollar ) among the 3 guys ?
Options: a ) $ 4096 , b ) $ 5904 , c ) $ 7892 , d ) $ 10052 , e ) $ 20736
Rationale: 1 st - 20000 . 2 nd - 0.7 * 20000 = 14000 3 rd - 0.7 * 14000 = 9800 range = 20000 - 9800 = 10200 . answer : d .
Answer: d
Python program:
a = 20000 / 2
Problem: find 40 % of 440
Options: a ) 96 , b ) 94 , c ) 86 , d ) 176 , e ) 110
Rationale: "we know that r % of m is equal to r / 100 × m . so , we have 40 % of 440 40 / 100 × 440 = 176 answer : d"
Answer: d
Python program:
a = 40 / 440
Problem: in a class of 20 students , 2 students did not borrow any books from the library , 8 students each borrowed 1 book , 5 students each borrowed 2 books , and the rest of the students each borrowed at least 3 books . if the average ( arithmetic mean ) number of books borrowed per student was 2 , what is the maximum number of books that any single student could have borrowed ?
Options: a ) 3 , b ) 5 , c ) 10 , d ) 13 , e ) 15
Rationale: "the average number of books per student was 2 means that total of 2 * 20 = 40 books were borrowed ; 2 + 8 + 5 = 15 students borrowed total of 2 * 0 + 8 * 1 + 5 * 2 = 18 books ; so 40 - 18 = 22 books are left to distribute among 20 - 15 = 5 students , these 5 arethe rest who borrowed at least 3 books ; tomaximizethe number of books one student from above 5 could have borrowed we shouldminimizethe number of books other 4 students from 5 could have borrowed . minimum these 4 students could have borrowed is 3 books per student , so total number of books they could have borrowed is 4 * 3 = 12 books . so the 5 th student could have borrowed is 22 - 12 = 10 books . answer : c ."
Answer: c
Python program:
a = 20 * 2
b = 5 * 2
c = 8 + b 
d = 2 * 3
e = c + d 
f = a - e
g = f + 3
Problem: mukesh borrowed a sum of rs . 10000 at simple interest from a bank . after two years he takes rs . 12000 more as loan and discharge all the debt at the end of next 3 years depositing rs . 27160 to the bank . what is the rate of interest per annum ?
Options: a ) 5 % , b ) 6 % , c ) 8 % , d ) 10 % , e ) none of these
Rationale: si = 27160 - ( principal amount ) = 27160 - 22000 = 5160 . now , ( 10000 * 5 * r / 100 ) + ( 12000 * 3 * r / 100 ) = 5160 . 500 r + 360 r = 5160 . . . . . rate = 6 % . answer : b
Answer: b
Python program:
a = 10000 + 12000 
b = 27160 - a
c = 3 + 2 
d = 10000 * c
e = 12000 * 3
f = d + e 
g = b / f
h = g * 100
Problem: a player holds 13 cards of 4 suits , of which 7 are black and 6 are red . there are twice as many diamonds as spades and twice as many hearts as diamonds . how many clubs does he hold
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: explanation : clearly , the black cards are either clubs or spades while the red cards are either diamonds or hearts . let the number of spades be x . then , number of clubs = ( 7 - x ) . number of diamonds = 2 x number of spades = 2 x ; number of hearts = 2 x number of diamonds = 4 x . total number of cards = x + 2 x + 4 x + 7 - x = 6 x + 7 . therefore 6 x + 7 = 13 6 x = 6 x - 1 . hence , number of clubs = ( 7 - x ) = 6 . answer : c
Answer: c
Python program:
a = 13 - 7
b = 4 + 2 
c = a / b
d = 7 - c
Problem: a worker can load one truck in 6 hours . a second worker can load the same truck in 8 hours . if both workers load one truck simultaneously while maintaining their constant rates , approximately how long , in hours , will it take them to fill one truck ?
Options: a ) 2.6 , b ) 2.8 , c ) 3.0 , d ) 3.2 , e ) 3.4
Rationale: "the workers fill the truck at a rate of 1 / 6 + 1 / 8 = 14 / 48 = 7 / 24 of the truck per hour . then the time to fill one truck is 24 / 7 which is about 3.4 hours . the answer is e ."
