euclaise/mathqa_programs huggingface dataset:
Problem: a marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each . there can be no less than 8 musicians per row and no more than 30 musicians per row . how many different rectangular formations g are possible ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) g = 8
Rationale: "the combinations could be { ( 1,240 ) , ( 2,120 ) , ( 3,80 ) , ( 4,60 ) , ( 5,48 ) , ( 6,40 ) , ( 8,30 ) , ( 10,24 ) , ( 12,20 ) , ) 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) , ( 40,6 ) , ( 48,5 ) , ( 60,4 ) , ( 80,3 ) , ( 120,2 ) , ( 240,1 ) } of these we are told 8 < = t < = 30 so we can remove these pairs , and we are left only with . { ( 8,30 , ( 10 , 24 ) , ( 12,20 ) , ( 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) } hence 8 . . e"
Answer: e
Python program:
a = 240 / 30
Problem: the reciprocal of the hcf and lcm of two are 1 / 15 and 1 / 312 . if one of the number is 24 then other no . is
Options: a ) 126 , b ) 136 , c ) 146 , d ) 156 , e ) 195
Rationale: "reciprocal of the hcf and lcm of two are 1 / 15 and 1 / 312 so , hcf = 15 , lcm = 312 lcm * hcf = product of two numbers = a * b = > b = lcm * hcf / a so , other = 15 * 312 / 24 = 195 answer : e"
Answer: e
Python program:
a = 15 * 312
b = a / 24
Problem: x and y start a business with rs . 3000 and rs . 6000 respectively . hoe should they share their profits at the end of one year ?
Options: a ) 3 : 1 , b ) 2 : 1 , c ) 1 : 2 , d ) 1 : 3 , e ) 1 : 4
Rationale: explanation : they should share the profits in the ratio of their investments . the ratio of the investments made by x and y = 3000 : 6000 = > 1 : 2 answer : c
Answer: c
Python program:
a = 3000 / 6000
Problem: in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 60 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 389 $ , c ) 420 $ , d ) 450 $ , e ) 489 $
Rationale: total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 60 ) = 489 hence answer will be ( e )
Answer: e
Python program:
a = 0 * 65
b = a * 12
Problem: set x consists of 10 integers and has median of 10 and a range of 10 . what is the value of the greatest possible integer that can be present in the set ?
Options: a ) 32 , b ) 37 , c ) c . 40 , d ) 20 , e ) 50
Rationale: "note that both median and range do not restrict too many numbers in the set . range is only concerned with the smallest and greatest . median only cares about the middle . quick check of each option starting from the largest : ( e ) 50 range of 20 means the smallest integer will be 30 . so 20 can not lie in between and hence can not be the median . ( d ) 43 range of 20 means the smallest integer will be 23 . so 20 can not lie in between and hence can not be the median . ( c ) 40 range of 20 means the smallest integer will be 20 . 20 can lie in between such as : 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 this is possible . hence it is the greatest such number . answer ( d )"
Answer: d
Python program:
a = 10 + 10
Problem: a boy is traveling from his house to school at 3 km / hr and reached school 9 minutes late . next day he traveled 4 km / hr and reached 6 minutes early . then find the distance between house and school ?
Options: a ) 3 km , b ) 4.5 km , c ) 5 km , d ) 2.5 km , e ) 6 km
Rationale: "let distance be x s 1 = 3 km / hr s 2 = 4 km / hr t 1 = x / 3 hr t 2 = x / 4 hr difference in time = 9 + 6 = 15 m = 1 / 4 hr ( x / 3 ) - ( x / 4 ) = 1 / 4 x = 3 km answer is a"
Answer: a
Python program:
a = 9 * 3
b = a + 4 
c = 4 - 3
d = b / c
e = d + 9 
f = e * 3
Problem: a student chose a number , multiplied it by 2 , then subtracted 140 from the result and got 102 . what was the number he chose ?
