euclaise/mathqa_programs huggingface dataset:
Problem: sandy walked 20 meters towards south . then sandy turned to her left and walked 25 meters . she then turned to her left and walked 20 meters . she then turned to her right and walked 30 meters . what distance is she from the starting point and in which direction ?
Options: a ) 35 m east , b ) 35 m north , c ) 30 m west , d ) 45 m west , e ) 55 m east
Rationale: "the net distance is 25 + 30 = 55 meters to the east . the answer is e ."
Answer: e
Python program:
a = 20 + 30
Problem: in a sample of associates at a law firm , 25 percent are second - year associates , and 75 percent are not first - year associates . what percentage of the associates at the law firm have been there for more than two years ?
Options: a ) 0 , b ) 25 , c ) 50 , d ) 75 , e ) 100
Rationale: "75 percent are not first - year associates - - > this means 75 percent associates are either two or more than two years already , we know % of second - year associates = 25 % so , % of associates there for more than two years = 75 % - 25 % = 50 % . . = > ( c ) . . is it correct ?"
Answer: c
Python program:
a = 75 - 25
Problem: if ( 2 to the x ) - ( 2 to the ( x - 2 ) ) = 3 ( 2 to the 10 ) , what is the value of x ?
Options: a ) 9 , b ) 11 , c ) 13 , d ) 12 , e ) 17
Rationale: "( 2 to the power x ) - ( 2 to the power ( x - 2 ) ) = 3 ( 2 to the power 10 ) 2 ^ x - 2 ^ ( x - 2 ) = 3 . 2 ^ 10 hence x = 12 . answer is d"
Answer: d
Python program:
a = 10 + 2
Problem: a special municipal payroll tax charges not tax on a payroll less than $ 300,000 and only 1 % on a company ’ s payroll above $ 300,000 . if belfried industries paid $ 200 in this special municipal payroll tax , then they must have had a payroll of ?
Options: a ) $ 180,000 , b ) $ 202,000 , c ) $ 230,000 , d ) $ 400,000 , e ) $ 2 , 200,000
Rationale: "answer : c , ( with different approach ) : the 300 paid is 1 % of the additional amount above 200,000 . let it be x now 1 % of x = 300 therefore x = 30,000 total = 200,000 + x = 230,000"
Answer: c
Python program:
a = 200 * 100
b = a * 10
Problem: the compound interest earned by sunil on a certain amount at the end of two years at the rate of 8 % p . a . was rs . 2828.80 . find the total amount that sunil got back at the end of two years in the form of principal plus interest earned .
Options: a ) rs . 18 , 828.80 , b ) rs . 19 , 828.80 , c ) rs . 18 , 028.80 , d ) rs . 17 , 828.80 , e ) none of these
Rationale: "let the sum be rs . p p { [ 1 + 8 / 100 ] 2 - 1 } = 2828.80 p ( 8 / 100 ) ( 2 + 8 / 100 ) = 2828.80 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 2828.80 / ( 0.08 ) ( 2.08 ) = 1360 / 0.08 = 17000 principal + interest = rs . 19828.80 answer : b"
Answer: b
Python program:
a = 8 / 100
b = 1 + a 
c = b ** 2
d = c - 1
e = 2828 / 80
f = e + 2828
Problem: in a certain large company , the ratio of college graduates with a graduate degree to non - college graduates is 1 : 8 , and ratio of college graduates without a graduate degree to non - college graduates is 2 : 3 . if one picks a random college graduate at this large company , what is the probability r this college graduate has a graduate degree ?
Options: a ) 1 / 11 , b ) 1 / 12 , c ) 1 / 13 , d ) 3 / 19 , e ) 3 / 43
Rationale: "in believe the answer is d . please see below for explanation . 0 ) we are told the following ratios cgd - college graduate with degree ncg - non college graduate cgn - college graduate no degree cgd ncg cgn 1 8 3 2 in order to make cgd and cgn comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get cgd ncg cgn 3 24 16 if one picks a random college graduate at this large company , what is the probability this college graduate has a graduate degree ? nr of cgd = 3 nr of cg = 3 + 16 = 19 probability r of cgd / ( cg ) - > 3 / 19 answer d"
Answer: d
Python program:
a = 1 / 8
b = 2 / 3
c = a / b
d = 1 / 8
e = 2 / 3
f = d / e
g = f + 1 
h = c / g
Problem: if a / b = 5 / 4 , then ( 4 a + 3 b ) / ( 4 a - 3 b ) = ?
