euclaise/mathqa_programs huggingface dataset:
Problem: in a certain pond , 30 fish were caught , tagged , and returned to the pond . a few days later , 50 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ?
Options: a ) 750 , b ) 625 , c ) 1,250 , d ) 2,500 , e ) 10,000
Rationale: "this is a rather straight forward ratio problem . 1 . 30 fish tagged 2 . 2 out of the 50 fish caught were tagged thus 2 / 50 2 / 50 = 30 / x thus , x = 750 think of the analogy : 2 fish is to 50 fish as 50 fish is to . . . ? you ' ve tagged 50 fish and you need to find what that comprises as a percentage of the total fish population - we have that information with the ratio of the second catch . a"
Answer: a
Python program:
a = 2 / 50
b = 30 / a
Problem: in an examination , there are 100 questions divided into 3 groups a , b and c such that each group contains at least one question . each question in group a carries 1 mark , each question in group b carries 2 marks and each question in group c carries 3 marks . it is known that the questions in group a together carry at least 60 % of the total marks . if group b contains 23 questions , then how many questions are there in group c ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: explanation : since group b contains 23 questions , the marks associated with this group are 46 . now , check for option ( 1 ) , if group ( c ) has one question , the marks associated with this group will be 3 . thus total marks will be 49 . total number of questions = 100 , group ( a ) will have 76 questions , the corresponding weightage being 76 marks . answer : a
Answer: a
Python program:
a = 60 / 100
b = 1/(a)
c = b - 1
d = 100 - 23
e = c * d
f = 2 * 23
g = e - f
h = 60 / 100
i = 1/(h)
j = i - 1
k = 3 + j 
l = g / k
m = math.floor(l)
Problem: 897.7 – 573.07 – 95.007 = ?
Options: a ) 229.623 , b ) 224.777 , c ) 233.523 , d ) 414.637 , e ) none of these
Rationale: "solution given expression = 897.7 - ( 573.07 + 95.007 ) = 897.7 - 668.077 = 229.623 . answer a"
Answer: a
Python program:
a = 573 / 7
b = 897 - 7
Problem: 78 , 64 , 48 , 30 , 10 , ( . . . )
Options: a ) - 12 number , b ) - 14 , c ) 2 , d ) 8 , e ) 6
Rationale: "explanation : 78 - 14 = 64 64 - 16 = 48 48 - 18 = 30 30 - 20 = 10 10 - 22 = - 12 answer : option a"
Answer: a
Python program:
a = negate - (
Problem: a and b finish the job in 15 days . while a , b and c can finish it in 5 days . c alone will finish the job in
Options: a ) 4.50 days , b ) 3.50 days , c ) 6.0 days , d ) 7.5 days , e ) 5.50 days
Rationale: "explanation : 5 = ( 15 * x ) / ( 15 + x ) 75 + 5 x = 15 x 10 x = 75 x = 7.5 answer : option d"
Answer: d
Python program:
a = 5 * 15
b = 15 - 5
c = a / b
Problem: working together at their respective constant rates , machine a and machine b can produce 1,500 units in 8 hours . working alone , machine b would complete that same output in 50 % more time . if machine a were to work on its own for an 8 - hour shift , what percent of the 1,500 unit total would it produce ?
Options: a ) 25 , b ) 36 , c ) 30 , d ) 67 , e ) 75
Rationale: "1 / a + 1 / b = 1 / t 1 / a + 1 / 14 = 1 / 8 ( 50 % more of 8 is 14 ) 1 / a = 1 / 24 machine a can produce 1500 units in 24 hrs , so it can produce 1500 * 8 / 24 = 500 units is 8 hrs . 500 is 30 % of 1500 . c is the answer"
Answer: c
Python program:
a = 4 * 4
b = a * 100
c = b / 8
d = 4 * 4
e = d * 100
f = 8 * 50
g = f / 100
h = 8 + g 
i = e / h
j = c - i
k = j * 8
l = 4 * 4
m = l * 100
n = k / m
o = n * 100
Problem: at a local appliance manufacturing facility , the workers received a 30 % hourly pay raise due to extraordinary performance . if one worker decided to reduce the number of hours that he worked so that his overall pay would remain unchanged , by approximately what percent would he reduce the number of hours that he worked ?