Options: a ) 90 , b ) 100 , c ) 120 , d ) 160 , e ) 121
Rationale: "solution : let x be the number he chose , then 2 * x * 140 = 102 2 x = 242 x = 121 correct answer e"
Answer: e
Python program:
a = 102 + 140 
b = a / 2
Problem: a can do a work in 15 days and b in 20 days . if they work on it together for 6 days , then the fraction of the work that is left is
Options: a ) 8 / 17 , b ) 7 / 15 , c ) 3 / 10 , d ) 8 / 15 , e ) 1 / 4
Rationale: "person ( a ) ( b ) ( a + b ) time - ( 15 ) ( 20 ) ( - ) rate - ( 20 ) ( 15 ) ( 35 ) work - ( 300 ) ( 300 ) ( 300 ) therefore a + b requires ( 300 / 35 ) days to complete entire work for 1 st 4 days they work 35 * 6 = 210 remaining work is 300 - 210 = 90 remaining fraction of work is = 90 / 300 = 3 / 10 answer c"
Answer: c
Python program:
a = 1 / 15
b = 1 / 20
c = a + b 
d = c * 6
e = 1 - d
Problem: a certain quantity is measured on two different scales , the p - scale and the s - scale , that are related linearly . measurements on the p - scale of 6 and 24 correspond to measurements on the s - scale of 30 and 60 , respectively . what measurement on the p - scale corresponds to a measurement of 100 on the s - scale ?
Options: a ) 20 , b ) 36 , c ) 48 , d ) 60 , e ) 84
Rationale: first , we have to understand what linearly means . it ' s not a straight ratio ( since 6 : 30 does not equal 24 : 60 ) . we need to look at the increases in each measurement to see what the scalar actually is . from 6 to 24 we have an increase of 18 . from 30 to 60 we have an increase of 30 . therefore , the increase ratio is 18 : 30 or 3 : 5 . in other words , for every 3 that p increases , s increases by 5 . we know that s is 100 . to get from 60 to 100 , we went up by 40 , or 8 jumps of 5 ; therefore , p will go up by 8 jumps of 3 . 24 + 8 ( 3 ) = 24 + 24 = 48 = c
Answer: c
Python program:
a = 100 - 30
b = a / 30
c = 24 - 6
d = b * c
e = d + 6
Problem: set a contains all the even numbers between 2 and 50 inclusive . set b contains all the even numbers between 102 and 150 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?
Options: a ) 2500 , b ) 2550 , c ) 5050 , d ) 6275 , e ) 11325
Rationale: "set a contains 2,4 , 6 . . . 50 set b contains 102 , 104 , 106 . . . 150 number of terms in each set = 25 difference between corresponding terms in set a and b = 100 difference between sum of set b and set a = 100 * 25 = 2500 answer a"
Answer: a
Python program:
a = 102 - 2
b = 50 - 2
c = b / 2
d = c + 1 
e = a * d
Problem: a whale goes on a feeding frenzy that lasts for 12 hours . for the first hour he catches and eats 30 kilos of plankton . in every hour after the first , it consumes 2 kilos of plankton more than it consumed in the previous hour . if by the end of the frenzy the whale will have consumed a whopping accumulated total 600 kilos of plankton , how many kilos did he consume on the 10 th hour ?
Options: a ) 36 , b ) 45 , c ) 28 , d ) 48 , e ) 52
Rationale: therefor in 10 th hour he consume x + 2 * 9 = 30 + 18 = 48 correct option is d
Answer: d
Python program:
a = 600 / 12
Problem: the average age of 19 students in a group is 17 years . when teacher ’ s age is included to it , the average increases by one . what is the teacher ’ s age in years ?
