euclaise/mathqa_programs huggingface dataset:
Problem: the h . c . f . of two numbers is 12 and their l . c . m . is 600 . if one of the number is 12 , find the other ?
Options: a ) 100 , b ) 600 , c ) 120 , d ) 200 , e ) 150
Rationale: "other number = 12 * 600 / 12 = 600 answer is b"
Answer: b
Python program:
a = 12 * 12
Problem: if below equation are true 24 $ 6 = 64 35 $ 5 = 87 63 $ 7 = 99 by using same logic what is the value of the below question 88 $ 8 = ?
Options: a ) 1621 , b ) 1711 , c ) 1611 , d ) 1511 , e ) 1311
Rationale: correct answer : c the number on the right side is formed as ( sum of digits of the 1 st number ) no 1 / no 2 ex : 35 $ 5 = 87 ( 3 + 5 = 8 ) ( 35 / 5 = 7 ) 63 $ 7 = 99 ( 6 + 3 = 9 ) ( 63 / 7 = 9 )
Answer: c
Python program:
a = 8 + 8 
b = a * 100
c = 88 / 8
d = b + c
Problem: the average weight of 10 persons increases by 3.2 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 76 kg , b ) 80 kg , c ) 85 kg , d ) 97 kg , e ) none
Rationale: "solution total weight increased = ( 10 x 3.2 ) kg = 32 kg . weight of new person = ( 65 + 32 ) kg = 97 kg . answer d"
Answer: d
Python program:
a = 10 * 3
b = 65 + a
Problem: the average of runs of a cricket player of 10 innings was 37 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 76 , b ) 81 , c ) 85 , d ) 87 , e ) 89
Rationale: "explanation : average = total runs / no . of innings = 37 so , total = average x no . of innings = 37 x 10 = 370 . now increase in avg = 4 runs . so , new avg = 37 + 4 = 41 runs total runs = new avg x new no . of innings = 41 x 11 = 451 runs made in the 11 th inning = 451 - 370 = 81 answer : b"
Answer: b
Python program:
a = 10 + 1 
b = 4 + 37 
c = a * b
d = 10 * 37
e = c - d
Problem: what will be the vulgar fraction of 0.75
Options: a ) 3 / 5 , b ) 3 / 4 , c ) 3 / 2 , d ) 3 / 7 , e ) 3 / 8
Rationale: "explanation : 0.75 = 75 / 100 = 3 / 4 option b"
Answer: b
Python program:
a = 0 / 75
b = circle_area / (
Problem: a company decreased the price of its main product by 75 % . subsequently , the number of units sold increased such that the total revenue remained unchanged . what was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product ?
Options: a ) 1.33 , b ) 2.33 , c ) 3.33 , d ) 4.33 , e ) 1.45
Rationale: "for the total revenue to remain the same when the price is 3 / 4 , the number of products sold must 3 / 4 times . therefore increase in the number of products sold is 100 % = > the required ratio = 100 % / 75 % = 1.33 answer : a"
Answer: a
Python program:
a = 100 / 75
Problem: a ' s speed is 15 / 13 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that b beats a by 25 % of the length of the race ?
Options: a ) 35 % , b ) 48 % , c ) 52 % , d ) 42 % , e ) 46 %
Rationale: first calculate the distance , b has covered with his speed in the time , in which a reached 80 % of the race . then add the remaining distance as head start for b to win the race . its best to apply ratios concept here . since a ' s speed is 15 / 13 of b , therefore , b ' s speed is 13 / 15 of a distance covered by b = speed x time = ( 13 / 15 ) x ( 0.75 ) = 0.65 % ( which means b would have covered 0.65 of the race length during the time in which a has covered 0.75 of the race length . therefore to win , b needs a headstart of ( 1 - 0.65 = ) 0.35 of the race length . so the answer is a
Answer: a
Python program:
a = 100 - 25
b = a / 100
c = 13 / 15
d = b * c
e = 1 - d
f = e * 100
Problem: company c sells a line of 20 products with an average retail price of $ 1200 . if none of these products sells for less than $ 400 , and exactly 10 of the products sell for less than $ 1000 , what is the greatest possible selling price of the most expensive product ?
