euclaise/mathqa_programs huggingface dataset:
Problem: for every x , the action [ x ] is defined : [ x ] is the greatest integer less than or equal to x . what is the value of [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.6 ?
Options: a ) 12.6 . , b ) 14.4 . , c ) 15.8 . , d ) 16.2 . , e ) 16.4
Rationale: [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.6 = 6 * 0 + 2 * 7.2 + 8 - 6.6 = 0 + 14.4 + 1.4 15.8 answer c
Answer: c
Python program:
a = 2 * 7
b = 4 / 10
c = 8 - 4
d = a + c 
e = d - 6
Problem: a train traveling at 144 kmph crosses a platform in 30 seconds and a man standing on the platform in 12 seconds . what is the length of the platform in meters ?
Options: a ) 240 meters , b ) 360 meters , c ) 480 meters , d ) 600 meters , e ) can not be determined
Rationale: "answer distance covered by the train when crossing a man and when crossing a platform when a train crosses a man standing on a platform , the distance covered by the train is equal to the length of the train . however , when the same train crosses a platform , the distance covered by the train is equal to the length of the train plus the length of the platform . the extra time that the train takes when crossing the platform is on account of the extra distance that it has to cover . i . e . , length of the platform . compute length of platform length of the platform = speed of train * extra time taken to cross the platform . length of platform = 144 kmph * 12 seconds convert 144 kmph into m / sec 1 kmph = 5 / 18 m / s ( this can be easily derived . but if you can remember this conversion , it saves a good 30 seconds ) . ∴ 144 kmph = 5 / 18 ∗ 144 = 40 m / sec therefore , length of the platform = 40 m / s * 12 sec = 480 meters . choice c"
Answer: c
Python program:
a = 144 * 1000
b = a / 3600
c = b * 30
d = 144 * 1000
e = d / 3600
f = e * 12
g = c - f
Problem: the cost of registration at a professional association meeting was $ 50 per person ; a lunch for registrants only was available for an additional $ 22 per person . if the number of registrants who paid for lunch was 40 more than the number who did not , and if receipts for registration and lunch totaled $ 39,480 , how many people paid just for registration at the meeting ?
Options: a ) 700 , b ) 800 , c ) 300 , d ) 1,500 , e ) 1,800
Rationale: "hope this might be useful to you . let the number of people who have opted only to register = x now since the registration cost is 50 $ per person , the total amount sums to = 50 x $ as per the information given in the question , the number of registrants who paid for lunch was 40 more than the number who did not . that means , total number of people who registered and paid for lunch = 40 + x . for the people who registered for lunch the cost is 50 $ ( for the event registration ) + 22 $ ( for lunch ) = 72 $ . total amount in this case sums to = 72 ( 40 + x ) = 2880 + 72 x now , total amount received was 39480 thus , from the above data , 50 x + 2880 + 72 x = 39480 122 x = 39480 - 2880 122 x = 36600 x = 300 . hence the correct ans is c"
Answer: c
Python program:
a = 1 * 1
Problem: at 1 : 00 pm , there were 10.0 grams of bacteria . the bacteria increased to x grams at 4 : 00 pm , and 25.6 grams at 7 : 00 pm . if the amount of bacteria present increased by the same fraction during each of the 3 - hour periods , how many grams of bacteria were present at 4 : 00 pm ?
Options: a ) 15.1 , b ) 15.4 , c ) 15.7 , d ) 16.0 , e ) 16.3
Rationale: let x be the factor by which the bacteria increases every three hours . at 4 : 00 pm , the amount of bacteria was 10 x and at 7 : 00 pm it was 10 x ^ 2 . 10 x ^ 2 = 25.6 x ^ 2 = 2.56 x = 1.6 at 4 : 00 pm , the amount of bacteria was 10 ( 1.6 ) = 16 grams . the answer is d .
Answer: d
Python program:
a = 25 / 6
b = math.sqrt(a)
c = b * 10
Problem: a bag contains 6 red , 4 blue and 2 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 1 / 13 , b ) 2 / 23 , c ) 5 / 26 , d ) 5 / 22 , e ) 3 / 23
Rationale: "p ( both are red ) , = 6 c 212 c 2 = 6 c 212 c 2 = 15 / 66 = 5 / 22 d"
Answer: d
Python program:
a = math.comb(6, 2)
b = 6 + 4 
c = b + 2 
d = math.comb(c, 2)
e = a / d
Problem: the true discount on a bill of rs . 2560 is rs . 360 . what is the banker ' s discount ?