Options: a ) 36 , b ) 37 , c ) 38 , d ) can not be determined , e ) none of these
Rationale: "age of the teacher = ( 20 × 18 – 19 × 17 ) years = 37 years . answer b"
Answer: b
Python program:
a = 19 + 1
Problem: machine x takes 10 hours longer than machine y to produce 1080 widgets . machine y produces 20 percent more widgets in an hour than machine x does in an hour . how many widgets per hour does machine x produce
Options: a ) 100 , b ) 65 , c ) 25 , d ) 11 , e ) 18
Rationale: "machine y produces 20 percent more widgets in an hour than machine x does in an hour . so if machine x produces 100 widgets , then machine y produces 120 widgets . ratio of 120 / 100 = 6 / 5 . this is their speed of work ( y : x ) . i . e . speed of their work ( x : y ) = 5 / 6 now , time is inversely proportional to speed . hence the ratio of the time spent ( x : y ) = 6 / 5 let us assume that they spend 6 x and 5 x hours . given that 6 x - 5 x = 10 so , x = 10 . hence 6 x = 6 * 10 = 60 hours . hence x takes 120 hours to produce 1080 widgets . so , in 1 hour , it can produce ( 1 * 1080 ) / 60 = 18 hence option ( e ) ."
Answer: e
Python program:
a = const_60 / 0
b = a * 10
c = 1080 / b
Problem: a train is running at a speed of 40 km / hr and it crosses a post in 16.2 seconds . what is the length of the train ?
Options: a ) 190 metres , b ) 160 metres , c ) 200 metres , d ) 120 metres , e ) 250 metres
Rationale: "speed of the train , v = 40 km / hr = 40000 / 3600 m / s = 400 / 36 m / s time taken to cross , t = 16.2 s distance covered , d = vt = ( 400 / 36 ) ã — 16.2 = 160 m distance covered is equal to the length of the train = 160 m correct answer is 160 metres b"
Answer: b
Python program:
a = 40 * const_0_2778
b = 16 * 2
Problem: a fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans . a customer bought the pair of jeans for 30 percent more than the retailer paid for them . the price the customer paid was what percent greater than the cost of manufacturing the jeans ?
Options: a ) 65 % , b ) 70 % , c ) 75 % , d ) 82 % , e ) 95 %
Rationale: find the product of the two increases : ( 14 / 10 ) * ( 13 / 10 ) which is 1.82 and a 82 % increase . d
Answer: d
Python program:
a = 40 / 100
b = 1 + a 
c = 100 * b
d = 30 / 100
e = 1 + d 
f = c * e
g = f / 100
h = g - 1
i = h * 100
Problem: if 4 % more is gained by selling an article for rs . 350 than by selling it for rs . 340 , the cost of the article is
Options: a ) 250 , b ) 231 , c ) 200 , d ) 288 , e ) 111
Rationale: "explanation : let c . p . be rs . x . then , 4 % of x = 350 - 340 = 10 x / 25 = 10 = > x = 250 answer : a"
Answer: a
Python program:
a = 350 - 340
b = 4 / 100
c = a / b
Problem: on increasing the price of t . v . sets by 50 % , their sale decreases by 20 % . what is the effect on the revenue receipts of the shop ?
Options: a ) 4 , b ) 5 , c ) 56 , d ) 20 , e ) 7
Rationale: "explanation : let the price be = rs . 100 , and number of units sold = 100 then , sale value = rs . ( 100 × 100 ) = rs . 10000 new sale value = rs . ( 150 × 80 ) = rs . 12000 increase % = 2000 / 10000 × 100 = 20 % answer : d"
Answer: d
Python program:
a = 100 + 50 
b = 100 + 50 
c = b * 20
d = c / 100
e = d + 100 
f = a - e
Problem: p software has coding line 5 % more than n , n software has coding line 4 / 13 more than m . m software has 78 lines of coding . find p lines .