Options: a ) 12000 , b ) 11000 , c ) 10000 , d ) 13000 , e ) 15000
Rationale: the average price of 20 products is $ 1,200 means that the total price of 20 products is 20 * 1,200 = $ 24,000 . next , since exactly 10 of the products sell for less than $ 1,000 , then let ' s make these 10 items to be at $ 400 each ( min possible ) . now , the remaining 9 items can not be priced less than $ 1,000 , thus the minimum possible price of each of these 9 items is $ 1,000 . thus the minimum possible value of 19 products is 10 * 400 + 9 * 1,000 = $ 13,000 . therefore , the greatest possible selling price of the most expensive product is $ 24,000 - $ 13,000 = $ 11,000 . answer : b .
Answer: b
Python program:
a = 20 * 1200
b = 10 - 1
c = b * 1000
d = 400 * 10
e = c + d 
f = a - e
Problem: in a box of 6 pencils , a total of 2 are defective . if a customer buys 3 pencils selected at random from the box , what is the probability that neither pencils will be defective ?
Options: a ) 1 / 2 , b ) 1 / 5 , c ) 2 / 3 , d ) 2 / 5 , e ) 1 / 7
Rationale: "first , there are 4 c 3 ways you can select 3 good pencils from 4 good ones . second , there are 6 c 3 ways you select 3 pencils from 6 ones in the box . then , the probability that neither pen will be defective is : 4 c 3 / 6 c 3 = 4 / 20 = 1 / 5 answer is b"
Answer: b
Python program:
a = 6 - 2
b = math.factorial(a)
c = 6 - 2
d = c - 3
e = math.factorial(d)
f = math.factorial(3)
g = e * f
h = b / g
i = math.factorial(6)
j = 6 - 3
k = math.factorial(j)
l = math.factorial(3)
m = k * l
n = i / m
o = h / n
Problem: a candidate appearing for an examination has to secure 52 % marks to pass paper i . but he secured only 45 marks and failed by 35 marks . what is the maximum mark for paper i ?
Options: a ) 110 , b ) 154 , c ) 130 , d ) 140 , e ) 150
Rationale: "he secured 45 marks nd fail by 35 marks so total marks for pass the examinatn = 80 let toal marks x x * 52 / 100 = 80 x = 154 answer : b"
Answer: b
Python program:
a = 45 + 35 
b = 52 / 100
c = a / b
Problem: jim drove 768 miles of a 1200 miles journey . how many more miles does he need to drive to finish his journey ?
Options: a ) 432 miles , b ) 651 miles , c ) 387 miles , d ) 954 miles , e ) 556 miles
Rationale: "the number of miles to drive to finish his journey is given by 1200 - 768 = 432 miles correct answer a"
Answer: a
Python program:
a = 1200 - 768
Problem: if | 20 x - 10 | = 110 , then find the product of the values of x ?
Options: a ) - 45 , b ) 50 , c ) - 62 , d ) 35 , e ) - 30
Rationale: | 20 x - 10 | = 110 20 x - 10 = 110 or 20 x - 10 = - 110 20 x = 120 or 20 x = - 100 x = 6 or x = - 5 product = - 5 * 6 = - 30 answer is e
Answer: e
Python program:
a = 110 - 10
b = 110 + 10 
c = a - b
d = c - 10
Problem: when positive integer n is divided by positive integer j , the remainder is 10 . if n / j = 205.08 , what is value of j ?
Options: a ) 125 , b ) 100 , c ) 75 , d ) 150 , e ) 50
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 205.08 here 205 is the quotient . given that remainder = 10 so , 205.08 = 205 + 10 / j so , j = 125 answer : a"
Answer: a
Python program:
a = 4 * 10
b = a + 2 
c = 100 + b 
d = 205 - 8
e = 10 / d
Problem: in a certain kindergarten , half of the children are allergic to peanuts , 10 children are not allergic to cashew nuts , 10 children are allergic to both peanuts and cashew nuts , and 18 children are allergic to cashew nuts . how many of the kindergarten ' s children are not allergic to peanuts and are not allergic to cashew nuts ?
