euclaise/mathqa_programs huggingface dataset:
Problem: how many positive integers less than 17 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3 ?
Options: a ) 14 , b ) 13 , c ) 12 , d ) 11 , e ) 10
Rationale: "the number = 2 a + 3 b < 17 when a = 1 , b = 1 , 2 , 3 , 4 , 5 - > 2 a = 2 ; 3 b = 3 , 6 , 9 , 12 , 15 - > the number = 5 , 8 , 11 , 14 - - > 4 numbers when a = 2 , b = 1,2 , 3,4 - > . . . . - - > 4 numbers when a = 3 , b = 1 , 2,3 - - > . . . . - - > 3 numbers total number is already 11 . look at the answer there is no number greater than 11 - - > we dont need to try any more answer must be d"
Answer: d
Python program:
a = 17 - 2
b = a - 4
c = b - 1
Problem: what least number should be added to 1056 , so that the sum is completely divisible by 23 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "that is 1056 / 23 = 45 remainder = 21 = > 21 + 2 = 23 hence 2 should be added to 1056 so that the sum will be divisible by 23 answer is option b"
Answer: b
Python program:
a = 23 - reminder
Problem: at a restaurant , glasses are stored in two different - sized boxes . one box contains 12 glasses , and the other contains 16 glasses . if the average number of glasses per box is 15 , and there are 16 more of the larger boxes , what is the total number of glasses t at the restaurant ? ( assume that all boxes are filled to capacity . )
Options: a ) 96 , b ) 240 , c ) t = 256 , d ) t = 384 , e ) t = 480
Rationale: "most test takers would recognize the system of equations in this prompt and just do algebra to get to the solution ( and that ' s fine ) . the wording of the prompt and the ' spread ' of the answer choices actually provide an interesting ' brute force ' shortcut that you can take advantage of to eliminate the 4 wrong answers . . . . we ' re told that there are 2 types of boxes : those that hold 12 glasses and those that hold 16 glasses . since the average number of boxes is 15 , we know that there must be at least some of each . we ' re also told that that there are 16 more of the larger boxes . this means , at the minimum , we have . . . 1 small box and 17 large boxes = 1 ( 12 ) + 17 ( 16 ) = 12 + 272 = 284 glasses at the minimum since the question asks for the total number of glasses , we can now eliminate answers a , b and c . . . . the difference in the number of boxes must be 16 though , so we could have . . . . 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc . with every additional small box + large box that we add , we add 12 + 16 = 28 more glasses . thus , we can justadd 28 suntil we hit the correct answer . . . . 284 + 28 = 312 312 + 28 = 340 340 + 28 = 368 368 + 28 = 396 at this point , we ' ve ' gone past ' answer d , so the correct answer must be answer e . . . . . but here ' s the proof . . . . 396 + 28 = 424 424 + 28 = 452 452 + 28 = 480 final answer : e"
Answer: e
Python program:
a = 16 * 2
b = a * 15
Problem: a discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price . if , during a special sale , an additional 20 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 200 before any discount ?
Options: a ) $ 112.00 , b ) $ 145.60 , c ) $ 163.80 , d ) $ 182.00 , e ) $ 100.00
Rationale: "since the question is essentially just about multiplication , you can do the various mathstepsin a variety of ways ( depending on whichever method you find easiest ) . we ' re told that the first discount is 10 % to 30 % , inclusive . we ' re told that the next discount is 20 % off of the discounted price . . . . we ' re told to maximize the discount ( thus , 30 % off the original price and then 20 % off of the discounted price ) . thatmathcan be written in a number of different ways ( fractions , decimals , etc . ) : 30 % off = ( 1 - . 3 ) = ( 1 - 30 / 100 ) = ( . 7 ) and the same can be done with the 20 % additional discount . . . the final price of an item that originally cost $ 200 would be . . . . . ( $ 200 ) ( . 7 ) ( . 8 ) = ( $ 200 ) ( . 56 ) = 112 final answer : a"
Answer: a
Python program:
a = 30 + 20 
b = a / 100
c = 200 * b
Problem: a train 550 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 30
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 550 * 3 / 55 = 30 sec . answer : option e"
Answer: e
Python program:
a = 60 + 6 
b = a * const_0_2778
c = 550 / b
Problem: students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 186 cms . what was the ratio of men to women ?