Options: a ) rs . 432 , b ) rs . 422 , c ) rs . 419 , d ) rs . 442 , e ) none of these
Rationale: "explanation : f = rs . 2560 td = rs . 360 pw = f - td = 2560 - 360 = rs . 2200 true discount is the simple interest on the present value for unexpired time = > simple interest on rs . 2200 for unexpired time = rs . 360 banker ' s discount is the simple interest on the face value of the bill for unexpired time = simple interest on rs . 2160 for unexpired time = 360 / 2200 × 2560 = 0.16 × 2560 = rs . 419 answer : option c"
Answer: c
Python program:
a = 2560 - 360
b = 360 / a
c = b * 2560
Problem: a man took loan from a bank at the rate of 4 % p . a . s . i . after 10 years he had to pay rs . 2000 interest only for the period . the principal amount borrowed by him was ?
Options: a ) 5000 , b ) 4500 , c ) 3200 , d ) 6000 , e ) 1592
Rationale: "principal = ( 100 * 2000 ) / ( 4 * 10 ) = rs . 5000 answer : a"
Answer: a
Python program:
a = 2000 * 100
b = a / 10
c = b / 4
Problem: the mean of 50 observations was 36 . it was found later that an observation 46 was wrongly taken as 23 . the corrected new mean is
Options: a ) 35.24 , b ) 36.16 , c ) 36.24 , d ) 36.46 , e ) none
Rationale: "solution correct sum = ( 36 x 50 + 46 - 23 ) = 1823 . â ˆ ´ correct mean = 1823 / 50 = 36.46 . answer d"
Answer: d
Python program:
a = 36 * 50
b = 50 - 2
c = b - 23
d = a + c 
e = d / 50
Problem: a fruit seller had some oranges . he sells 40 % oranges and still has 300 oranges . how many oranges he had originally ?
Options: a ) 420 , b ) 700 , c ) 220 , d ) 500 , e ) none of these
Rationale: "explanation : he sells 40 % of oranges and still there are 300 oranges remaining = > 60 % of oranges = 300 ⇒ ( 60 × total oranges ) / 100 = 300 ⇒ total oranges / 100 = 5 ⇒ total oranges = 5 × 100 = 500 answer : option d"
Answer: d
Python program:
a = 40 / 100
b = 300 * a
c = 300 + b
Problem: average weight of 15 boys in a class is 48 kgs . the average weight of the class of 25 students is 45 kgs . what is the average weight of the 15 girls in the class ?
Options: a ) 45 , b ) 47.3 , c ) 39.8 , d ) 45.5 , e ) 40.5
Rationale: total weight of boys in class 15 x 48 = 720 kg total weight of all student in the class room 25 x 45 = 1125 kg total no of girls in the class 1125 - 720 = 405 kg average weight of girls 405 / 10 = 40.5 kg correct ans is e
Answer: e
Python program:
a = 25 * 45
b = 15 * 48
c = a - b
d = c / 10
Problem: the sum of two numbers is 84 , and one of them is 12 more than the other . what are the two numbers ?
Options: a ) 48 , 36 , b ) 36 , 48 , c ) 32 , 48 , d ) 48 , 32 , e ) 32 , 42
Rationale: 2 x = 84 − 12 = 72 . x = 72 / 2 = 36 . this is the first number . therefore the other number is x + 12 = 36 + 12 = 48 . the sum of 36 + 48 is 84 . answer is b .
Answer: b
Python program:
a = 84 - 12
b = a / 2
Problem: 12.5 * 3.2 * 6.8 = ?
Options: a ) 352 , b ) 272 , c ) 224 , d ) 646 , e ) 742
Rationale: "b 272 ? = 12.5 * 3.2 * 6.8 = 352"
Answer: b
Python program:
a = 12 * 5
Problem: a man started driving at a constant speed , from the site of a blast , the moment he heard the blast . he heard a second blast after a time of 30 mins and 25 seconds . if the second blast occurred exactly 30 mins after the first , how many meters was he from the site when he heard the second blast ? ( speed of sound = 330 m / s )
Options: a ) 8250 , b ) 9350 , c ) 10,450 , d ) 11,550 , e ) 12,650
Rationale: "the distance the sound traveled to the man is 25 * 330 = 8250 meters the answer is a ."
Answer: a
Python program:
a = 330 * 25
Problem: john had a stock of 1400 books in his bookshop . he sold 62 on monday , 62 on tuesday , 60 on wednesday , 48 on thursday and 40 on friday . what percentage of the books were not sold ?