Answer: e
Python program:
a = 1 / 6
b = 1 / 8
c = a + b 
d = 1/(c)
Problem: here is a simple arithmetical puzzle in his own flowery , poetical language . if one - fifth of a hive of bees flew to the badamba flower , one - third flew to the slandbara , 3 times the difference of these two numbers flew to an arbour , and one bee continued to fly about , attracted on each side by the fragrant ketaki and malati , what was the total number of bees ?
Options: a ) 11 , b ) 15 , c ) 18 , d ) 17 , e ) 19
Rationale: b 15 the number of bees was 15
Answer: b
Python program:
a = 1 + 4 
b = 1 / a
c = 1 / 3
d = b + c 
e = 1 / 3
f = 1 + 4 
g = 1 / f
h = e - g
i = h * 3
j = d + i 
k = 1 - j
l = 1 / k
Problem: if the digits 35 in the decimal 0.00035 repeat indefinitely , what is the value of ( 10 ^ 5 - 10 ^ 3 ) ( 0.00035 ) ?
Options: a ) 37 , b ) 41 , c ) 3.5 e - 05 , d ) 35 , e ) 3.5 e - 07
Rationale: "99 * 0.35 = 34.65 approx . 35 answer : b"
Answer: b
Python program:
a = 10 * 10
b = 10 * 10
c = b - 1
d = a * c
e = 10 * 10
f = e - 1
g = 35 / f
h = d * g
i = h / 1000
j = i * 10
Problem: product of two co - prime numbers is 117 . their l . c . m should be
Options: a ) 222 , b ) 117 , c ) 278 , d ) 767 , e ) 298
Rationale: h . c . f of co - prime numbers is 1 . so , l . c . m = \ inline \ fn _ jvn \ frac { 117 } { 1 } = 117 answer : b
Answer: b
Python program:
a = 117 * 1
Problem: if to a certain number , 720 be added , and the sum be divided by 125 ; the quotient will be equal to 7392 divided by 462 . what is that number ?
Options: a ) 1280 , b ) 1270 , c ) 1260 , d ) 1250 , e ) none
Rationale: solution let x = the number required . a = 720 d = 7392 b = 125 h = 462 then by the conditions of the problem ( x + a ) / b = d / h therefore x = ( bd - ah ) / h restoring the numbers , x = [ ( 125.7392 ) - ( 720.462 ) ] / 462 = 1280 . answer a
Answer: a
Python program:
a = 125 * 7392
b = 462 * 720
c = a - b
d = c / 462
Problem: 10 women can complete a work in 9 days and 10 children take 12 days to complete the work . how many days will 6 women and 7 children take to complete the work ?
Options: a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 2
Rationale: "1 women ' s 1 day work = 1 / 90 1 child ' s 1 day work = 1 / 120 ( 6 women + 7 children ) ' s 1 day work = ( 6 / 90 + 7 / 120 ) = 1 / 8 6 women and 7 children will complete the work in 8 days . d"
Answer: d
Python program:
a = 10 * 9
b = 6 / a
c = 10 * 12
d = 10 / c
e = b + d 
f = 1/(e)
Problem: a cricket player whose bowling average was 22.5 runs per wicket , takes 5 wicket for 52 runs in a match . due to this his average decreases by 0.5 . what will be the number of wickets taken by him till the last match ?