Options: a ) 83 % , b ) 80 % , c ) 23 % , d ) 17 % , e ) 12 %
Rationale: "let ' s say he works usually 10 hours and earns 100 per hour . 10 * 100 = 1000 10 * 130 = 1300 ( this are the new earnings after the raise ) to figure out how much he needs to work with the new salary in order to earn the original 1000 : 1000 / 130 = 7.67 so he can reduce his work by 2.33 hours . which is > 23 % . answer c"
Answer: c
Python program:
a = 30 - 1
Problem: calculate how many days it will take for 7 boys to wash a 35 m long wall if 5 boys can wash a 25 m long wall in 4 days ,
Options: a ) 6 days , b ) 3 days , c ) 4 days , d ) 2 days , e ) 5 days
Rationale: "the length of wall painted by one boy in one day = 25 / 5 * 1 / 4 = 1.25 m no . of days required to paint 50 m cloth by 8 boys = 35 / 7 * 1 / 1.25 = 4 days . c"
Answer: c
Python program:
a = 5 * 4
b = a * 35
c = 25 * 7
d = b / c
Problem: how many diagonals does a 61 - sided convex polygon have ?
Options: a ) 1182 , b ) 1769 , c ) 2456 , d ) 3538 , e ) 4209
Rationale: "a 61 - sided convex polygon has 61 vertices . if we examine a single vertex , we can see that we can connect it with 58 other vertices to create a diagonal . note that we ca n ' t connect the vertex to itself and we ca n ' t connect it to its adjacent vertices , since this would not create a diagonal . if each of the 61 vertices can be connected with 58 vertices to create a diagonal then the total number of diagonals would be ( 61 ) ( 58 ) = 3538 however , we must recognize that we have counted every diagonal twice . to account for counting each diagonal twice , we must divide 3538 by 2 to get 1769 . the answer is b ."
Answer: b
Python program:
a = math.factorial(61)
b = 61 - 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e
Problem: balls of equal size are arranged in rows to form an equilateral triangle . the top most row consists of one ball , the 2 nd row of two balls and so on . if 253 balls are added , then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did . how many balls made up the triangle ?
Options: a ) 903 , b ) 2209 , c ) 2878 , d ) 1210 , e ) 1560
Rationale: "as expected , this question boils down to 2 equation , consider total number of balls in triangle = t and number of balls in last row = x . 1 + 2 + 3 + . . . + x = t x ( x + 1 ) / 2 = t - - - - ( a ) as mentioned in the question , side of a square will be ( x - 8 ) and total number of balls in square will be ( t + 253 ) ( x - 8 ) ^ 2 = t + 253 - - - - - ( b ) now the hardest part of the question will be to solve these 2 equations and this looks like time consuming but the easy way will be plug and play . also , we ' ve to find a value of t ( from 5 optiosn given below ) which can make a square of a a number . one we know this , it will be a cake walk . we can see that option a fits this criteria in eq ( b ) . add - 903 + 253 = 1156 = 34 ^ 2 = ( x - 8 ) ^ 2 hence , x = 42 . cross check by putting in eq ( a ) = x ( x + 1 ) / 2 = t = > 42 * 43 / 2 = 903 hence , answer is a ."
Answer: a
Python program:
a = 4 * 100
b = 253 - a
c = 4 * 100
d = 253 - c
e = d * 2
f = e + 1 
g = b * f
Problem: a new home buyer pays 4 % annual interest on her first mortgage and 9 % annual interest on her second mortgage . if she borrowed a total of $ 310,000 , 80 % of which was in the first mortgage , what is her approximate monthly interest payment ?
Options: a ) $ 1,292 , b ) $ 1,733 , c ) $ 3,466 , d ) $ 12,917 , e ) $ 20,796
Rationale: 0.04 x + 0.09 y = 310000 [ 1 ] 0.04 x = 0.80 * 310000 = 248000 [ 2 ] 248000 + 0.09 y = 310000 - - > 0.09 y = 62000 [ 3 ] 248000 / 12 = 258333.3333 [ 4 ] 62000 / 12 = 5166.67 [ 5 ] adding [ 4,5 ] we get : 25833 [ 6 ] dividing [ 6 ] / 2 to get an average we get 1.292 , ans a
Answer: a
Python program:
a = 4 * 2
b = 9 - a
Problem: what is ( 16 ^ 7 + 16 ) / 16 ?