Options: a ) 5 : 2 , b ) 5 : 1 , c ) 5 : 3 , d ) 4 : 1 , e ) 3 : 1
Rationale: "we ' re given a few facts to work with : 1 ) the average height of the females is 170 cm 2 ) the average height of the males is 186 cm 3 ) the average of the group is 180 cm we ' re asked for the ratio of men to women . w = number of women m = number of men ( 170 w + 186 m ) / ( w + m ) = 180 170 w + 186 m = 180 w + 180 m 6 m = 10 w 3 m = 5 w m / w = 5 / 3 the ratio of men to women is 5 to 3 . c"
Answer: c
Python program:
a = 180 - 170
b = 186 - 180
c = a / b
Problem: a person travels equal distances with speeds of 3 km / hr , 4 km / hr and 5 km / hr and takes a total time of 50 minutes . the total distance is ?
Options: a ) 1 km , b ) 2 km , c ) 3.19 km , d ) 4 km , e ) 5 km
Rationale: "c 3 km let the total distance be 3 x km . then , x / 3 + x / 4 + x / 5 = 50 / 60 47 x / 60 = 50 / 60 = > x = 1.06 . total distance = 3 * 1.06 = 3.19 km ."
Answer: c
Python program:
a = 50 / const_60
b = 1 / 3
c = 1 / 4
d = b + c 
e = 1 / 5
f = d + e 
g = a / f
h = g * 3
i = h * 1000
Problem: how many digits are used to number a book containg 300 pages .
Options: a ) 694 , b ) 792 , c ) 698 , d ) 784 , e ) 789
Rationale: explanation : number of digits in 1 digit numbers = 1 to 9 = 9 number of digits in 2 digit numbers = 10 to 99 = 90 ( 2 ) = 180 number of digits in 3 digit numbers = 100 to 300 = 201 ( 3 ) = 603 total = 792 answer : option b
Answer: b
Python program:
a = 300 * 2
b = a + 100 
c = 100 - 4
d = c - 4
e = b + d
Problem: barbata invests $ 2800 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?
Options: a ) 1200 , b ) 3000 , c ) 1000 , d ) 1400 , e ) 2400
Rationale: "let the additional invested amount for 8 % interest be x ; equation will be ; 2800 + 0.05 * 2800 + x + 0.08 x = 2800 + x + 0.06 ( 2800 + x ) 0.05 * 2800 + 0.08 x = 0.06 x + 0.06 * 2800 0.02 x = 2800 ( 0.06 - 0.05 ) x = 2800 * 0.01 / 0.02 = 1400 ans : ` ` d ' '"
Answer: d
Python program:
a = 6 / 100
b = a * 2800
c = 5 / 100
d = 2800 * c
e = b - d
f = 8 / 100
g = 6 / 100
h = f - g
i = e / h
Problem: at what rate percent on simple interest will rs . 600 amount to rs . 950 in 5 years ?
Options: a ) 3.33 % , b ) 5.93 % , c ) 4.33 % , d ) 9.33 % , e ) 11.67 %
Rationale: "350 = ( 600 * 5 * r ) / 100 r = 11.67 % answer : e"
Answer: e
Python program:
a = 950 - 600
b = a / 600
c = b / 5
d = c * 100
Problem: a , b and c can do a work in 90 , 45 and 6 days respectively . if they work together , in how many days will they complete the work ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 11
Rationale: one days ' s work of a , b and c = 1 / 90 + 1 / 45 + 1 / 6 = ( 1 + 2 + 15 ) / 90 = 1 / 5 a , b and c together can do the work in 5 days . answer : a
Answer: a
Python program:
a = 1 / 6
b = 1 / 90
c = 1 / 45
d = b + c 
e = a + d 
f = 1/(e)
Problem: a man can row upstream at 25 kmph and downstream at 41 kmph , and then find the speed of the man in still water ?
Options: a ) 33 , b ) 67 , c ) 30 , d ) 15 , e ) 17
Rationale: "us = 25 ds = 41 m = ( 41 + 25 ) / 2 = 33 answer : a"
Answer: a
Python program:
a = 25 + 41 
b = a / 2
Problem: i bought two books ; for rs . 450 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) 337 , b ) 262.5 , c ) 299.5 , d ) 266.5 , e ) 299
Rationale: "x * ( 85 / 100 ) = ( 450 - x ) 119 / 100 x = 262.5 answer : b"
Answer: b
Python program:
a = 100 + 19 
b = 450 * a
c = 100 - 15
d = 100 + 19 
e = c + d 
f = b / e
Problem: how many multiples of 5 are there between 1 and 100 ( both are inclusive ) ?