Options: a ) 64 , b ) 72 , c ) 121 , d ) 984 , e ) 108
Rationale: average = total runs / total wickets total runs after last match = 22.5 w + 52 total wickets after last match = w + 5 ( 22.5 w + 52 ) / ( w + 5 ) = 22.5 - 0.5 = 22 w = 116 so total wickets aftr last match = w + 5 = 121 answer : c
Answer: c
Python program:
a = 22 - 5
b = a * 5
c = b - 52
d = c / 0
Problem: the radius of the wheel of a bus is 35 cms and the speed of the bus is 66 km / h , then the r . p . m . ( revolutions per minutes ) of the wheel is
Options: a ) 200 , b ) 250 , c ) 300 , d ) 500 , e ) none of these
Rationale: radius of the wheel of bus = 35 cm . then , circumference of wheel = 2 ï € r = 70 ï € = 220 cm distance covered by bus in 1 minute = 66 â  „ 60 ã — 1000 ã — 100 cms distance covered by one revolution of wheel = circumference of wheel = 220 cm â ˆ ´ revolutions per minute = 6600000 / 60 ã — 220 = 500 answer d
Answer: d
Python program:
a = 1000 * 66
b = 100 * a
c = const_60 * 1
d = b / c
e = 2 * 35
f = 3 * 4
g = 2 + f 
h = 4 * 2
i = 2 + h 
j = i ** 2
k = g / j
l = 3 + k 
m = e * l
n = d / m
Problem: a furniture manufacturer has two machines , but only one can be used at a time . machine e is utilized during the first shift and machine b during the second shift , while both work half of the third shift . if machine e can do the job in 12 days working two shifts and machine b can do the job in 15 days working two shifts , how many days will it take to do the job with the current work schedule ?
Options: a ) 14 , b ) 13 , c ) 11 , d ) 9 , e ) 7
Rationale: machine e finish the job in 2 * 12 shifts = 24 shifts machine b finish the job in 2 * 15 shifts = 30 shifts lets assume total work require 120 shifts therefore , rate of e = 5 shifts / day rate of b = 4 shifts / day rate of ( e + b ) = 9 shifts / day according to current schedule work complete in a day = 5 + 4 + ( 9 / 2 ) = 13.5 shifts / day therefore , time required to finish 120 shifts = ( 120 / 13.5 ) = 8.88 . . days ~ 9 days = d
Answer: d
Python program:
a = 12 * 2
b = 1 / a
c = 12 * 2
d = 1 / c
e = d / 2
f = b + e 
g = 15 * 2
h = 1 / g
i = f + h 
j = 15 * 2
k = 1 / j
l = k / 2
m = i + l 
n = 1/(m)
Problem: a train 110 m long is running with a speed of 84 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 7 sec , b ) 6 sec , c ) 8 sec , d ) 4.4 sec , e ) 2 sec
Rationale: "speed of train relative to man = 84 + 6 = 90 km / hr . = 90 * 5 / 18 = 25 m / sec . time taken to pass the men = 110 / 25 = 4.4 sec . answer : d"
Answer: d
Python program:
a = 84 + 6 
b = a * const_0_2778
c = 110 / b
Problem: a certain debt will be paid in 52 installments from january 1 to december 31 of a certain year . each of the first 25 payments is to be $ 500 ; each of the remaining payments is to be $ 100 more than each of the first 25 payments . what is the average ( arithmetic mean ) payment that will be made on the debt for the year ?
Options: a ) 500 , b ) 450 , c ) 552 , d ) 600 , e ) 400
Rationale: "total = 500 ( 25 ) + 600 ( 27 ) number of installments = 52 average = total / number of installments = 552 approximately answer : c"
Answer: c
Python program:
a = 25 * 500
b = 500 + 100 
c = 52 - 25
d = b * c
e = a + d 
f = e / 52
Problem: there are 6 fictions and 6 non - fictions . how many cases are there such that 2 fictions and 2 non - fictions are selected from them ?
Options: a ) 90 , b ) 120 , c ) 225 , d ) 180 , e ) 200
Rationale: "number of ways of selecting 2 fiction books = 6 c 2 number of ways of selecting 2 non fiction books = 6 c 2 6 c 2 * 6 c 2 = 15 * 15 = 225 answer : c"
Answer: c
Python program:
a = 6 * 4
b = 6 * 6
c = a * b
d = math.factorial(2)
e = d ** 2
f = c / e
Problem: a certain school implemented a reading program for its students , with the goal of getting each student to read 4 books per month year - round . if the school has c classes made up of s students in each class , how many books will the entire student body read in one year ?