Options: a ) 81.57 % , b ) 36.5 % , c ) 80.67 % , d ) 56.5 % , e ) 80.57 %
Rationale: "let n be the total number of books sold . hence n = 62 + 62 + 60 + 48 + 40 = 272 let m be the books not sold m = 1400 - n = 1400 - 272 = 1128 percentage books not sold / total number of books = 1128 / 1200 = 0.81 = 80.57 % correct answer e"
Answer: e
Python program:
a = 62 + 62 
b = 60 + 48 
c = a + b 
d = c + 40 
e = 1400 - d
f = e / 1400
g = f * 100
Problem: if you multiply all the numbers on your mobile phone except 0 and 9 , what is the answer ?
Options: a ) 25869 , b ) 48586 , c ) 40320 , d ) 58964 , e ) 45698
Rationale: "we have to multiply 1 to 8 to find the answer . therefore 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 = 40320 answer is c"
Answer: c
Python program:
a = 1 - 1
b = 1 * a
Problem: a train 250 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?
Options: a ) 15 sec , b ) 9 sec , c ) 12 sec , d ) 15 sec , e ) 18 sec
Rationale: "speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 250 m at 50 / 3 m / sec = 250 * 3 / 50 sec = 15 sec answer : a ."
Answer: a
Python program:
a = 68 - 8
b = a * const_0_2778
c = 250 / b
Problem: in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 30 percent , but profits were 20 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
Options: a ) 80 % , b ) 105 % , c ) 140 % , d ) 124.2 % , e ) 138 %
Rationale: "0,14 r = x / 100 * 0.1 r answer c"
Answer: c
Python program:
a = 30 / 100
b = 1 - a
c = 20 / 100
d = b * c
e = 10 / 100
f = d / e
g = f * 100
Problem: the sum of two numbers is 96 , and one of them is 12 more than the other . what are the two numbers ?
Options: a ) 36 - 48 , b ) 50 - 34 , c ) 60 - 24 , d ) 42 - 54 , e ) 21 - 63
Rationale: "in this problem , we are asked to find two numbers . therefore , we must let x be one of them . let x , then , be the first number . we are told that the other number is 12 more , x + 12 . the problem states that their sum is 96 : word problem = 96 the line over x + 12 is a grouping symbol called a vinculum . it saves us writing parentheses . we have : 2 x = 96 â ˆ ’ 12 = 84 . x = 84 / 2 = 42 . this is the first number . therefore the other number is x + 12 = 42 + 12 = 54 . the sum of 42 + 54 is 96 . d"
Answer: d
Python program:
a = 96 - 12
b = a / 2
Problem: in a certain game , each player scores either 2 points or 5 points . if n players score 2 points and m players score 5 points , and the total number of points scored is 50 , what is the least possible positive difference q between n and m ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "we have equation 2 n + 5 m = 50 we have factor 2 in first number and we have factor 5 in second number . lcm ( 2 , 5 ) = 10 so we can try some numbers and we should start from 5 because it will be less list than for 2 2 * 5 = 10 and n should be equal 20 4 * 5 = 20 and n should be equal 15 6 * 5 = 30 and n should be equal 10 8 * 5 = 40 and n should be equal 5 10 * 5 = 50 and n should be equal 0 third variant give us the mininal difference n - m = 10 - 6 = 4 and there is some mistake in my way of thinking because we do n ' t have such answer ) if we change the task and will seek for difference between m and n than minimal result q will be 8 - 5 = 3 and answer b"
Answer: b
Python program:
a = 5 - 2
Problem: a motorcyclist started riding at highway marker a , drove 120 miles to highway marker b , and then , without pausing , continued to highway marker c , where she stopped . the average speed of the motorcyclist , over the course of the entire trip , was 20 miles per hour . if the ride from marker a to marker b lasted 3 times as many hours as the rest of the ride , and the distance from marker b to marker c was half of the distance from marker a to marker b , what was the average speed , in miles per hour , of the motorcyclist while driving from marker b to marker c ?
Options: a ) 40 , b ) 135 , c ) 50 , d ) 55 , e ) 60
Rationale: a - b = 120 miles b - c = 60 miles avg speed = 20 miles time taken for a - b 3 t and b - c be t avg speed = ( 120 + 60 ) / total time 20 = 180 / 4 t t = 135 b - c = 135 mph answer b
Answer: b
Python program:
a = 120 / 2
b = a + 120 
c = b / 20
d = c / 4
e = 120 / 2
f = d * e
Problem: the difference between the place values of 9 and 4 in the number 529435 is
Options: a ) 8500 , b ) 8900 , c ) 8600 , d ) 6970 , e ) none
Rationale: sol . = ( place value of 9 ) – ( place value of 4 ) = ( 9000 - 400 ) = 8600 answer c
Answer: c
Python program:
a = 10 * 9
b = a - 9
Problem: at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 450 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 200 ?