Options: a ) 14 , b ) 10 , c ) 8 , d ) 6 , e ) 4
Rationale: we are given children allergic to cashew nuts as 18 and not allergic to cashew nuts as 10 , so total = 10 + 18 = 28 . . . children allergic to both are 10 . . . 18 are allergic to cashew nuts , so and half or 28 / 2 = 14 are allergic to peanuts . . so children allergic to at least one of the two are 18 + 14 - 10 = 22 . . therefore children not allergic to any of the two are 28 - 22 = 6 answer : d
Answer: d
Python program:
a = 18 + 10 
b = 18 + 10 
c = b / 2
d = 18 + c 
e = d - 10
f = a - e
Problem: a train 1100 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 288 m , b ) 256 m , c ) 200 m , d ) 278 m , e ) 287 m
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 1100 + x ) / 60 = 65 / 3 x = 200 m . answer : c"
Answer: c
Python program:
a = 78 - 1
b = a * const_0_2778
c = 1100 / b
Problem: the sum of number of boys and girls in a school is 300 . if the number of boys is x , then the number of girls becomes x % of the total number of students . the number of boys is ?
Options: a ) 50 , b ) 40 , c ) 60 , d ) 100 , e ) 75
Rationale: "we have x + x % of 300 = 300 x + x / 100 * 300 = 300 4 * x = 300 x = 75 answer is e"
Answer: e
Python program:
a = 300 / 100
b = a + 1 
c = 300 / b
Problem: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.82 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.55
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.82 = 3 * x - - > x = $ 0.55 . answer : e ."
Answer: e
Python program:
a = 1 + 1 
b = a * 0
c = 1 + 2 
d = b / c
Problem: the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 162 ° of the circle , what percentage of megatek employees are in manufacturing ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 45 % , e ) 72 %
Rationale: answer : d 162 ° divided by 360 ° equals 0.45 , therefore the sector is equal to 45 % of the total
Answer: d
Python program:
a = 3600 / 10
b = 162 / a
c = b * 100
Problem: 1100 boys and 700 girls are examined in a test ; 42 % of the boys and 30 % of the girls pass . the percentage of the total who failed is ?
Options: a ) 63.3 % , b ) 52.4 % , c ) 81.2 % , d ) 75.4 % , e ) 69.1 %
Rationale: total number of students = 1100 + 700 = 1800 number of students passed = ( 42 % of 1100 + 30 % of 700 ) = 462 + 210 = 672 number of failures = 1128 * 100 / 1800 = 190 / 3 % = 63.3 % answer is a
Answer: a
Python program:
a = 1100 + 700 
b = 42 / 100
c = 1100 * b
d = 30 / 100
e = 700 * d
f = c + e 
g = a - f
h = 1100 + 700 
i = g / h
j = 100 * i
Problem: john makes $ 60 a week from his job . he earns a raise and nowmakes $ 70 a week . what is the % increase ?
Options: a ) 16 % , b ) 16.66 % , c ) 17 % , d ) 17.2 % , e ) 18 %
Rationale: "increase = ( 10 / 60 ) * 100 = ( 1 / 6 ) * 100 = 16.66 % . b"
Answer: b
Python program:
a = 70 - 60
b = a / 60
c = b * 100
Problem: two heavily loaded sixteen - wheeler transport trucks are 690 kilometers apart , sitting at two rest stops on opposite sides of the same highway . driver a begins heading down the highway driving at an average speed of 90 kilometers per hour . exactly one hour later , driver b starts down the highway toward driver a , maintaining an average speed of 80 kilometers per hour . how many kilometers farther than driver b , will driver a have driven when they meet and pass each other on the highway ?
Options: a ) 120 , b ) 130 , c ) 150 , d ) 320 , e ) 450
Rationale: "i ' ve been reading the website for a while and i ' m always keen to see different approaches so i would like to share one that works for me : short version : truck a travels for an hour . distance remaining = 690 - 90 = 600 k ratio of speeds 9 : 8 - > 510 / 17 = 30 truck a = 90 + 30 * 9 = 360 truck b = 30 * 8 = 240 delta = 120 km answer a"
Answer: a
Python program:
a = 690 - 90
b = 90 + 80 
c = a / b
d = 90 - 80
e = c * d
f = 90 + e
Problem: on a map the distance between two mountains is 312 inches . the actual distance between the mountains is 136 km . ram is camped at a location that on the map is 42 inch from the base of the mountain . how many km is he from the base of the mountain ?