Options: a ) 15467118 , b ) 16777217 , c ) 17827343 , d ) 18047455 , e ) 19357579
Rationale: "( 16 ^ 7 + 16 ) / 16 = 16 * ( 16 ^ 6 + 1 ) / 16 = 16 ^ 6 + 1 clearly this is a number which ends with a 7 in the units place . the answer is b ."
Answer: b
Python program:
a = 16 ** 7
b = a + 16 
c = b / 16
Problem: if the sum of a number and its square is 240 , what is the number ?
Options: a ) 15 , b ) 77 , c ) 25 , d ) 87 , e ) 171
Rationale: "explanation : let the integer be x . then , x + x 2 = 240 x 2 + x - 240 = 0 ( x + 16 ) ( x – 15 ) = 0 x = 15 answer : a"
Answer: a
Python program:
a = math.sqrt(240)
b = math.floor(a)
Problem: youseff lives x blocks from his office . it takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work . it is takes him exactly 6 minutes more to walk to work than to ride his bike to work , then x equals ?
Options: a ) 4 , b ) 7 , c ) 9 , d ) 15 , e ) 20
Rationale: "please follow posting guidelines , link is in my signatures . as for your question , x / 60 = blocks / time / block = block ^ 2 / time . this is not what you want . you are given x blocks and 60 seconds per block . thus you need to put it as 60 * x to give you units of seconds as you are equating this to 360 ( which is time in seconds . ) . thus the correct equation is : 60 * x - 20 * x = 360 - - - - > 40 x = 360 - - > x = 9 . option c"
Answer: c
Python program:
a = 6 * 3
b = a / 2
Problem: two family reunions are happening at the leela hotel , the oates reunion and the hall reunion . all 100 guests at the hotel attend at least one of the reunions . if 50 people attend the oates reunion and 62 people attend the hall reunion , how many people attend both reunions ?
Options: a ) 2 , b ) 5 , c ) 12 , d ) 16 , e ) 22
Rationale: no of people in oates reunion = 50 no of people in hall reunion = 62 attending both = x all guests attend at least one . therefore , 100 = 50 + 62 - ( both ) both = 12 answer c
Answer: c
Python program:
a = 62 - 50
Problem: ashok and pyarelal invested money together in a business and share a capital of ashok is 1 / 9 of that of pyarelal . if the incur a loss of rs 1600 then loss of pyarelal ?
Options: a ) 600 , b ) 700 , c ) 840 , d ) 940 , e ) 1440
Rationale: "let the capital of pyarelal be x , then capital of ashok = x / 9 so ratio of investment of pyarelal and ashok = x : x / 9 = 9 x : x hence out of the total loss of 1600 , loss of pyarelal = 1600 * 9 x / 10 x = 1440 answer : e"
Answer: e
Python program:
a = 9 * 1600
b = 1 + 9 
c = a / b
Problem: following an increase in prices , the price of a candy box was 10 pounds and the price of a can of soda was 9 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ?
Options: a ) 11 . , b ) 12 . , c ) 13 . , d ) 14 . , e ) 14.5
Rationale: "price of candy before price increase = 10 / 1.25 = 8 price of soda before price increase = 9 / 1.5 = 6 total price = 8 + 6 = 14 d is the answer"
Answer: d
Python program:
a = 10 * 100
b = 100 + 25 
c = a / b
d = 9 * 100
e = 100 + 50 
f = d / e
g = c + f
Problem: in a factory , an average of 65 tv ' s are produced per day for the fist 25 days of the months . a few workers fell ill for the next 5 days reducing the daily avg for the month to 60 sets / day . the average production per day for day last 5 days is ?