Options: a ) 1,108 , b ) 3,700 , c ) 2,108 , d ) 2,124 , e ) 2,256
Rationale: "we have $ 200 and we have to maximize the number of hot dogs that we can buy with this amount . let ' s try to find out what is the maximum number of hot dogs that we can buy for a lesser amount of money , which in this case is 450 for $ 22.95 . for the sake of calculation , let ' s take $ 23 . 23 x 8 gives 184 , i . e . a total of 450 x 8 = 3600 hot dogs . we are left with ~ $ 16 . similarly , let ' s use $ 3 for calculation . we can buy 5 20 - pack hot dogs ( 3 x 5 ) , a total of 20 x 5 = 100 hot dogs . so we have 3700 hot dogs . 2108 looks far - fetched ( since we are not likely to be left with > $ 1.55 ) . hence , ( b ) 3700 ( answer b )"
Answer: b
Python program:
a = 200 / 22
b = a * 450
Problem: from a total of 3 boys and 4 girls , how many 4 - person committees can be selected if the committee must have exactly 2 boys and 2 girls ?
Options: a ) 18 , b ) 24 , c ) 60 , d ) 120 , e ) 240
Rationale: "answer = c = 18 no of 4 person committees that can be formed = 3 c 2 * 4 c 2 = 18 answer a"
Answer: a
Python program:
a = 3 * 3
b = 3 * 2
c = a * b
Problem: mary is expected to pay back a total sum of $ 819200 to her bank as mortgage . if she is expected to make a payment which is double of the previous months amount , how long will it take her to fully repay the loan if her initial payment was $ 400 .
Options: a ) 13 , b ) 15 , c ) 12 , d ) 10 , e ) 11
Rationale: first payment - - $ 400 total amount to be repaid - - $ 819200 first month payment - - $ 400 second month payment - - $ 400 * 2 = $ 800 third month payment - - $ 800 * 2 = $ 1600 fourth month payment - - $ 1600 * 2 = $ 3200 fifth month payment - - $ 3200 * 2 = $ 6400 sixth month payment - - $ 6400 * 2 = $ 12800 seventh month payment - - $ 25600 * 2 = $ 51200 eight month payment - - $ 51200 * 2 = $ 102400 ninth month payment - - $ 102400 * 2 = $ 204800 tenth month payment - - $ 204800 * 2 = $ 409600 eleventh month payment - - $ 409600 * 2 = $ 819200 answer is e
Answer: e
Python program:
a = 819200 / 100
b = a / 2
c = b / 2
d = c / 4
e = d - 10
f = e - 100
g = f - 10
h = g - 4
i = h + 1 
j = 400 - i
Problem: irin , ingrid and nell bake chocolate chip cookies in the ratio of 9.18 : 5.17 : 2.05 . if altogether they baked a batch of 148 cookies , what percent of the cookies did nell bake ?
Options: a ) 0.125 % , b ) 1.25 % , c ) 12.5 % , d ) 125 % , e ) 0.152 %
Rationale: "9.18 x + 5.17 x + 2.05 x = 16.4 x = 148 cookies x = 148 / 16.4 = 9 ( approx ) so , tell baked 9 * 2.05 cookies or 19 cookies ( approx ) % share = 19 / 148 = 12.5 approx hence , answer is c ."
Answer: c
Python program:
a = 148 * 5
b = 9 + 18 
c = b + 2 
d = a / c
e = d / 148
f = e * 100
Problem: a jar contains a mixture of ab in the ratio 4 : 1 . when 30 l of mixture is replaced with liquid b , ratio becomes 2 : 3 . how many liters of liquid a was present in mixture initially .