Options: a ) 106 , b ) 107 , c ) 108 , d ) 109 , e ) 110
Rationale: "m s / w has 78 line of code n s / w has = 78 + 78 * 4 / 13 = 102 line of code p s / w 5 % more n ' code 102 + 5.1 = 107.1 or 107 line of code answer : b"
Answer: b
Python program:
a = 78 / 13
b = 78 + a
Problem: a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 1600 . the difference between the profit shares of a and c is ?
Options: a ) 288 , b ) 266 , c ) 155 , d ) 600 , e ) 640
Rationale: ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 1600 = > 5 parts out of 15 parts is rs . 1600 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 1600 ) = rs . 640 answer : e
Answer: e
Python program:
a = 12000 / 10000
b = 8000 / 10000
c = a - b
d = c * 1600
Problem: machine a can finish a job in 4 hours , machine в can finish the job in 12 hours , and machine с can finish the job in 6 hours . how many hours will it take for a , b , and с together to finish the job ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "the combined rate is 1 / 4 + 1 / 12 + 1 / 6 = 1 / 2 of the job per hour . the time to complete the job is 2 / 1 = 2 hours . the answer is b ."
Answer: b
Python program:
a = 1/(4)
b = 1/(12)
c = a + b 
d = 1/(6)
e = c + d 
f = 1/(e)
Problem: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 720 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 92 , c ) 68 , d ) 88 , e ) none
Rationale: "explanation we have : l = 20 ft and lb = 720 sq . ft . so , b = 36 ft . length of fencing = ( l + 2 b ) = ( 20 + 72 ) ft = 92 ft . answer b"
Answer: b
Python program:
a = 720 / 20
b = a * 2
c = b + 20
Problem: positive integer y is 50 percent of 50 percent of positive integer x , and y percent of x equals 4 . what is the value of x ?
Options: a ) 40 , b ) 100 , c ) 200 , d ) 400 , e ) 600
Rationale: "y = 0.5 * 0.5 * x = x / 4 y % * x = 4 ( y / 100 ) * x = 4 ( x / 400 ) * x = 4 x ^ 2 = 4 * 400 x = 40 the answer is a ."
Answer: a
Python program:
a = 50 / 4
b = 50 / 4
c = a * b
d = c * 1000
Problem: walking with 3 / 5 of my usual speed , i miss the bus by 5 minutes . what is my usual time ?
Options: a ) 16 min , b ) 26 min , c ) 34 min , d ) 20 min , e ) 15 min
Rationale: "speed ratio = 1 : 3 / 5 = 5 : 3 time ratio = 3 : 5 1 - - - - - - - - 5 3 - - - - - - - - - ? è 15 answer : e"
Answer: e
Python program:
a = 5 / 3
b = 5 / a
c = b * 5
Problem: [ ( 3.241 x 14 ) / 100 ] = ?
Options: a ) 0.045374 , b ) 4.5388 , c ) 453.88 , d ) 473.88 , e ) none of these
Rationale: "answer multiplying 3.241 x 14 = 4.5374 now divide 4.5374 by 100 so , 4.5374 ÷ 100 = 0.045374 ∴ shift the decimal two places to the left as 100 correct option : a"
Answer: a
Python program:
a = 3 * 241
b = a / 100
c = b / 10
Problem: a person borrows rs . 4000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 6 p . a for 2 years . find his gain in the transaction per year .
Options: a ) 100 rs , b ) 80 rs , c ) 160 rs , d ) 180 rs , e ) 200 rs
Rationale: "gain in 2 years = [ ( 4000 * 6 * 2 ) / 100 ] - [ ( 4000 * 4 * 2 ) / 100 ] 480 - 320 = 160 gain in 1 year = ( 160 / 2 ) = 80 rs answer : b"
Answer: b
Python program:
a = 4000 * 6
b = a * 2
c = b / 100
d = 4000 * 4
e = d * 2
f = e / 100
g = c - f
h = g / 2
Problem: 365 : 90 : : 623 : ?