Options: a ) 1.2 , b ) 20.8 , c ) 2.3 , d ) 6.7 , e ) 8.2
Rationale: "the answer is ( 100 - 1 ) / 5 + 1 = 20.8 answer is b"
Answer: b
Python program:
a = 100 - 1
b = a / 5
c = b + 1
Problem: when a certain tree was first planted , it was 4 feet tall , and the height of the tree increased by a constant amount each year for the next 6 years . at the end of the 6 th year , the tree was 2 / 5 taller than it was at the end of the 4 th year . by how many feet did the height of the tree increase each year ?
Options: a ) 3 / 10 , b ) 2 / 5 , c ) 1 / 2 , d ) 4 , e ) 6 / 5
Rationale: "say , the tree grows by x feet every year . then , 4 + 6 x = ( 1 + 2 / 5 ) ( 4 + 4 x ) or , x = 4 answer d"
Answer: d
Python program:
a = 6 - 4
b = a * 5
c = b - 4
d = 4 / c
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 14 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 98 %
Rationale: 0,098 r = x / 100 * 0.1 r answer e
Answer: e
Python program:
a = 30 / 100
b = 1 - a
c = 14 / 100
d = b * c
e = 10 / 100
f = d / e
g = f * 100
Problem: the speed of a train is 110 kmph . what is the distance covered by it in 11 minutes ?
Options: a ) 15 kmph , b ) 11 kmph , c ) 88 kmph , d ) 20 kmph , e ) 12 kmph
Rationale: "110 * 11 / 60 = 20 kmph answer : d"
Answer: d
Python program:
a = 11 / const_60
b = a * 110
Problem: a sum of money at simple interest amounts to rs . 2240 in 2 years and to rs . 2600 in 5 years . the sum is :
Options: a ) rs . 1500 , b ) rs . 2000 , c ) rs . 1000 , d ) rs . 1200 , e ) rs . 1800
Rationale: "s . i . for 3 years = rs . ( 2600 - 2240 ) = rs . 360 . s . i . for 1 year = rs . 360 / 3 = rs . 120 . s . i . for 2 years = rs . ( 120 x 2 ) = rs . 240 . principal = rs . ( 2240 - 240 ) = rs . 2000 . answer : option b"
Answer: b
Python program:
a = 2600 - 2240
b = a * 2
c = b / 5
d = 2240 - c
Problem: mother , her daughter and her grand child weighs 120 kg . daughter and her daughter ( child ) weighs 60 kg . child is 1 / 5 th of her grand mother . what is the age of the daughter ?
Options: a ) 46 , b ) 47 , c ) 48 , d ) 49 , e ) 50
Rationale: "mother + daughter + child = 120 kg daughter + child = 60 kg mother = 120 - 60 = 60 kg child = 1 / 5 th of mother = ( 1 / 5 ) * 60 = 12 kg so now daughter = 120 - ( mother + child ) = 120 - ( 60 + 12 ) = 48 kg answer : c"
Answer: c
Python program:
a = 120 - 60
b = a / 5
c = 60 - b
Problem: a meeting has to be conducted with 5 managers . find the number of ways in which the managers may be selected from among 8 managers , if 2 managers will not attend the meeting together .
Options: a ) 1.35 , b ) 2.91 , c ) 3.12 , d ) 4.36 , e ) 5.15
Rationale: "8 managers , but two of them can not attend the meeting together . we can split it into two cases . 1 . meeting without these two managers in it . that would mean selecting 5 , from the remaining 6 which is 6 c 5 = 6 2 . meeting with one of the two managers . select 1 manager from two , and then select 4 from the remaining 6 , which is 2 c 1 x 6 c 4 = 15 . so , answer is 30 + 6 = 36 . answer : d"
Answer: d
Python program:
a = math.comb(8, 5)
b = 8 - 2
c = math.comb(b, 2)
d = a - c
Problem: 150 is what percent of 60 ?
Options: a ) 250 % , b ) 20 % , c ) 50 % , d ) 200 % , e ) 500 %
Rationale: "60 * x = 150 - - > x = 2.5 - - > 2.5 expressed as percent is 250 % . answer : a ."
Answer: a
Python program:
a = 150 / 60
b = a * 100
Problem: if each edge of cube increased by 25 % , the percentage increase in
Options: a ) 55 , b ) 52.25 , c ) 59.75 , d ) 51.75 , e ) 56.25
Rationale: "100 × ( 125 ) / 100 × ( 125 ) / 100 = 156.25 = > 56.25 % answer is e ."