Options: a ) 12 , b ) 48 , c ) 16 , d ) 20 , e ) 25
Rationale: "30 litres of mixture that is replaced will contain 24 litres of a and 6 litres of b ( as a : b = 4 : 1 ) let the initial volume of the mixture be 4 k + 1 k = 5 k so by condition , [ 4 k - 24 ] / [ k - 6 + 30 ] = 2 / 3 = > 12 k - 72 = 2 k - 12 + 60 = > 10 k = 120 solve for k which is k = 12 so initial volume of liquid a = 4 k = 48 litres answer : b"
Answer: b
Python program:
a = 3 * 2
b = 2 * 2
c = a + b 
d = 3 * 2
e = d - 1
f = 30 / e
g = c * f
h = 4 + 1 
i = g / h
j = i * 4
Problem: two trains are moving at 50 kmph and 70 kmph in opposite directions . their lengths are 150 m and 100 m respectively . the time they will take to pass each other completely is ?
Options: a ) 7 1 / 2 sec , b ) 7 1 / 7 sec , c ) 7 8 / 2 sec , d ) 7 1 / 9 sec , e ) 7 2 / 2 sec
Rationale: "70 + 50 = 120 * 5 / 18 = 100 / 3 mps d = 150 + 100 = 250 m t = 250 * 3 / 100 = 15 / 2 = 7 1 / 2 sec answer : d"
Answer: d
Python program:
a = 150 + 100 
b = 50 + 70 
c = b * const_0_2778
d = a / c
Problem: if there are 56 laborers in a crew , and on a certain day , 30 were present . calculate the percentage that showed up for work ? ( round to the nearest tenth ) .
Options: a ) 53.6 % , b ) 52.6 % , c ) 54.6 % , d ) 55.6 % , e ) 59.6 %
Rationale: 30 / 56 * 100 = 53.57 53.6 % correct answer a
Answer: a
Python program:
a = 30 * 100
b = a / 56
Problem: how many of the positive factors of 24 are not factors of 30
Options: a ) 2 , b ) 3 , c ) 4 , d ) 1 , e ) 5
Rationale: "factors of 24 - 1 , 2 , 3 , 4 , 6 , 8 , 12,24 factors of 30 - 1 , 2 , 3 , 5 , 6 , 10 , 15 and 30 . comparing both , we have four factors of 24 which are not factors of 30 - 4,8 , 12,24 answer ( c )"
Answer: c
Python program:
a = 30 / 24
Problem: if f ( x ) = 12 - x ^ 2 / 2 and f ( 2 k ) = 5 k , what is one possible value for k ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 8
Rationale: "first of all , see thisgmat blog postand check the related lesson linked below for some background on function notation . we can plug anything in for x and get a result . you can find f ( 1 ) , for example , by plugging in 1 where x is , and you would get 12 - 1 / 2 = 11.5 . or we could find f ( 2 ) , which would be 12 - 4 / 2 = 10 . so the notation f ( 2 k ) means that we are going to plug a 2 k in for x everywhere in the formula for f ( x ) . that would be : f ( 2 k ) = 12 - ( 2 k ) ^ 2 / 2 = 12 - 2 k ^ 2 . remember that we have to square both the 2 and the k , to get 4 k 2 . now , this expression , the output , we will set equal to 2 k . 12 - 2 k ^ 2 = 2 k - - > k = - 3 or k = 5 . all the answers are positive , so we choose k = 5 . answer = d"
Answer: d
Python program:
a = 2 ** 2
b = a / 2
c = b + 1
Problem: the average runs scored by a batsman in 20 matches is 40 . in the next 10 matches the batsman scored an average of 13 runs . find his average in all the 30 matches ?
Options: a ) 31 , b ) 67 , c ) 88 , d ) 69 , e ) 12
Rationale: total score of the batsman in 20 matches = 800 . total score of the batsman in the next 10 matches = 130 . total score of the batsman in the 30 matches = 930 . average score of the batsman = 930 / 30 = 31 . answer : a
Answer: a
Python program:
a = 40 * 20
b = 13 * 10
c = a + b 
d = 20 + 10 
e = c / d
Problem: p , q and r have rs . 9000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
Options: a ) rs . 3000 , b ) rs . 3600 , c ) rs . 2400 , d ) rs . 4000 , e ) none of these
Rationale: "let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 9000 - r ) = > 3 r = 18000 - 2 r = > 5 r = 18000 = > r = 3600 . answer : b"
Answer: b
Python program:
a = 2 / 3
b = 1 + a 
c = 9000 / b
d = 2 / 3
e = c * d
Problem: a car gets 60 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 170 kilometers ?
Options: a ) 3.5 gallons , b ) 2.37 gallons , c ) 5.7 gallons , d ) 4.25 gallons , e ) 2.83 gallons
Rationale: "each 60 kilometers , 1 gallon is needed . we need to know how many 60 kilometers are there in 170 kilometers ? 60 ã · 170 = 2.83 ã — 1 gallon = 2.83 gallons correct answer is e ) 2.83 gallons"
Answer: e
Python program:
a = 170 / 60
Problem: if jake loses 8 pounds , he will weigh twice as much as his sister kendra . together they now weigh 293 pounds . what is jake ’ s present weight , in pounds ?