Options: a ) 7 , b ) 6 , c ) 3 , d ) 5 , e ) 4
Rationale: "answer dividing numerator as well as denominator by b , we get given exp . = ( 4 a + 3 b ) / ( 4 a - 3 b ) = ( 4 a / b + 3 ) / ( 4 a / b - 3 ) since a / b = 5 / 4 this implies that = [ ( 4 * 5 ) / 4 + 3 ] / [ ( 4 * 5 ) / 4 - 3 ) ] = ( 5 + 3 ) / ( 5 - 3 ) = 4 option : e"
Answer: e
Python program:
a = 4 * 5
b = 3 * 4
c = a + b 
d = 4 * 5
e = 3 * 4
f = d - e
g = c / f
Problem: total 63 matches are conducted in knockout match type . how many players will be participated in that tournament ?
Options: a ) 60 , b ) 61 , c ) 62 , d ) 63 , e ) 64
Rationale: "64 players answer : e"
Answer: e
Python program:
a = 63 + 1
Problem: if f ( f ( n ) ) + f ( n ) = 2 n + 3 , f ( 0 ) = 1 then f ( 2012 ) = ?
Options: a ) 2013 , b ) 2088 , c ) 270 , d ) 1881 , e ) 1781
Rationale: "f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 ⇒ ⇒ f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 ⇒ ⇒ f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 ⇒ ⇒ f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2012 ) = 2013 ans : a"
Answer: a
Python program:
a = 1 + 2012
Problem: what is ( 21 ^ 7 + 21 ) / 21 ?
Options: a ) 82216043 , b ) 83786095 , c ) 84316108 , d ) 85766122 , e ) 86426237
Rationale: ( 21 ^ 7 + 21 ) / 21 = 21 * ( 21 ^ 6 + 1 ) / 21 = 21 ^ 6 + 1 clearly this is a number which ends with a 2 in the units place . the answer is d .
Answer: d
Python program:
a = 21 ** 7
b = a + 21 
c = b / 21
Problem: if 102 x = 25 , then 10 - x equals :
Options: a ) a ) 3 , b ) b ) 2 , c ) c ) 6 , d ) d ) 9 , e ) e ) 1 / 5
Rationale: "102 x = 25 ( 10 x ) 2 = 52 10 x = 5 1 / 10 x = 1 / 5 10 - x = 1 / 5 answer : e"
Answer: e
Python program:
a = 102 * 100
b = a / 2
c = b - 2
d = 102 * 100
e = d / 2
f = e + 2 
g = c / f
Problem: in an examination 35 % of the students passed and 520 failed . how many students appeared for the examination ?
Options: a ) a ) 540 , b ) b ) 400 , c ) c ) 800 , d ) d ) 650 , e ) e ) 840
Rationale: "let the number of students appeared be x then , 65 % of x = 520 65 x / 100 = 520 x = 520 * 100 / 65 = 800 answer is c"
Answer: c
Python program:
a = 520 * 100
b = 100 - 35
c = a / b
Problem: a train crosses a platform of 170 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ?
Options: a ) 70 , b ) 88 , c ) 167 , d ) 197 , e ) 161
Rationale: "length of the train be ‘ x ’ x + 170 / 15 = x + 250 / 20 20 x + 3400 = 15 x + 3750 5 x = 350 x = 70 m answer : a"
Answer: a
Python program:
a = 15 / 3
b = 15 / a
c = 250 * b
d = 15 / 3
e = 20 / d
f = 170 * e
g = c - f
Problem: a 6 litre sol is 25 % alcohol . how many litres of pure alcohol must be added to produce a sol that is 50 % alcohol ?