Answer: e
Python program:
a = 100 + 25 
b = a ** 3
c = 100 ** 3
d = b - c
e = 100 ** 3
f = d / e
g = 100 * f
Problem: in a class of students , 1 / 2 of the number of girls is equal to 1 / 5 of the total number of students . what is the ratio of boys to girls in the class ?
Options: a ) 1 / 2 , b ) 3 / 2 , c ) 1 / 3 , d ) 2 / 3 , e ) 4 / 3
Rationale: "( 1 / 2 ) g = ( 1 / 5 ) ( b + g ) 5 g = 2 b + 2 g 3 g = 2 b b / g = 3 / 2 . the answer is b ."
Answer: b
Python program:
a = 1 / 2
b = 1 / 5
c = a - b
d = 1 / 5
e = c / d
Problem: how many 3 - digit positive integers are there , where each digit is positive , and no 3 adjacent digits are same ?
Options: a ) 1236 , b ) 504 , c ) 4096 , d ) 4608 , e ) 6561
Rationale: "first digit . . 9 posibilities second digit , 8 possibilities third digit , 7 possibilities 9 * 8 * 7 = 504 . b"
Answer: b
Python program:
a = 3 + 3 
b = 3 + 3 
c = a * b
d = 3 + 3 
e = 3 * 3
f = d * e
g = c * f
Problem: if n = ( 33 ) ^ 43 + ( 23 ) ^ 33 what is the units digit of n ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "first of all , the units digit of ( 33 ) ^ 23 is the same as that of 3 ^ 23 and the units digit of ( 23 ) ^ 33 is the same as that of 3 ^ 33 . so , we need to find the units digit of 3 ^ 23 + 3 ^ 33 . next , the units digit of 3 in positive integer power repeats in blocks of four { 3 , 9 , 7 , 1 } : 3 ^ 1 = 3 ( the units digit is 3 ) 3 ^ 2 = 9 ( the units digit is 9 ) 3 ^ 3 = 27 ( the units digit is 7 ) 3 ^ 4 = 81 ( the units digit is 1 ) 3 ^ 5 = 243 ( the units digit is 3 again ! ) . . . thus : the units digit of 3 ^ 23 is the same as the units digit of 3 ^ 3 , so 7 ( 43 divided by the cyclicity of 4 gives the remainder of 3 ) . the units digit of 3 ^ 33 is the same as the units digit of 3 ^ 1 , so 3 ( 33 divided by the cyclicity of 4 gives the remainder of 1 ) . therefore the units digit of ( 33 ) ^ 23 + ( 23 ) ^ 33 is 3 + 3 = 6 . answer : d ."
Answer: d
Python program:
a = reminder ** (
b = a + reminder 
c = reminder - (
Problem: for a positive integer n , if 5 ^ n is a factor of 20 ! , but 5 ^ n + 1 is not a factor of 20 ! , what is the value of n ?
Options: a ) 4 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: 20 ! has four 5 ' s 20 / 5 = 4 thus 5 ^ 4 can completely divide 20 ! and 5 ^ 5 can not divide 20 ! so , answer will be ( a ) 4
Answer: a
Python program:
a = 5 * 5
b = a - 20
c = b - 1
Problem: a side of beef lost 35 percent of its weight in processing . if the side of beef weighed 570 pounds after processing , how many pounds did it weigh before processing ?
Options: a ) 191 , b ) 355 , c ) 737 , d ) 876 , e ) 1,560
Rationale: "let weight of side of beef before processing = x ( 65 / 100 ) * x = 570 = > x = ( 570 * 100 ) / 65 = 876 answer d"
Answer: d
Python program:
a = 570 * 100
b = 100 - 35
c = a / b
Problem: the volume of a rectangular swimming pool is 840 cubic meters and water is flowing into the swimming pool . if the surface level of the water is rising at the rate of 0.5 meters per minute , what is the rate r , in cubic meters per minutes , at which the water is flowing into the swimming pool ?
Options: a ) 0.125 , b ) 0.25 , c ) 0.5 , d ) 0.75 , e ) not enough information to determine the rate
Rationale: "the correct answer is e . there are not enough info to answer the question . a 840 cubic meters rectangle is built from : height * length * width . from the question we know the volume of the pool and the filling rate . a pool can have a height of 10 * width 8.4 * length 10 and have a volume of 840 cubic meters , and it can have a height of 1 meter , width of 100 meters and length of 8.4 . in both cases the pool will fill up in a different rate = e"
Answer: e
Python program:
a = 840 / 0
Problem: in what time will a railway train 96 m long moving at the rate of 45 kmph pass a telegraph post on its way ?