Options: a ) 20 cs , b ) cs / 2 , c ) 48 cs , d ) ( 2 cs ) / 12 , e ) ( 24 c ) / s
Rationale: "ans : c solution : simple multiplication s students , c classes , 4 books / month = 48 books a year total number of books = 48 cs"
Answer: c
Python program:
a = 4 * 12
Problem: in a certain quiz that consists of 10 questions , each question after the first is worth 4 points more than the preceding question . if the 10 questions on the quiz are worth a total of 340 points , how many points is the third question worth ?
Options: a ) 39 , b ) 24 , c ) 28 , d ) 26 , e ) 30
Rationale: "x x + 4 x + 8 x + 12 x + 16 x + 20 x + 24 x + 28 x + 32 x + 36 10 x + 180 = 340 10 x = 160 x = 16 3 rd question = x + 8 = 16 + 8 = 24 answer b"
Answer: b
Python program:
a = 340 / 10
b = 10 - 4
c = b - 1
d = a + c
Problem: how many natural numbers are there between 43 and 200 which are exactly divisible by 6 ?
Options: a ) 26 , b ) 25 , c ) 24 , d ) 22 , e ) 23
Rationale: "43 / 6 = 7 , remainder = 1 . hence 5 more should be added to 43 to get the minimum number divisible by 6 between 43 and 200 . = > minimum number divisible by 6 between 43 and 200 = 43 + 5 = 48 200 / 6 = 33 , remainder = 2 . hence 2 should be decreased from 200 to get the maximum number divisible by 6 between 43 and 200 . = > maximum number divisible by 6 between 43 and 200 = 200 - 2 = 198 hence , natural numbers numbers divisible by 6 between 43 and 200 are 48 , 54 , 60 , . . . 198 this is arithmetic progression with a = 48 , d = 6 , l = 198 number of terms = ( l − a ) / d + 1 = ( 198 − 48 ) / 6 + 1 = 150 / 6 + 1 = 25 + 1 = 26 answer is a"
Answer: a
Python program:
a = 200 - 4
b = 43 + 1 
c = a - b
d = c / 6
e = d + 1
Problem: right triangle pqr is to be constructed in the xy - plane so that the right angle is at p and pr is parallel to the x - axis . the x - and y - coordinates of p , q , and r are to be integers that satisfy the inequalities - 4 < = x < = 5 and 6 < = y < = 16 . how many different triangles with these properties could be constructed ?
Options: a ) 110 , b ) 1,100 , c ) 9,900 , d ) 10,000 , e ) 12,100
Rationale: "p can take a total of 10 * 11 co - ordinates . for a given p , r can take a total of 9 co - ordinates and q can take a total of 10 co - ordinates . hence , total = 110 * 9 * 10 = 9900 ans : c"
Answer: c
Python program:
a = 10 - 1
b = 6 + 4 
c = 16 - 5
d = b * c
e = a * d
f = e * 10
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 160 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 ) = 160 = > 5 x = 220 = > x = 44 answer : e"
Answer: e
Python program:
a = 160 + 60 
b = 4 + 1 
c = a / b
Problem: in the coordinate plane , points ( x , 1 ) and ( 18 , y ) are on line k . if line k passes through the origin and has slope 1 / 2 , then x + y =
Options: a ) 4.5 , b ) 7 , c ) 8 , d ) 11 , e ) 12
Rationale: "line k passes through the origin and has slope 1 / 2 means that its equation is y = 1 / 2 * x . thus : ( x , 1 ) = ( 2 , 1 ) and ( 18 , y ) = ( 18,9 ) - - > x + y = 2 + 9 = 11 . answer : d ."
Answer: d
Python program:
a = 18 * 2
b = 1 / 2
c = a * b
Problem: find the simple interest on $ 1200 for 5 years at 20 % per annum ?
Options: a ) $ 1200 , b ) $ 1000 , c ) $ 500 , d ) $ 1100 , e ) $ 1500
Rationale: "si = ptr / 100 = 1200 * 5 * 20 / 100 = $ 1200 answer is a"
Answer: a
Python program:
a = 5 / 100
b = 1200 * a
Problem: a batsman makes a score of 50 runs in the 17 th inning and thus increases his averages by 2 . what is his average after 17 th inning ?