Options: a ) 36 , b ) 45 , c ) 123 , d ) 63 , e ) none of these
Rationale: "365 - - - 3 * 6 * 5 . . . . 90 623 - - - 6 * 2 * 3 . . . . 36 answer a"
Answer: a
Python program:
a = 365 / 90
b = 623 * a
Problem: the volumes of two cones are in the ratio 1 : 20 and the radii of the cones are in the ratio of 1 : 2 . what is the length of the wire ?
Options: a ) 4 : 5 , b ) 4 : 9 , c ) 4 : 2 , d ) 5 : 2 , e ) 2 : 8
Rationale: "the volume of the cone = ( 1 / 3 ) π r 2 h only radius ( r ) and height ( h ) are varying . hence , ( 1 / 3 ) π may be ignored . v 1 / v 2 = r 1 ^ 2 . h 1 / r 2 ^ 2 . h 2 = > 1 / 20 = ( 1 ) ^ 2 h 1 / ( 2 ) ^ 2 h 2 = > h 1 / h 2 = 4 / 5 i . e . h 1 : h 2 = 4 : 5 answer : a"
Answer: a
Python program:
a = 1 / 20
b = 1 / 2
c = b ** 2
d = a / c
Problem: let p and q be the root of the quadratic equation x 2 - ( ∝ - 2 ) x - ∝ - 1 = 0 . what is the minimum possible value of p 2 + q 2 ?
Options: a ) 0 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: explanation : p + q = α – 2 and pq = – α – 1 ( p + q ) 2 = p 2 + q 2 + 2 pq , thus ( α – 2 ) 2 = p 2 + q 2 + 2 ( – α – 1 ) p 2 + q 2 = α 2 – 4 α + 4 + 2 α + 2 p 2 + q 2 = α 2 – 2 α + 6 p 2 + q 2 = α 2 – 2 α + 1 + 5 p 2 + q 2 = ( α – 1 ) 2 + 5 thus , minimum value of p 2 + q 2 is 5 . answer : d
Answer: d
Python program:
a = 2 + 2 
b = a + 2 
c = b - 1
Problem: each of the 35 points is placed either inside or on the surface of a perfect sphere . if 88 % or fewer of the points touch the surface , what is the maximum number of segments which , if connected from those points to form chords , could be the diameter of the sphere ?
Options: a ) 7 , b ) 11 , c ) 13 , d ) 14 , e ) 15
Rationale: "maximum number of points on the surface is 88 % * 35 = 30.8 . . . or 30 since it has to be an integer now note that if two points form a diameter , they can not be part of any other diameter . so in the best case we can pair up the points we have 30 points , so at best we can form 15 pairs ( 30 ) . so , answer is ( e )"
Answer: e
Python program:
a = 88 / 100
b = 35 * a
c = b / 2
Problem: 6 years ago , p was half of q in age . if the ratio of their present ages is 3 : 4 , what will be the total of their present ages
Options: a ) a ) 21 , b ) b ) 34 , c ) c ) 45 , d ) d ) 25 , e ) e ) 26
Rationale: explanation : let the present age of p and q be 3 x and 4 x respectively . six years ago , p was half of q in age = > 2 ( 3 x – 6 ) = ( 4 x – 6 ) = > 6 x – 12 = 4 x – 6 = > 2 x = 6 = > x = 3 7 x = 7 * 3 = 21 answer : option a
Answer: a
Python program:
a = 2 * 6
b = 2 * 6
c = 3 * b
d = c / 4
e = a + d
Problem: the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 12 % , then the cost price of the article is :
Options: a ) 500 , b ) 277 , c ) 266 , d ) 288 , e ) 261
Rationale: "110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 110 * 560 ) / 112 = rs . 500 . answer : a"
Answer: a
Python program:
a = 616 * 100
b = 100 + 10 
c = a / b
d = 100 + 10 
e = c * d
f = 100 + 12 
g = e / f
Problem: if 2 log ( 4 * 5 ^ 2 ) = x , find x
Options: a ) 5 , b ) 6 , c ) 7 , d ) 4 , e ) 8
Rationale: "2 ( log 2 ^ 2 * 5 ^ 2 ) = x 2 log ( 5 * 2 ) ^ 2 = x 2 * 2 log ( 5 * 2 ) = x 4 log 10 = x log 10 base 10 = 1 so 4 * 1 = x x = 4 answer : d"
Answer: d
Python program:
a = 5 ** 2
b = 4 * a
c = b ** 2
Problem: a certain automobile company ’ s best - selling model is the speedster . the speedster , like all of their other models , comes in coupe and convertible styles . 3 / 4 of the current inventory is speedsters , of which 3 / 5 are convertibles . if there are 30 vehicles that are not speedsters , how many speedster convertibles are there ?