Options: a ) 14.83 , b ) 14.81 , c ) 14.8 , d ) 14.82 , e ) 18.3
Rationale: "explanation : since 312 inch = 136 km so 1 inch = 136 / 312 km so 42 inch = ( 136 ã — 42 ) / 312 = 18.3 km answer : e"
Answer: e
Python program:
a = 42 * 136
b = a / 312
Problem: on a certain day , tim invested $ 500 at 10 percent annual interest , compounded annually , and lana invested 800 at 5 percent annual interest , compounded annually . the total amount of interest earned by tim ’ s investment in the first 2 years was how much greater than the total amount of interest earned by lana ’ s investment in the first 2 years ?
Options: a ) $ 5 , b ) $ 15 , c ) $ 23 , d ) $ 100 , e ) $ 105
Rationale: "compounded annually means that the interest is applied once per year . one can have 10 % annual interest compounded monthly - in this case 10 % / 12 would be applied each month , or 10 % annual interest compounded daily etc . with respect to the problem at hand , at the end of two years , tim would have 500 ( 1.10 ) ^ 2 = 500 ( 1.21 ) = 605 and lana would have 800 ( 1.05 ) ^ 2 = 800 ( 1.1025 ) = 882 thus , tim earned 105 dollars , while lana earned 82 dollars the difference is $ 23 and the answer is c ."
Answer: c
Python program:
a = 10 / 100
b = 1 + a 
c = b ** 2
d = 500 * c
e = d - 500
f = 5 / 100
g = 1 + f 
h = g ** 2
i = h * 800
j = i - 800
k = e - j
Problem: the h . c . f of two numbers is 11 and their l . c . m is 7700 . if one of the numbers is 275 , then the other is :
Options: a ) 279 , b ) 283 , c ) 308 , d ) 318 , e ) 328
Rationale: "other number = ( 11 * 7700 ) / 275 = 308 . answer : c"
Answer: c
Python program:
a = 11 * 275
Problem: in measuring the sides of a rectangle , one side is taken 8 % in excess and other 5 % in deficit . find the error percentage in the area calculated from these measurements .
Options: a ) 3.5 % , b ) 2.4 % , c ) 3 % , d ) 5 % , e ) 2.6 %
Rationale: "let the sides of the rectangle be a and b . actual area of the rectangle without error = ab new side a ( 8 % in excess ) = a + 0.08 a = 1.08 a new side b ( 5 % in deficit ) = b - 0.05 b = 0.95 b area of the new rectangle = ( 1.08 a ) ( 0.95 b ) = ( 1.0260 ) ab say a = 1 and b = 1 area of the original rectangle = 1 area of the new rectangle = 1.026 change in the area calculation = . 026 error percentage in the area calculated = 2.6 % answer : e"
Answer: e
Python program:
a = 8 - 5
b = 8 * 5
c = b / 100
d = a - c
Problem: every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 3200 ?
Options: a ) 8100 , b ) 3388 , c ) 7767 , d ) 4050 , e ) 2288
Rationale: "3200 * 9 / 8 * 9 / 8 = 4050 answer : d"
Answer: d
Python program:
a = 1 / 8
b = a * 3200
c = 3200 + b 
d = 1 / 8
e = 1 / 8
f = e * 3200
g = 3200 + f 
h = d * g
i = c + h
Problem: on a certain test , bill scored 20 more points than john , but half as many points as sue . if the sum of the scores of the 3 students was 160 points , how many points did bill receive ?
Options: a ) 30 , b ) 45 , c ) 50 , d ) 80 , e ) 100
Rationale: consider john ' s points as x so bill ' s points are x + 20 so sue ' s points are 2 x + 40 total of all three students is 4 x + 60 , but this total is given as 160 x = 25 so bill ' s points = 25 + 20 = 45 correct answer option b
Answer: b
Python program:
a = 160 + 20 
b = 1 + 1 
c = b + 2 
d = a / c
Problem: two vessels having volumes in the ratio 3 : 5 are filled with water and milk solutions . the ratio of milk and water in the two vessels are 2 : 3 and 3 : 1 respectively . if the contents of both the vessel are empties into a larger vessel , find the ratio of milk and water in the larger vessel .