Options: a ) 20 , b ) 35 , c ) 48 , d ) 50 , e ) 59
Rationale: "production during these 5 days = total production in a month - production in first 25 days . = 30 x 60 - 25 x 65 = 175 ∴ average for last 5 days = 175 / 5 = 35 aswer : b"
Answer: b
Python program:
a = 25 + 5 
b = a * 60
c = 25 * 65
d = b - c
e = d / 5
Problem: how many integers k greater than 100 and less than 1000 are there such that if the hundreds and the unit digits of k are reversed , the resulting integer is k + 99 ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: kk is 3 - digit integer . any 3 digit integer can be expressed as 100 a + 10 b + c 100 a + 10 b + c . now , we are told that ( 100 a + 10 b + c ) + 99 = 100 c + 10 b + a ( 100 a + 10 b + c ) + 99 = 100 c + 10 b + a - - > 99 c − 99 a = 9999 c − 99 a = 99 - - > c − a = 1 c − a = 1 - - > there are 8 pairs of cc and aa possible such that their difference to be 1 : ( 9,8 ) , ( 8,7 ) , . . . , and ( 2,1 ) ( note that aa can not be 0 as kk is 3 - digit integer and its hundreds digit , aa , is more than or equal to 1 ) . also , bb , tens digit of kk , could tale 10 values ( 0 , 1 , . . . , 9 ) so there are total of 8 * 10 = 80 such numbers possible . example : 102 - 201 ; 112 - 211 ; 122 - 221 ; . . . 899 - 998 . answer : d .
Answer: d
Python program:
a = 10 - 2
b = 10 * a
Problem: if 225 / 999 = 0.225 , what is the 81 st digit to the right of the decimal point in the decimal equivalent of the fraction ?
Options: a ) 9 , b ) 8 , c ) 7 , d ) 6 , e ) 5
Rationale: "0 . [ u ] 225 [ / u = 0.225225225 . . . . . every 3 rd digit is 5 and every multiple of 3 will be the digit 5 . since 81 is multiple of 3 , the 81 st digit is 5 . answer e"
Answer: e
Python program:
a = 2 + 3
Problem: if the numerator of a fraction is increased by 20 % and its denominator is diminished by 25 % value of the fraction is 2 / 15 . find the original fraction .
Options: a ) 1 / 12 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 4 , e ) 1 / 2
Rationale: x * ( 120 / 100 ) - - - - - - - - - - - - - - - - = 2 / 15 y * ( 75 / 100 ) x / y = 1 / 12 answer : a
Answer: a
Python program:
a = 2 / 15
b = 20 + 100 
c = b / 100
d = 100 - 25
e = d / 100
f = c / e
g = a / f
Problem: . 007 / ? = . 01
Options: a ) . 7 , b ) . 07 , c ) . 007 , d ) . 0007 , e ) none of them
Rationale: "let . 007 / x = . 01 ; then x = . 007 / . 01 = . 7 / 1 = . 7 answer is a"
Answer: a
Python program:
a = 7 / 1000
b = 1 / 100
c = a / b
Problem: jerry went to a shop and bought things worth rs . 30 , out of which 30 % went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
Options: a ) 19 , b ) 19.7 , c ) 21.3 , d ) 21.5 , e ) 24.7
Rationale: "total cost of the items he purchased = rs . 30 given that out of this rs . 30 , 30 % is given as tax = > total tax incurred = 30 % = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 30 − 30 / 100 − x ) 6 / 100 = 30 / 100 ⇒ 6 ( 30 − 0.3 − x ) = 30 ⇒ ( 30 − 0.3 − x ) = 5 ⇒ x = 30 − 0.3 − 5 = 24.7 e )"
Answer: e
Python program:
a = 30 / 100
b = 100 / 6
c = a * b
d = 30 / 100
e = c + d 
f = 30 - e
Problem: a train 250 m long is running at a speed of 27 km / hr . in what time will it pass a bridge 200 m long ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "speed = 27 * 5 / 18 = 15 / 2 m / sec total distance covered = 250 + 200 = 450 m required time = 450 * 2 / 15 = 60 sec answer : e"
Answer: e
Python program:
a = 27 - 200
b = a * const_0_2778
c = 250 / b
Problem: if 75 percent of a class answered the first question on a certain test correctly , 35 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 ) 10 % , b ) ( 8 ) 20 % , c ) 30 % , d ) 50 % , e ) 65 %
Rationale: "i did n ' t understand how to connect 20 percent with the whole equation . why 20 is out of the percentile diagram ( circles ) but inside of 100 ? 20 % appeared in the exam ; however did not answer question aquestion b correctly so they are out of the two circles , however as they have appeared in the exam , they have to be taken into consideration for calculation purpose i am doing it this way : suppose the total class size is 100 , then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both . now , 100 - [ ( 75 - x ) + x + ( 35 - x ) ] = 20 . . . . . . . . . . values are in percent x = 20 - 100 + 110 x = 30 ans : c"
Answer: c
Python program:
a = 75 + 35 
b = a + 20 
c = b - 100
Problem: fresh grapes contain 90 % by weight while dried grapes contain 20 % water by weight . what is the weight of dry grapes available from 30 kg of fresh grapes ?