Options: a ) 30 , b ) 54 , c ) 60 , d ) 70 , e ) 90
Rationale: "total vehicle = 3 / 4 of speedster + 1 / 4 of others . speedster convertibles = 3 / 4 total vehicle * 3 / 5 given : 1 / 4 constitutes 30 vehicles . hence 3 / 4 constitutes 90 speedster convertibls = 90 * 3 / 5 = 54 b"
Answer: b
Python program:
a = 3 / 4
b = 1 - a
c = 30 / b
d = 3 / 4
e = c * d
f = 3 / 5
g = e * f
Problem: a rower can row 6 km / h in still water . when the river is running at 1 km / h , it takes the rower 1 hour to row to big rock and back . how many kilometers is it to big rock ?
Options: a ) 2.66 , b ) 2.78 , c ) 2.8 , d ) 2.87 , e ) 2.92
Rationale: "let x be the distance to big rock . time = x / 5 + x / 7 = 1 x = 35 / 12 = 2.92 the answer is e ."
Answer: e
Python program:
a = 6 - 1
b = 6 + 1 
c = 6 - 1
d = b + c 
e = a / d
f = 6 + 1 
g = e * f
Problem: in a stockpile of products produced by 3 machines m 1 , m 2 and m 3 , 40 % and 30 % were manufactured by m 1 and m 2 respectively . 3 % of the products of m 1 are defective , 1 % of products of m 2 defective , while 93 % of the products of m 3 iii are not defective . what is the percentage of defective in the stockpile ?
Options: a ) 3 % , b ) 5 % , c ) 2.5 % , d ) 4 % , e ) 3.6 %
Rationale: explanation : let there be 100 products in the stockpile . 40 % and 30 % were manufactured by m 1 and m 2 respectively . so , 30 % are manufactured by m 3 . products from m 1 = 40 , from m 2 = 30 and from m 3 = 30 . number of defective products from m 1 = 0.03 x 40 = 1.2 , from m 2 = 0.01 x 30 = 0.3 and from m 3 = 0.07 x 30 = 2.1 therefore , total number of defective products = 3.6 answer : e
Answer: e
Python program:
a = 100 - 93
b = a / 100
c = 40 + 30 
d = 100 - c
e = b * d
f = 1 / 100
g = f * 30
h = e + g 
i = 3 / 100
j = i * 40
k = h + j
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 10 cm . find the circumference of a semicircle whose diameter is equal to the side of the square .
Options: a ) 44.0 , b ) 23.59 , c ) 23.55 , d ) 23.53 , e ) 23.57
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 18 + 10 ) = 56 cm parameter of the square = 56 cm i . e . 4 a = 56 a = 14 diameter of the semicircle = 14 cm circimference of the semicircle = 1 / 2 ( â ˆ  ) ( 14 ) = 22 / 7 * 14 = 44 cm answer : a"
Answer: a
Python program:
a = square_edge_by_perimeter / (
b = circumface / (
Problem: the average mark obtained by 22 candidates in an examination is 48 . the average of the first 10 is 55 while the last 11 is 40 . the marks obtained by the 11 th candidate is ?