Options: a ) 182 , b ) 186 , c ) 190 , d ) 194 , e ) 198
Rationale: "j + k = 293 and so k = 293 - j j - 8 = 2 k j - 8 = 2 ( 293 - j ) 3 j = 594 j = 198 the answer is e ."
Answer: e
Python program:
a = 293 - 8
b = a / 3
c = b * 2
d = c + 8
Problem: the radius of a circle is 4 / π cm then its perimeter is ?
Options: a ) 10
b ) 9
c ) 8
d ) 12
e ) 15
Rationale: perimeter = 2 π r 2 π * 4 / π = 8 cm answer : c
Answer: c
Python program:
a = 4 / math.pi
b = math.pi * a
c = 2 * b
Problem: the effective annual rate of interest corresponding to a nominal rate of 6 % per annum payable half - yearly is ?
Options: a ) 6.99 % , b ) 6.89 % , c ) 6.08 % , d ) 6.09 % , e ) 6.19 %
Rationale: "amount of rs . 100 for 1 year when compounded half - yearly = [ 100 * ( 1 + 3 / 100 ) 2 ] = rs . 106.09 effective rate = ( 106.09 - 100 ) = 6.09 % answer : d"
Answer: d
Python program:
a = 6 / 2
b = 6 / 2
c = a + b 
d = 6 / 2
e = 6 / 2
f = d * e
g = f / 100
h = c + g
Problem: from a pack of 52 cards , 1 card is drawn at random . what is the probability that a heart is drawn ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 13 , e ) 3 / 26
Rationale: "the total number of cards is 52 . the number of hearts is 13 . p ( heart ) = 13 / 52 = 1 / 4 the answer is c ."
Answer: c
Python program:
a = 4 * 3
b = a / 52
Problem: if each year the population of the country grows by 50 % , how many years will elapse before the population of the country doubles ?
Options: a ) 3 , b ) 4 , c ) 2 , d ) 6 , e ) 7
Rationale: "till year 2000 , population is 100 . year 2001 : population becomes 150 . . . . . . . . . . . . . 1 year elapsed year 2002 : population > 200 . . . . . . . . . . . . . 2 year elapsed answer : c"
Answer: c
Python program:
a = 4 + 4
Problem: for any integer p , * p is equal to the product of all the integers between 1 and p , inclusive . how many prime numbers are there between * 7 + 3 and * 7 + 7 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "7 ! = 720 * 7 = 5040 # in question = 5043 , 5044 , 5045 , 5046 , 5047 none of these are prime answer - a"
Answer: a
Python program:
a = 7 * 3
b = a * 2
c = b * 4
d = c + 7 
e = 7 * 3
f = e * 2
g = f * 4
h = g + 3 
i = d - h
j = i - 1
Problem: two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 12 seconds . find the length of the faster train ?
Options: a ) 270 , b ) 288 , c ) 266 , d ) 120 , e ) 126
Rationale: "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 12 sec = 27 * 10 = 270 m . the length of the faster train = 120 m . answer : d"
Answer: d
Python program:
a = 72 - 36
b = a / const_3_6
c = b * 12
Problem: two trains of equal are running on parallel lines in the same direction at 44 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?
Options: a ) 40 m , b ) 72 m , c ) 80 m , d ) 82 m , e ) 84 m
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 44 - 36 = 8 km / hr . = 8 * 5 / 18 = 20 / 9 m / sec . 2 x / 36 = 20 / 9 = > x = 40 . answer : a"
Answer: a
Python program:
a = 44 - 36
b = a * 1000
c = b / 3600
d = 36 * c
e = d / 2
Problem: a man sold 20 articles for $ 60 and gained 20 % . how many articles should he sell for $ 50 to incur a loss 20 % ?
Options: a ) 25 , b ) 36 , c ) 40 , d ) 50 , e ) 48
Rationale: production cost per article : $ 60 * ( 100 % - 20 % ) / 20 = $ 2.40 required production costs for a loss of 20 % : $ 50 * ( 100 % + 20 % ) = $ 60 number of articles to be sold for $ 60 to incur a 20 % loss : $ 60 / $ 2.40 = 25 thus , solution a is correct .
Answer: a
Python program:
a = original_price_before_loss / (