Options: a ) 3.75 kg , b ) 2.4 kg , c ) 2.5 kg , d ) 10 kg , e ) none of these
Rationale: "the weight of non - water in 30 kg of fresh grapes ( which is 100 - 90 = 10 % of whole weight ) will be the same as the weight of non - water in x kg of dried grapes ( which is 100 - 20 = 80 % of whole weight ) , so 30 â ˆ — 0.1 = x â ˆ — 0.8 - - > x = 3.75 answer : a"
Answer: a
Python program:
a = 100 - 90
b = a * 30
c = b / 100
d = 100 - 20
e = c / d
f = e * 100
Problem: what least number must be added to 1056 , so that the sum is completely divisible by 23 ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "23 ) 1056 ( 45 92 - - - 136 115 - - - 21 - - - required number = ( 23 - 21 ) = 2 . a )"
Answer: a
Python program:
a = 4 * 10
b = a + 2 
c = b * 23
d = c - 1056
Problem: 4 ! / ( 4 - 3 ) ! = ?
Options: a ) 24 , b ) 34 , c ) 35 , d ) 36 , e ) 39
Rationale: 4 ! / ( 4 - 3 ) ! = 4 ! / 1 ! = 4 * 3 * 2 = 24 . hence , the correct answer is a .
Answer: a
Python program:
a = math.factorial(4)
b = 4 - 3
c = math.factorial(b)
d = a / c
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 1.5 kilometers per hour , what was her average speed ( in kilometers per hour ) while climbing to the top ?
Options: a ) 1.065 , b ) 1.125 , c ) 1.225 , d ) 1.375 , e ) 1.425
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 1.5 km / hour x / 3 = 1.5 x = 4.5 km the average speed while climbing = distance / time = 4.5 / 4 = 1.125 km / h the answer is b ."
Answer: b
Python program:
a = 4 + 2 
b = a * 1
c = b / 2
d = c / 4
Problem: 5358 x 61 = ?
Options: a ) 326838 , b ) 323758 , c ) 323298 , d ) 273258 , e ) 327382
Rationale: "a 5358 x 61 = 5358 x ( 60 + 1 ) = 5358 x 60 + 5358 x 1 = 321480 + 5358 = 326838 ."
Answer: a
Python program:
a = 5358 / 61
b = a * 100
Problem: if n = 4 ^ 11 – 4 , what is the units digit of n ?
Options: a ) 0 , b ) 1 , c ) 4 , d ) 6 , e ) 8
Rationale: always divide the power ( incase 11 ) by 4 and use the remainder as the new power . the question now becomes 4 ^ 3 - 4 . now 4 ^ 3 has last digit 4 . , we subtract 4 from 4 = 0 is the answer . option a
Answer: a
Python program:
a = math.log(4)
b = 4 ** 11
c = math.log(b)
d = a / c
Problem: company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 2 / 3 were basic and the rest were deluxe . if it takes 11 / 5 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 11 / 21 , b ) 14 / 31 , c ) 7 / 15 , d ) 17 / 35 , e ) 1 / 2
Rationale: "# of basic stereos was 2 / 3 of total and # of deluxe stereos was 1 / 3 of total , let ' s assume total = 15 , then basic = 10 and deluxe = 5 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 11 / 5 units . total time for basic would be 10 * 1 = 10 and total time for deluxe would be 5 * 11 / 5 = 11 - - > total time for both of them would be 10 + 11 = 21 - - > deluxe / total = 11 / 21 . answer : a ."
Answer: a
Python program:
a = 3 + 2 
b = a / 10
Problem: after decreasing 24 % in the price of an article costs rs . 608 . find the actual cost of an article ?