Options: a ) 99 : 61 , b ) 99 : 160 , c ) 61 : 160 , d ) 61 : 99 , e ) 99 : 160
Rationale: "vessel a = 300 gallons - - > milk = 120 , water = 180 ; vessel b = 500 gallons - - > milk = 375 , water = 125 ; vessel a + b = 800 gallons - - > milk = 495 , water 305 . the ratio = 495 / 305 - - > reduce by 5 = 99 / 61 . answer : a ."
Answer: a
Python program:
a = 2 ** 3
Problem: a man swims downstream 45 km and upstream 18 km taking 3 hours each time , what is the speed of the man in still water ?
Options: a ) 2 , b ) 8 , c ) 9 , d ) 10 , e ) 10.5
Rationale: "45 - - - 3 ds = 15 ? - - - - 1 18 - - - - 3 us = 6 ? - - - - 1 m = ? m = ( 15 + 6 ) / 2 = 10.5 answer : e"
Answer: e
Python program:
a = 18 / 3
b = 45 / 3
c = a + b 
d = c / 2
Problem: the product of two successive numbers is 1122 . which is the smaller of the two numbers ?
Options: a ) 34 , b ) 36 , c ) 33 , d ) 38 , e ) 31
Rationale: "c 33 from the given alternatives , 33 × 34 = 1122 ∴ smaller number = 33"
Answer: c
Python program:
a = math.sqrt(1122)
Problem: a library has an average of 630 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 250 , b ) 305 , c ) 280 , d ) 285 , e ) none
Rationale: "since the month begins with sunday , to there will be five sundays in the month average required = ( 630 x 5 + 240 x 25 / 30 ) = 305 answer : option b"
Answer: b
Python program:
a = 3 + 4 
b = 30 / a
c = math.floor(b)
d = c + 1 
e = d * 630
f = 3 + 4 
g = 30 / f
h = math.floor(g)
i = h + 1 
j = 30 - i
k = j * 240
l = e + k 
m = l / 30
Problem: the sale price of a trolley bag including the sale tax is rs . 1232 . the rate of sale tax is 10 % . if the shopkeeper has made a profit of 12 % , the cost price of the trolley bag is :
Options: a ) rs 1000 , b ) rs 1515 , c ) rs 1525 , d ) rs 1250 , e ) none of these
Rationale: "explanation : 110 % of s . p . = 1232 s . p . = rs . ( 1232 x 100 / 110 ) = rs . 1120 . c . p . = rs ( 100 / 112 x 1120 ) = rs 1000 answer : a"
Answer: a
Python program:
a = 10 / 100
b = 1232 * a
c = 1232 - b
d = 12 / 100
e = d + 1 
f = c / e
Problem: rs 4000 is divided into two parts such that one part is put out at 3 % and the other at 5 % . if the annual interest earned from both the investments be rs 144 , find the first part .
Options: a ) rs 4000 , b ) rs 2800 , c ) rs 3800 , d ) rs 3500 , e ) rs 3100
Rationale: "explanation : average rate = ( 144 / 4000 ) * 100 = 3.6 ratio = 14 : 6 = 7 : 3 so , first part = ( 7 / 10 ) * 4000 = rs 2800 . answer : b"
Answer: b
Python program:
a = 5 / 100
b = 4000 * a
c = b - 144
d = 5 / 100
e = 3 / 100
f = d - e
g = c / f
Problem: a train of 24 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 4.5 km long ?
Options: a ) 4 , b ) 3 , c ) 5 , d ) 6 , e ) 9
Rationale: "d = 25 * 60 + 4500 = 6000 m t = 6000 / 60 * 18 / 5 = 360 sec = 6 mins answer : d"
Answer: d
Python program:
a = 24 + 1 
b = a * 60
c = b / 1000
d = c + 4
Problem: the only items of clothing at michelle ’ s boutique are 4 shirts , 8 pairs of pants and 18 ties . what is the probability of randomly selecting 2 ties out of all the items in michelle ’ s boutique ?