Options: a ) a . 0.6 , b ) b . 1 , c ) c . 2.1 , d ) d . 3 , e ) e . 5.4
Rationale: "25 % of 6 = 1.5 50 % of 6 = 3 shortage is 1.5 so we need to have 1.5 / 50 % to get 50 % alcohol content . = 3 d"
Answer: d
Python program:
a = 25 / 100
b = a * 6
c = 2 * b
d = 6 - c
Problem: the ratio of incomes of two person p 1 and p 2 is 5 : 4 and the ratio of their expenditures is 3 : 2 . if at the end of the year , each saves rs . 2000 , then what is the income of p 1 ?
Options: a ) s . 5000 , b ) s . 2400 , c ) s . 4000 , d ) s . 3200 , e ) s . 4200
Rationale: "let the income of p 1 and p 2 be rs . 5 x and rs . 4 x respectively and let their expenditures be rs . 3 y and 2 y respectively . then , 5 x – 3 y = 2000 … ( i ) and 4 x – 2 y = 2000 … … . . ( ii ) on multiplying ( i ) by 2 , ( ii ) by 3 and subtracting , we get : 2 x = 2000 - > x = 1000 p 1 ’ s income = rs 5 * 1000 = rs . 5000 answer : a"
Answer: a
Python program:
a = 2000 / 2
b = a * 3
c = b - 2000
d = c * 5
Problem: cubes with each side one inch long are glued together to form a larger cube . the larger cube ' s face is painted with red color and the entire assembly is taken apart . 26 small cubes are found with no paints on them . how many of unit cubes have at least one face that is painted red ?
Options: a ) 64 , b ) 72 , c ) 86 , d ) 98 , e ) 99
Rationale: "use the options . the options which after getting added to 26 shows a cube of a number could be right . here 64 + 26 = 90 72 + 26 = 98 86 + 26 = 112 98 + 26 + 124 99 + 26 = 125 - - - ( 5 * 5 * 5 ) so we have 99 as the answer ! e"
Answer: e
Python program:
a = 1 + 3 
b = 1 + a 
c = b ** 3
d = c - 26
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 320 points , how many points is the third question worth ?
Options: a ) 39 , b ) 24 , c ) 22 , d ) 20 , e ) 18
Rationale: "x x + 4 x + 8 x + 12 x + 16 x + 20 x + 24 x + 28 x + 32 x + 36 10 x + 180 = 320 10 x = 140 x = 14 3 rd question = x + 8 = 14 + 8 = 22 answer c"
Answer: c
Python program:
a = 320 / 10
b = 10 - 4
c = b - 1
d = a + c
Problem: it takes 30 days to fill a laboratory dish with bacteria . if the size of the bacteria doubles each day , how long did it take for the bacteria to fill 1 / 32 of the dish ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: "the bacteria doubles each day , so after 29 days , the dish was half full . after 28 days , the dish was one quarter full . after 27 days , the dish was one eighth full . after 26 days , the dish was one sixteenth full . after 25 days , the dish was 1 / 32 full . the answer is a ."
Answer: a
Python program:
a = math.log(32)
b = 30 - a
Problem: rahim bought 32 books for rs . 1500 from one shop and 60 books for rs . 340 from another . what is the average price he paid per book ?
Options: a ) s . 17 , b ) s . 18 , c ) s . 12 , d ) s . 11 , e ) s . 20
Rationale: "average price per book = ( 1500 + 340 ) / ( 32 + 60 ) = 1840 / 92 = rs . 20 answer : e"
Answer: e
Python program:
a = 1500 + 340 
b = 32 + 60 
c = a / b
Problem: the average of numbers 0.64204 , 0.64203 , 0.64202 and 0.64201 is ?
Options: a ) 0.64202 , b ) 0.64204 , c ) 0.642022 , d ) 0.642025 , e ) none
Rationale: "answer average = ( 0.64204 + 0.64203 + 0.64202 + 0.64201 ) / 4 = 2.5681 / 4 = 0.642025 correct option : d"
Answer: d
Python program:
a = 0 * 64204
b = 0 * 64204
c = a + b 
d = c / 0
Problem: there are 16 teams in a tournament . if during the first round , each team plays every other team exactly once , how many games will be played in the first round ?