Options: a ) 3 sec , b ) 8 sec , c ) 5 sec , d ) 6 sec , e ) 7 sec
Rationale: "t = 96 / 45 * 18 / 5 = 8 sec answer : b"
Answer: b
Python program:
a = 45 * const_0_2778
b = 96 / a
Problem: what is x if x + 2 y = 10 and y = 3 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "substitute y by 3 in x + 2 y = 10 x + 2 ( 3 ) = 10 x + 6 = 10 if we substitute x by 4 in x + 6 = 10 , we have 4 + 6 = 10 . hence x = 4 correct answer d"
Answer: d
Python program:
a = 2 * 3
b = 10 - a
Problem: if 10 a = 6 b = 20 , then 120 ab =
Options: a ) 800 , b ) 1000 , c ) 1200 , d ) 1400 , e ) 1600
Rationale: "10 a * 6 b = 20 * 20 = 400 60 ab = 400 i . e . 120 ab = 800 answer : option a"
Answer: a
Python program:
a = 20 / 10
b = 20 / 6
c = a * b
d = 120 * c
Problem: which number need to add to 7844213 to get a number exactly divisible by 549 ?
Options: a ) 418 , b ) 148 , c ) 448 , d ) 248 , e ) 348
Rationale: "7844213 / 549 = 14288 and reminder = 101 . 549 - 101 = 448 so , the next number divisible by 549 is 448 places in front of 7844213 which means 448 + 7844213 = 7844661 448 should be added to 7844213 c"
Answer: c
Python program:
a = 7844213 / 549
b = math.floor(a)
c = b + 1 
d = 7844213 / 549
e = c - d
f = 549 * e
Problem: a scale 7 ft . 12 inches long is divided into 4 equal parts . find the length of each part .
Options: a ) 20 inches , b ) 77 inches , c ) 24 inches , d ) 97 inches , e ) 66 inches
Rationale: "explanation : total length of scale in inches = ( 7 * 12 ) + 12 = 96 inches length of each of the 4 parts = 96 / 4 = 24 inches answer : c"
Answer: c
Python program:
a = 7 * 12
b = a + 12 
c = b / 4
Problem: the population of a town increases 10 % and 20 % respectively in two consecutive years . after the growth the present population of the town is 1320 . then what is the population of the town 2 years ago ?
Options: a ) 1100 , b ) 1001 , c ) 1010 , d ) 1000 , e ) 1002
Rationale: "explanation : formula : ( after = 100 denominator ago = 100 numerator ) 1320 * 100 / 110 * 100 / 120 = 1000 answer : option d"
Answer: d
Python program:
a = 10 / 100
b = 1 + a 
c = 20 / 100
d = 1 + c 
e = b * d
f = 1320 / e
Problem: there were two candidates in an election . winner candidate received 62 % of votes and won the election by 408 votes . find the number of votes casted to the winning candidate ?
Options: a ) 288 , b ) 1054 , c ) 788 , d ) 298 , e ) 177
Rationale: "w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 408 62 % - - - - - - - - ? = > 1054 answer : b"
Answer: b
Python program:
a = 100 - 62
b = 62 - a
c = b / 100
d = 408 / c
e = d * 62
f = e / 100
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 1104 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 ) 2145 , 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 + 1104 ) ( x - 8 ) ^ 2 = t + 1104 - - - - - ( 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 - 2145 + 1104 = 3249 = 57 ^ 2 = ( x - 8 ) ^ 2 hence , x = 65 . cross check by putting in eq ( a ) = x ( x + 1 ) / 2 = t = > 65 * 66 / 2 = 2145 hence , answer is a ."
Answer: a
Python program:
a = 4 * 100
b = 1104 - a
c = 4 * 100
d = 1104 - c
e = d * 2
f = e + 1 
g = b * f
Problem: 20 beavers , working together in a constant pace , can build a dam in 3 hours . how many v hours will it take 12 beavers that work at the same pace , to build the same dam ?
Options: a ) 2 . , b ) v = 4 . , c ) v = 5 . , d ) v = 6 . , e ) 8 .
Rationale: "c . 5 hrs if there were 10 beavers it qould have taken double v = 6 hrs . . so closest to that option is 5 ."