Options: a ) 39 , b ) 18 , c ) 42 , d ) 40.5 , e ) 41.5
Rationale: "let the average after 16 th inning = x then total run after 16 th inning = 16 x then total run after 17 th inning = 16 x + 50 then average run after 17 th inning = ( 16 x + 50 ) / 17 ( 16 x + 50 ) / 17 = x + 2 = > 16 x + 50 = 17 x + 34 = > x = 16 x = 16 ; average after 17 th inning = 16 + 2 = 18 answer : b"
Answer: b
Python program:
a = 17 * 2
b = 50 - a
c = b + 2
Problem: to produce an annual income of rs . 800 from a 8 % stock at 90 , what is the amount of stock needed ?
Options: a ) 10000 , b ) 11000 , c ) 12000 , d ) 13000 , e ) 14000
Rationale: "since face value is not given , take it as rs . 100 . as it is an 8 % stock , income ( dividend ) per stock = rs . 8 ie , for an income of rs . 8 , amount of stock needed = rs . 100 for an income of rs . 800 , amount of stock needed = 100 × 800 / 8 = 10000 answer is a ."
Answer: a
Python program:
a = 100 - 90
Problem: ramu bought an old car for rs . 40000 . he spent rs . 13000 on repairs and sold it for rs . 64900 . what is his profit percent ?
Options: a ) a ) 14 % , b ) b ) 16 % , c ) c ) 18 % , d ) d ) 21.6 % , e ) of these
Rationale: "total cp = rs . 40000 + rs . 13000 = rs . 53000 and sp = rs . 64900 profit ( % ) = ( 64900 - 53000 ) / 55000 * 100 = 21.6 % answer : d"
Answer: d
Python program:
a = 40000 + 13000 
b = 64900 - a
c = 40000 + 13000 
d = b / c
e = d * 100
Problem: on a map , 1.5 inches represent 24 miles . how many miles approximately is the distance if you measured 44 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 174.2 , b ) 277 , c ) 288.1 , d ) 296 , e ) 282.4
Rationale: "1.5 inch = 2.54 * 1.5 cm . so , 2.54 * 1.5 represents 24 miles . so for 44 cm . : 44 / ( 2.54 * 1.5 ) = x / 24 - - - > x = 24 * 44 / ( 3.81 ) = 277 answer will be b ."
Answer: b
Python program:
a = 44 / 2
b = 24 / 1
c = a * b
Problem: if 0.12 ÷ x 2 = 12 , than x = ?
Options: a ) 0.001 , b ) 0.01 , c ) 0.1 , d ) 1 , e ) 0
Rationale: explanation : 0.12 ÷ x 2 = 12 = > 0.12 / x 2 = 12 = > x 2 = 0.12 / 12 = 0.01 = > x = 0.1 answer : option c
Answer: c
Python program:
a = 0 / 12
b = math.sqrt(a)
Problem: a woman complete a journey in 30 hours . she travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .
Options: a ) 334 km . , b ) 216 km . , c ) 314 km . , d ) 224 km . , e ) 672 km .
Rationale: "0.5 x / 21 + 0.5 x / 24 = 30 - - > x / 21 + x / 24 = 60 - - > x = 672 km . e"
Answer: e
Python program:
a = 30 * 24
b = 24 + 21 
c = a / b
d = c * 21
e = d * 2
Problem: in a class of 35 students 26 play football and play 20 long tennis , if 17 play above , many play neither ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "26 + 20 - 17 = 29 35 - 29 = 6 play neither answer is a"
Answer: a
Python program:
a = 26 + 20 
b = a - 17
c = 35 - b
Problem: a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 4 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ?
Options: a ) 480 , b ) 488 , c ) 882 , d ) 269 , e ) 298
Rationale: 1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 4 = 480 answer : a
Answer: a
Python program:
a = 24 * 20
Problem: the least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ratio less than 16 : 21 , is ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: let x be subtracted . then , 6 - x 7 - x < 16 21 21 ( 6 - x ) < 16 ( 7 - x ) 5 x > 14 x > 2.8 least such whole number is 3 . answer : a
Answer: a
Python program:
a = 21 * 6
b = 7 * 16
c = a - b
d = 21 - 16
e = c / d
f = 2 / 10
g = e + f