Options: a ) 15 , b ) 30 , c ) 120 , d ) 240 , e ) 256
Rationale: number of ways to pick 2 teams from a total of 16 = 16 c 2 = 16 ! / 14 ! * 2 ! = 120 . hence c .
Answer: c
Python program:
a = math.factorial(16)
b = 16 - 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e
Problem: there are 193 items that are members of set u . of these items , 49 are members of set b , 59 are not members of either of set a or set b , and 25 are members of both sets a and b . how many of the members of set u are members of set a ?
Options: a ) 72 , b ) 85 , c ) 110 , d ) 98 , e ) 108
Rationale: you had the answer almost right . the x = 85 refers to only set a . however what ' s being asked is how many members are part of set a . this will include : 1 . only set a 2 . set a and set b so the answer is set a = 85 + set ab = 85 + 25 = 110 c
Answer: c
Python program:
a = 193 - 59
b = a + 25 
c = b - 49
Problem: 18 balls are numbered 1 to 18 . a ball is drawn and then another ball is drawn without replacement . what is the probability that both balls have even numbers ?
Options: a ) 2 / 9 , b ) 4 / 17 , c ) 6 / 29 , d ) 8 / 35 , e ) 10 / 43
Rationale: "p ( 1 st ball is even ) = 9 / 18 p ( 2 nd ball is also even ) = 8 / 17 p ( both balls are even ) = 9 / 18 * 8 / 17 = 4 / 17 the answer is b ."
Answer: b
Python program:
a = 4 + 4 
b = a / 18
c = 4 + 4 
d = c - 1
e = 18 - 1
f = d / e
g = b * f
Problem: what is the probability that the sum of two dice will yield a 8 , and then when both are thrown again , their sum will again yield a 8 ? assume that each die has 7 sides with faces numbered 1 to 7 .
Options: a ) 1 / 144 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 49
Rationale: "solution - rolling dices is an independent event . the combinations to get 8 are ( 1,7 ) , ( 7,1 ) , ( 2,6 ) , ( 6,2 ) , ( 3,5 ) , ( 5,3 ) , ( 4 , , 4 ) and total combinations of both dices is 49 . the probability of getting 8 in first attempt is 7 / 49 = 1 / 7 . probability of getting 8 again in second attempt = ( 1 / 7 ) * ( 1 / 7 ) = 1 / 49 . ans e"
Answer: e
Python program:
a = 7 ** 2
b = 7 / a
c = 7 ** 2
d = 7 / c
e = b * d
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 15 seconds . find the length of the faster train ?
Options: a ) 270 , b ) 277 , c ) 187 , d ) 257 , e ) 150
Rationale: "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 15 sec = 15 * 10 = 150 m . the length of the faster train = 150 m . answer : e"
Answer: e
Python program:
a = 72 - 36
b = a / const_3_6
c = b * 15
Problem: a man swims downstream 72 km and upstream 45 km taking 12 hours each time ; what is the speed of the current ?
Options: a ) 1.125 , b ) 1.128 , c ) 1.126 , d ) 1.123 , e ) 1.121
Rationale: "72 - - - 12 ds = 6 ? - - - - 1 45 - - - - 12 us = 3.75 ? - - - - 1 s = ? s = ( 6 - 3.75 ) / 2 = 1.125 answer : a"
Answer: a
Python program:
a = 45 / 12
b = 72 / 12
c = a + b 
d = c / 2
Problem: find the simple interest on rs . 850 for 10 months at 7 paisa per month ?
Options: a ) s . 768 , b ) s . 329 , c ) s . 595 , d ) s . 600 , e ) s . 725
Rationale: "explanation : i = ( 850 * 10 * 7 ) / 100 = 595 answer : option c"
Answer: c
Python program:
a = 10 / 100
b = 850 * a
Problem: sandy bought 65 books for $ 1480 from one shop and 55 books for $ 920 from another shop . what is the average price that sandy paid per book ?