Options: a ) 22 , b ) 0 , c ) 49 , d ) 58 , e ) 66
Rationale: it is clear that 22 x 48 = 10 x 55 + k + 11 x 40 ⇒ ⇒ k = 66 answer : e
Answer: e
Python program:
a = 22 * 48
b = 10 * 55
c = 11 * 40
d = b + c 
e = a - d
Problem: ' a ' and ' b ' are positive integers such that their lcm is 20 and their hcf is 1 . what is the difference between the minimum and maximum possible values of ' a + b ' ?
Options: a ) 0 , b ) - 24 , c ) - 32 , d ) - 20 , e ) - 12
Rationale: "possible values of a and b can be 5,4 ; 4,5 ( which are same for a + b ) and 1,20 ; 20,1 ( same result for a + b ) so 9 - 21 = - 12 . ans e ."
Answer: e
Python program:
a = 20 / 4
b = a + 4 
c = 20 / 4
d = c + 4 
e = b - d
Problem: a certain company reported that the revenue on sales increased 50 % from 2000 to 2003 , and increased 80 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?
Options: a ) 20 % , b ) 40 % , c ) 35 % , d ) 32 % , e ) 29 %
Rationale: "assume the revenue in 2000 to be 100 . then in 2003 it would be 150 and and in 2005 180 , so from 2003 to 2005 it increased by ( 180 - 150 ) / 150 = 30 / 150 = ~ 20 % . answer : a"
Answer: a
Python program:
a = 80 / 100
b = 1 + a 
c = 50 / 100
d = 1 + c 
e = b - d
f = 50 / 100
g = 1 + f 
h = e / g
i = h * 100
Problem: if 21 lines are drawn in a plane such that no two of them are parallel and no three are concurrent , then in how many points do they intersect ?
Options: a ) 150 , b ) 170 , c ) 190 , d ) 210 , e ) 230
Rationale: "if two lines are not parallel , then they will intersect in exactly one point . lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel . we are also given that no three lines are concurrent . this means that no three lines intersect at the same point . so every pair of two lines we select will have a unique point of intersection which they will not share with any third line . the number of ways to select 2 lines from 21 lines is 21 c 2 = 210 the answer is d ."
Answer: d
Python program:
a = math.factorial(21)
b = 21 - 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e
Problem: three rugs have a combined area of 200 square meters . by overlapping the rugs to cover floor area of 140 square meters , the area that is covered by exactly two layers of rug is 22 square meters . what is the area that is covered with three layers of rug ?
Options: a ) 18 square meters
b ) 20 square meters
c ) 24 square meters
d ) 19 square meters
e ) 30 square meters
Rationale: total = rug 1 + rug 2 + rug 3 - { overlap of exactly 2 rugs } - 2 * { overlap of exactly 3 rugs } 140 = 200 - 22 - 2 * { overlap of exactly 2 rugs } - - > { overlap of exactly 3 rugs } = 19 . answer : d .
Answer: d
Python program:
a = 200 - 140
b = a - 22
c = b / 2
Problem: find the simple interest on $ 3200 for 3 years at 10 % per annum ?
Options: a ) $ 250 , b ) $ 300 , c ) $ 500 , d ) $ 600 , e ) $ 960
Rationale: "si = ptr / 100 = 3200 * 3 * 10 / 100 = $ 960 answer is e"
Answer: e
Python program:
a = 3 / 100
b = 3200 * a
Problem: if a person walks at 12 km / hr instead of 8 km / hr , he would have walked 20 km more . the actual distance traveled by him is ?
Options: a ) 50 km , b ) 58 km , c ) 60 km , d ) 40 km , e ) 65 km
Rationale: "let the actual distance traveled be x km . then , x / 8 = ( x + 20 ) / 12 3 x - 2 x = 40 = > x = 40 km . answer : d"
Answer: d
Python program:
a = 12 - 8
b = 20 / a
c = 8 * b