Options: a ) 128 , b ) 277 , c ) 800 , d ) 2688 , e ) 1991
Rationale: "cp * ( 76 / 100 ) = 608 cp = 8 * 100 = > cp = 800 answer : c"
Answer: c
Python program:
a = 24 / 100
b = 1 - a
c = 608 / b
Problem: in a zoo there are 30 penguins , 22 zebras , and 8 tigers with some zookeepers . if the total number of heads are 132 less than the number of feet , the number of zookeepers is
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 22
Rationale: explanation : let number of zookeepers be x . then , total number of feet = 2 x 30 + 4 x 22 + 4 x 8 + 2 x = 2 x + 180 . total number of heads = 30 + 22 + 8 + x = 60 + x . therefore ( 2 x + 180 ) - 132 = ( 60 + x ) + or x = 12 . answer : a
Answer: a
Python program:
a = 30 * 2
b = 30 * 2
c = 22 * 4
d = b + c 
e = 8 * 4
f = d + e 
g = f - 132
h = a - g
Problem: what is the greatest number of identical bouquets that can be made out of 21 white and 91 red tulips if no flowers are to be left out ? ( two bouquets are identical whenever the number of red tulips in the two bouquets is equal and the number of white tulips in the two bouquets is equal )
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: since no flowers are to be left out , then the number of bouquets must be a factor of both 21 and 91 . for example , we can not have 2 bouquets since we can not divide 91 red tulips into 2 bouquets without one tulip left over . only answer choice which is a factor of 91 is e ( 7 ) . answer : e .
Answer: e
Python program:
a = 21 / 3
Problem: what least number must be added to 1049 , so that the sum is completely divisible by 25 ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 1
Rationale: if we divide 1049 by 25 remainder is 24 25 - 24 = 1 answer : e
Answer: e
Python program:
a = 4 * 10
b = a + 2 
c = b * 25
d = c - 1049
Problem: man can row upstream at 25 kmph and downstream at 35 kmph , and then find the speed of the man in still water ?
Options: a ) 12 , b ) 22 , c ) 30 , d ) 88 , e ) 13
Rationale: "us = 25 ds = 35 m = ( 35 + 25 ) / 2 = 30 answer : c"
Answer: c
Python program:
a = 25 + 35 
b = a / 2
Problem: according to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . how many 10 - ounce cans of the concentrate are required to prepare 200 6 - ounce servings of orange juice ?
Options: a ) 25 , b ) 34 , c ) 30 , d ) 67 , e ) 100
Rationale: "orange juice concentrate : water : : 1 : 3 total quantity of orange juice = 200 * 6 = 1200 oz so orange juice concentrate : water : : 300 oz : 900 oz no . of 10 oz can = 300 oz / 10 oz = 30 answer c , 30 cans"
Answer: c
Python program:
a = 6 * 200
b = 200 / 10
c = a / b
Problem: when positive integer n is divided by positive integer j , the remainder is 14 . if n / j = 213.28 , what is value of j ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 50 , e ) 60
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 = 213.28 here 213 is the quotient . given that remainder = 14 so , 213.28 = 213 + 14 / j so , j = 50"
Answer: d
Python program:
a = 4 * 10
b = a + 2 
c = 100 + b 
d = 213 - 28
e = 14 / d
Problem: if the cost price of 50 articles is equal to the selling price of 30 articles , then the gain or loss percent is ?
Options: a ) 16 , b ) 127 , c ) 12 , d ) 18 , e ) 67
Rationale: "percentage of profit = 20 / 30 * 100 = 67 % answer : e"
Answer: e
Python program:
a = 100 * 30
b = a / 50
c = 100 - b
d = 100 * 30
e = d / 50
f = c / e
g = 100 * f
Problem: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 percent of the distribution lies within one standard deviation d of the mean , what percent w of the distribution is less than m + d ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "d the prompt says that 68 % of the population lies between m - d and m + d . thus , 32 % of the population is less than m - d or greater than m + d . since the population is symmetric , half of this 32 % is less than m - d and half is greater than m + d . thus , w = ( 68 + 16 ) % or ( 100 - 16 ) % of the population is less than m + d ."
Answer: d
Python program:
a = 100 - 68
b = a / 2
c = 100 - b