Options: a ) $ 38 , b ) $ 18 , c ) $ 99 , d ) $ 27 , e ) $ 20
Rationale: "average price per book = ( 1480 + 920 ) / ( 65 + 55 ) = 2400 / 120 = $ 20 the answer is e ."
Answer: e
Python program:
a = 1480 + 920 
b = 65 + 55 
c = a / b
Problem: how many of the positive divisors d of 120 are also multiples of 4 not including 120 ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 8 .
Rationale: "4 , 8,12 , 20,24 , 40,60 . ( 7 ) is the answer other way : factors of 120 = 2 ^ 3 * 3 * 5 separate 2 ^ 2 ( which means 4 ) now , calculate the number of other factors . d = 2 * 3 * 5 = total positive factors are 2 * 2 * 2 = 8 this 8 factors include 120 so subtract 1 from 8 ans is 7 = d"
Answer: d
Python program:
a = 120 / 4
b = a / 2
c = b / 3
Problem: calculate 1307 x 1307 = ?
Options: a ) 1601249 , b ) 1607249 , c ) 1701249 , d ) 1708249 , e ) none
Rationale: "answer 1307 x 1307 = ( 1307 ) 2 = ( 1300 + 7 ) 2 = ( 1300 ) 2 + ( 7 ) 2 + 2 x 1300 x 7 = 1690000 + 49 + 18200 = 1708249 option : d"
Answer: d
Python program:
a = 1307 * 1307
Problem: the hcf and lcm of two numbers m and n are respectively 6 and 210 . if m + n = 80 , then 1 / m + 1 / n is equal to
Options: a ) 1 / 35 , b ) 3 / 35 , c ) 5 / 37 , d ) 4 / 63 , e ) none
Rationale: "answer we have , m x n = 6 x 210 = 1260 â ˆ ´ 1 / m + 1 / n = ( m + n ) / mn = 80 / 1260 = 4 / 63 correct option : d"
Answer: d
Python program:
a = 6 * 210
b = 80 / a
Problem: bottle r contains 100 capsules and costs $ 6.30 . bottle t contains 130 capsules and costs $ 2.99 . what is the difference between the cost per capsule for bottle r and the cost per capsule for bottle t ?
Options: a ) $ 0.04 , b ) $ 0.12 , c ) $ 0.05 , d ) $ 0.03 , e ) $ 0.002
Rationale: "cost per capsule in r is 6.30 / 100 = 0.063 cost per capsule in t is 2.99 / 130 = 0.023 the difference is 0.004 the answer is a"
Answer: a
Python program:
a = 2 / 99
b = 6 / 30
c = a - b
Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 250 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?
Options: a ) 140 , b ) 146 , c ) 152 , d ) 162 , e ) 183
Rationale: "the probability of survival for each of the first 3 months of life is 1 - 1 / 10 = 9 / 10 , so of 250 newborn 250 * 9 / 10 * 9 / 10 * 9 / 10 = ~ 183 is expected to survive . answer : e ."
Answer: e
Python program:
a = 1 / 10
b = 1 - a
c = 250 * b
d = 1 / 10
e = 1 - d
f = c * e
g = 1 / 10
h = 1 - g
i = f * h
Problem: if 3 a = 4 b and ab ≠ 0 , what is the ratio of a / 4 to b / 3 ?
Options: a ) 64 / 27 , b ) 9 / 16 , c ) 1 , d ) 6 / 8 , e ) 8 / 6
Rationale: "a nice fast approach is the first find a pair of numbers that satisfy the given equation : 3 a = 4 b here ' s one pair : a = 4 and b = 3 what is the ratio of a / 9 to b / 8 ? in other words , what is the value of ( a / 4 ) / ( b / 3 ) ? plug in values to get : ( a / 4 ) / ( b / 3 ) = ( 4 / 4 ) / ( 3 / 3 ) = 1 / 1 = 1 c"
Answer: c
Python program:
a = 3 * 4
b = 4 * 3
c = a / b
Problem: what is the smallest integer x such that 2 x + 2 is divisible by 33 , 44 , 55 , and 666 ?