Answer: c
Python program:
a = 3 * 20
b = a / 12
Problem: one week , a certain truck rental lot had a total of 20 trucks , all of which were on the lot monday morning . if 50 % of the trucks that were rented out during the week were returned to the lot on or before saturday morning of that week , and if there were at least 10 trucks on the lot that saturday morning , what is the greatest number of different trucks that could have been rented out during the week ?
Options: a ) 18 , b ) 20 , c ) 12 , d ) 8 , e ) 4
Rationale: "n - not rented trucks ; r - rented trucks n + r = 20 n + r / 2 = 10 r = 20 b"
Answer: b
Python program:
a = 50 / 100
b = 20 * a
c = 10 + b
Problem: the mean of 50 observations was 36 . it was found later that an observation 48 was wrongly taken as 47 . the corrected new mean is ?
Options: a ) 36.7 , b ) 36.1 , c ) 36.5 , d ) 36.02 , e ) 36.3
Rationale: "correct sum = ( 36 * 50 + 48 - 47 ) = 1801 . correct mean = 1801 / 50 = 36.02 answer : d"
Answer: d
Python program:
a = 36 * 50
b = 50 - 2
c = b - 47
d = a + c 
e = d / 50
Problem: hillary and eddy are climbing to the summit of mt . everest from a base camp 5000 ft from the summit . when they depart for the summit at 06 : 00 , hillary climbs at a rate of 800 ft / hr with eddy lagging behind at a slower rate of 500 ft / hr . if hillary stops 1000 ft short of the summit and then descends at a rate of 1000 ft / hr , at what time do hillary and eddy pass each other on her return trip ?
Options: a ) 11.0 , b ) 12.0 , c ) 13.0 , d ) 14.0 , e ) 15.0
Rationale: solution : h stopped 1000 ft before reaching the final point , time taken to reach 4000 ft = 4000 / 800 = 5 hrs . this means she reached there at 11 : 00 . speed difference between them is 800 - 500 = 300 ft / hr so by the time h stops they have 1500 ft of distance so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft / hr and distance bwn them is 1500 ft so time taken to meet = 1 hr from 11 : 00 means 12 : 00 is the answer . b
Answer: b
Python program:
a = 5000 - 1000
b = a / 800
c = 6 + b 
d = c + 1
Problem: $ 200 is divided amongst a , b and c so that a may get 2 / 3 as much as b and c together , b may get 6 / 9 as much as a and c together , then the share of a is
Options: a ) $ 80 , b ) $ 50 , c ) $ 25 , d ) $ 200 , e ) $ 50
Rationale: "a : ( b + c ) = 2 : 3 a ' s share = 200 * 2 / 5 = $ 80 answer is a"
Answer: a
Python program:
a = 2 / 3
b = a + 1 
c = 200 / b
d = 2 / 3
e = c * d
Problem: if a ( a + 6 ) = 27 and b ( b + 6 ) = 27 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 6 , c ) 2 , d ) 46 , e ) 48
Rationale: "a ( a + 6 ) = 27 and b ( b + 6 ) = 27 = > a , b must be integers and if a is - 9 or 3 , b will be 3 and - 9 respectively = > a + b = - 6 ans : b"
Answer: b
Python program:
a = 27 / 10
b = 27 / 10
c = 27 / b
d = a + c
Problem: the base of a right triangle is 8 and hypotenuse is 10 . its area is ?
Options: a ) 12
b ) 80
c ) 59
d ) 24
e ) 25
Rationale: explanation : h 2 = ( 10 ) 2 - ( 8 ) 2 - ( 6 ) 2 - > h = 6 1 / 2 * 8 * 6 = 24 answer is d
Answer: d
Python program:
a = 10 * 10
b = 8 * 8
c = a - b
d = math.sqrt(c)
e = d * 8
f = e / 2
Problem: jack and jill work at a hospital with 3 other workers . for an internal review , 2 of the 5 workers will be randomly chosen to be interviewed . what is the probability that jack and jill will both be chosen ?
Options: a ) 1 / 3 , b ) 1 / 10 , c ) 1 / 15 , d ) 3 / 8 , e ) 2 / 3
Rationale: 1 / 5 c 2 = 1 / 10 . answer : b .
Answer: b
Python program:
a = math.factorial(5)
b = math.factorial(2)
c = math.factorial(3)
d = b * c
e = a / d
f = 1/(e)