Options: a ) 51 / 145 , b ) 9 / 25 , c ) 3 / 5 , d ) 94 / 145 , e ) 5 / 6
Rationale: we have 4 shirts , 8 pairs of pants and 18 ties . i . e 30 items total ways of picking two items out of all = 30 c 2 = 435 total ways of picking two items out of all ties = 18 c 2 = 153 required probability = 153 / 435 = 51 / 145 answer : option a
Answer: a
Python program:
a = math.comb(18, 2)
b = 4 + 8 
c = b + 18 
d = math.comb(c, 2)
e = a / d
Problem: in a sample of 800 high school students in which all students are either freshmen , sophomores , juniors , or seniors , 26 percent are juniors and 75 percent are not sophomores . if there are 160 seniors , how many more freshmen than sophomores are there among the sample of students ?
Options: a ) 32 , b ) 40 , c ) 48 , d ) 54 , e ) 60
Rationale: "200 are sophomores . the number of freshmen is 600 - 160 - 0.26 ( 800 ) = 232 the answer is a ."
Answer: a
Python program:
a = 160 / 800
b = a * 100
c = 100 - b
d = c - 26
e = 100 - 75
f = d - e
g = f * 800
h = g / 100
i = 100 - 75
j = i * 800
k = j / 100
l = h - k
Problem: mary and mike enter into a partnership by investing $ 900 and $ 100 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if mary received $ 1600 more than mike did , what was the profit made by their business in that year ?
Options: a ) $ 3500 , b ) $ 3400 , c ) $ 3300 , d ) $ 3200 , e ) $ 3000
Rationale: "explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 9 : 1 . i . e . , 90 % of 2 x would go to mary and 10 % of 2 x would go to mike . hence , mary would get ( 90 - 10 ) % of 2 x more than mike or 80 % of 2 x = $ 1600 i . e . , ( 60 / 100 ) * 2 x = 1600 or 2 x = 2000 . hence , the profit made by the company during the year $ 3 x = $ 3000 . answer : e"
Answer: e
Python program:
a = 900 / 1000
b = 100 / 1000
c = a - b
d = 1 / 3
e = 1 - d
f = c * e
g = 1600 / f
Problem: if 63 percent of a class answered the first question on a certain test correctly , 49 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
Options: a ) 22 % , b ) 24 % , c ) 26 % , d ) 28 % , e ) 32 %
Rationale: "63 % answered the first question correctly and 20 % answered neither correctly . then 17 % missed the first question but answered the second question correctly . then the percent who answered both correctly is 49 % - 17 % = 32 % . the answer is e ."
Answer: e
Python program:
a = 63 + 49 
b = a + 20 
c = b - 100
Problem: the speed of a boat in still water is 12 kmph . what is the speed of the stream if the boat can cover 32 km downstream or 16 km upstream in the same time ?
Options: a ) 5 kmph , b ) 6 kmph , c ) 7 kmph , d ) 4 kmph , e ) 10 kmph
Rationale: "x = the speed of the stream ( 12 + x ) / ( 12 - x ) = 2 / 1 12 + x = 24 - 2 x 3 x = 12 x = 4 km / hour if the speed of the stream is 4 km / hour , then the ' downstream ' speed of the boat is 12 + 4 = 16 km / hour and the ' upstream ' speed of the boat is 12 - 4 = 8 km / hour . in that way , if the boat traveled for 2 hours , it would travel 2 x 8 = 16 km downstream and 2 x 16 = 32 km / hour upstream . answer : d"
Answer: d
Python program:
a = 1 + 2 
b = 12 / a
Problem: the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is ?
Options: a ) 2 : 7 , b ) 2 : 3 , c ) 2 : 1 , d ) 2 : 9 , e ) 2 : 2
Rationale: "let the ratio be k : 1 . then , k * 16.4 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.4 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.6 = 2 / 3 required ratio = 2 / 3 : 1 = 2 : 3 . answer : option b explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.4 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.6 = 2 / 3 required ratio = 2 / 3 : 1 = 2 : 3 . answer : b"
Answer: b
Python program:
a = 15 - 8
b = 16 - 4
c = a / b