Options: a ) x = 53186760 , b ) x = 26593379 , c ) x = 73260 , d ) x = 36629 , e ) x = 6666
Rationale: 33 = 3 * 11 44 = 2 * 2 * 11 55 = 5 * 11 666 = 2 * 3 * 3 * 37 so 2 x + 2 = 2 * 2 * 3 * 3 * 5 * 11 * 37 = 73260 , and x = ( 73260 - 2 ) / 2 = 36629 , which is option d .
Answer: d
Python program:
a = math.lcm(33, 44)
b = math.lcm(a, 55)
c = math.lcm(b, 666)
d = c - 2
e = d / 2
Problem: if 12 men do a work in 80 days , in how many days will 20 men do it ?
Options: a ) 18 days , b ) 38 days , c ) 42 days , d ) 48 days , e ) 44 days
Rationale: "12 * 80 = 20 * x x = 48 days answer : d"
Answer: d
Python program:
a = 12 * 80
b = a / 20
Problem: 5358 x 81 = ?
Options: a ) 423762 , b ) 433758 , c ) 433298 , d ) 433998 , e ) 437382
Rationale: "d 273258 5358 x 81 = 5358 x ( 80 + 1 ) = 5358 x 80 + 5358 x 1 = 428640 + 5358 = 433998"
Answer: d
Python program:
a = 5358 / 81
b = a * 100
Problem: if the ratio of the sum of the first 6 terms of a g . p . to the sum of the first 3 terms of the g . p . is 126 , what is the common ratio of the g . p ?
Options: a ) 3 , b ) 1 / 3 , c ) 2 , d ) 5 , e ) 1 / 5
Rationale: "126 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 126 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2 . . . . . . . . . 126 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 125 = ( r ^ 3 ( 1 + r ^ 1 + r ^ 2 ) ) / ( ( 1 + r ^ 1 + r ^ 2 ) ) 125 = r ^ 3 r = 5 d"
Answer: d
Python program:
a = 126 - 1
b = 1 / 3
c = a ** b
Problem: there are 6 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 15 other amateurs , what is the total number of chess games possible to be played in the tournament ?
Options: a ) 10 , b ) 20 , c ) 45 , d ) 60 , e ) 120
Rationale: "each person is one participant of 6 games . so there are in all 6 * 15 = 90 instances of one participant games . but each game has 2 participants so total number of games = 90 / 2 = 45 c"
Answer: c
Python program:
a = 6 * 15
b = a / 2
Problem: tough and tricky questions : probability . medical analysts predict that a quarter of all people who are infected by a certain biological agent could be expected to be killed for each day that passes during which they have not received an antidote . what fraction of a group of 1000 people could be expected to be killed if infected and not treated for 3 full days ?
Options: a ) 37 / 64 , b ) 8 / 27 , c ) 2 / 3 , d ) 19 / 27 , e ) 65 / 81
Rationale: at the end of each day we will have 3 / 4 alive . so after 3 days we will have ( 3 / 4 ) ^ 3 people alive . therefore , fraction of dead people will be 1 - ( 3 / 4 ) ^ 3 = 37 / 64 . the correct answer is a .
Answer: a
Python program:
a = 3 + 1 
b = 1 / a
c = 3 + 1 
d = 1 / c
e = 1 - d
f = 3 + 1 
g = 1 / f
h = e * g
i = b + h 
j = 3 + 1 
k = 1 / j
l = 1 - k
m = 3 + 1 
n = 1 / m
o = l * n
p = 3 + 1 
q = 1 / p
r = o + q 
s = 1 - r
t = 3 + 1 
u = 1 / t
v = s * u
w = i + v
Problem: if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of rs . 10800 ?
Options: a ) 11 , b ) 13 , c ) 14 , d ) 18 , e ) 10
Rationale: "required difference = [ 3 ½ % of rs . 10800 ] – [ 3 1 / 3 % of rs . 10800 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 10800 = 1 / 6 % of rs . 10800 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 10800 ] = rs . 18 . answer is d ."
Answer: d
Python program:
a = 1 / 2
b = a + 3 
c = 1 / 3
d = c + 3 
e = b - d
f = e * 10800
g = f / 100
Problem: in 1985 a company sold a brand of shoes to retailers for a fixed price per pair . in 1986 the number of pairs of the shoes that the company sold to retailers decreased by 20 percent , while the price per pair increased by 20 percent . if the company ’ s revenue from the sale of the shoes in 1986 was $ 3.0 million , what was the approximate revenue from the sale of the shoes in 1985 ?
Options: a ) $ 2.4 million , b ) $ 2.9 million , c ) $ 3.0 million , d ) $ 3.1 million , e ) $ 3.6 million
Rationale: let the number of pairs of shoes sold in 1985 = n let price per pair of shoe sold in 1985 = p in 1986 , number of pairs of shoes sold decreased by 20 % = . 8 n price per pair increased by 20 % = 1.2 p company ' s revenue from sale of shoes in 1986 = 3 million $ = > . 8 n * 1.2 p = 3 = > . 96 np = 3 = > np = 3 / . 96 = 3.125 million $ answer d
Answer: d
Python program:
a = 100 - 20
b = a - 20
c = b / 20
Problem: the ratio of the volumes of two cubes is 3375 : 1331 . what is the ratio of their total surface areas ?
Options: a ) 225 : 121 , b ) 221 : 127 , c ) 225 : 191 , d ) 181 : 161 , e ) 81 : 182
Rationale: "explanation : ratio of the sides = ³ √ 3375 : ³ √ 1331 = 15 : 11 ratio of surface areas = 15 ^ 2 : 11 ^ 2 = 225 : 121 answer : option a"
Answer: a
Python program:
a = 3375 / 1331
b = 1 / 3
c = a ** b
Problem: a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 2 hours . if the company used the same number of each type of machine to do job in 12 hours , how many machine r were used ?
Options: a ) 3 / 4 , b ) 4 , c ) 18 / 19 , d ) 9 , e ) 12
Rationale: yes there is a typo in the question , i got the same ques on my gmat prep last week , and the questions goes as : a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 2 hours . if the company used the same number of each type of machine to do job in 2 hours , how many machine r were used ? so for a job to be done in 2 hours r = 1 / 2 r _ a ( rate of machine r ) = 1 / 36 r _ s ( rate of machine s ) = 1 / 2 lets say x machines are used to attain the desired rate , thus x / 36 + x / 2 = 1 / 2 ( desired r = 1 / 2 i . e . to complete the job in 2 hours ) ( x + 18 x ) / 36 = 1 / 2 19 x / 36 = 1 / 2 x = 18 / 19 . qa = 18 / 19 ( answer c )
Answer: c
Python program:
a = 1 / 36
b = 1 / 2
c = a + b 
d = 2 * c
e = 1 / d
Problem: the difference between compound and simple interest on a particular sum of money for 3 years at 6 and 2 / 3 % p . a is rs . 184 . what is the sum ?
Options: a ) 13000 , b ) 13500 , c ) 14000 , d ) 14500 , e ) 15000
Rationale: "p = ( 184 * 10 ^ 6 ) / ( 6 2 / 3 * 6 2 / 3 * ( 300 * 6 2 / 3 ) ) = = > 13500 answer b"
Answer: b
Python program:
a = 184 * 3
b = a * 3
c = b * 3
d = c * 6
e = d / 2
f = e - 1000
Problem: triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 36 , what is the measure of side xy ?
Options: a ) 4 , b ) 4 √ 2 , c ) 12 , d ) 8 √ 2 , e ) can not be determined from the information provided
Rationale: "ans c . . 12 . . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 36 or yz = 3 * \ sqrt { 2 } . . therefore hyp = xy = 12"
Answer: c
Python program:
a = math.sqrt(36)
b = math.sqrt(2)
c = a * b
d = c ** 2
e = math.sqrt(36)
f = math.sqrt(2)
g = e * f
h = g ** 2
i = d + h 
j = math.sqrt(i)