euclaise/mathqa_programs huggingface dataset:
Problem: after decreasing 56 % in the price of an article costs rs . 4400 . find the actual cost of an article ?
Options: a ) 12000 , b ) 15000 , c ) 1200 , d ) 1000 , e ) 10000
Rationale: "cp * ( 44 / 100 ) = 4400 cp = 100 * 100 = > cp = 10000 answer : e"
Answer: e
Python program:
a = 56 / 100
b = 1 - a
c = 4400 / b
Problem: for each of her sales , a saleswoman receives a commission equal to 20 percent of the first $ 500 of the total amount of the sale , plus 45 percent of the total amount in excess of $ 500 . if the total amount of one of her sales was $ 800 , the saleswoman ’ s commission was approximately what percent of the total amount of the sale ?
Options: a ) 22 % , b ) 24 % , c ) 25 % , d ) 29 % , e ) 28 %
Rationale: total sales = 800 comission = ( 20 / 100 ) * 500 + ( 45 / 100 ) * 300 = 100 + 135 = 235 % comission = ( 235 / 800 ) * 100 = 29.4 ~ 29 % answer is d
Answer: d
Python program:
a = 20 / 100
b = a * 500
c = 45 / 100
d = 800 - 500
e = c * d
f = b + e 
g = f / 800
h = g * 100
Problem: a shop owner sells 50 mtr of cloth and gains sp of 10 mtrs . find the gain % ?
Options: a ) 25 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: here , selling price of 10 m cloth is obtained as profit . profit of 10 m cloth = ( s . p . of 50 m cloth ) – ( c . p . of 50 m cloth ) selling price of 40 m cloth = selling price of 50 m of cloth let cost of each metre be rs . 100 . therefore , cost price of 40 m cloth = rs . 4000 and s . p . of 40 m cloth = rs . rs . 5000 profit % = 10 / 40 × 100 = 25 % profit of 25 % was made by the merchant . a
Answer: a
Python program:
a = 50 - 10
b = 10 / a
c = b * 100
Problem: find compound interest on rs . 7500 at 4 % per annum for 2 years , compounded annually .
Options: a ) rs . 512 , b ) rs . 552 , c ) rs . 612 , d ) rs . 622 , e ) none
Rationale: "solution amount = rs [ 7500 x ( 1 + 4 / 100 ) ² ] = rs . ( 7500 x 26 / 25 x 26 / 25 ) = rs . 8112 . c . i = rs ( 8112 - 7500 ) = rs . 612 . answer c"
Answer: c
Python program:
a = 7500 * 4
b = a / 100
c = 7500 + b 
d = 7500 * 4
e = d / 100
f = 7500 + e 
g = f * 4
h = g / 100
i = c + h 
j = i - 7500
Problem: a number is 4 less than 6 times the other number . if the sum of both the number is 38 , what are the numbers ?
Options: a ) 632 , b ) 731 , c ) 533 , d ) 434 , e ) none of the above
Rationale: that numbers are x , 6 x - 4 so sum = x + 6 x - 4 = 38 7 x = 42 = = > x = 6 another no is 32 answer is 6 , 32 answer : a
Answer: a
Python program:
a = 38 - 6
b = 38 - a
c = b * 100
d = 38 - 6
e = c + d
Problem: two trains of length 250 m and 120 m are 50 m apart . they start moving towards each other on parallel tracks , at speeds 64 kmph and 42 kmph . after how much time will the trains meet ?
Options: a ) 15 / 10 , b ) 17 / 10 , c ) 16 / 10 , d ) 18 / 10 , e ) 16 / 10
Rationale: "they are moving in opposite directions , relative speed is equal to the sum of their speeds . relative speed = ( 64 + 42 ) * 5 / 18 = 7 * 5 = 29.4 mps . the time required = d / s = 50 / 29.4 = 17 / 10 sec . answer : b"
Answer: b
Python program:
a = 64 + 42 
b = a * const_0_2778
c = 50 / b
Problem: the area of sector of a circle whose radius is 12 metro and whose angle at the center is 38 ° is ?
Options: a ) 30 m 2 , b ) 40 m 2 , c ) 47.7 m 2 , d ) 50 m 2 , e ) 55 m 2
Rationale: "38 / 360 * 22 / 7 * 12 * 12 = 47.7 m 2 answer : c"
Answer: c
Python program:
a = 12 ** 2
b = 2 * 10
c = b + 2 
d = 4 + 3 
e = c / d
f = a * e
g = 3600 / 10
h = 38 / g
i = f * h
Problem: if the l . c . m of two numbers is 750 and their product is 18750 , find the h . c . f of the numbers .
Options: a ) 50 , b ) 30 , c ) 125 , d ) 25 , e ) none of these
Rationale: "h . c . f = ( product of the numbers ) / ( their l . c . m ) = 18750 / 750 = 25 . answer : d"
Answer: d
Python program:
a = 18750 / 750
Problem: the population of a bacteria culture doubles every 2 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 200,000 bacteria
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "the question basically asks how many minutes it takes for a population to increase by factor 200 ( 200,000 / 1,000 = 200 ) . now you know that every two minutes the population doubles , i . e . is multiplied by 2 . so the equation becomes : 2 ^ x > = 200 , where x represents the number of times the population doubles . a lot of people remember that 2 ^ 10 = 1,024 . hence , 2 ^ 8 = 256 , i . e . the population has to double 8 times . since it takes the population 2 minutes to double once it takes 8 * 2 minutes = 16 minutes to double 8 times . thus , solution d = 16 is correct ."
Answer: d
Python program:
a = 4 + 1 
b = a * 1
c = b * 100
d = c / 1
e = math.log(d)
f = e * 2
Problem: the marks obtained by polly and sandy are in the ratio 3 : 5 and those obtained by sandy and willy are in the ratio of 3 : 2 . the marks obtained by polly and willy are in the ratio of . . . ?
Options: a ) 3 : 4 , b ) 5 : 6 , c ) 7 : 8 , d ) 9 : 10 , e ) 11 : 12
Rationale: "polly : sandy = 3 : 5 = 9 : 15 sandy : willy = 3 : 2 = 15 : 10 polly : sandy : willy = 9 : 15 : 10 polly : willy = 9 : 10 the answer is d ."
Answer: d
Python program:
a = 3 * 3
b = 5 * 2
c = a / b
Problem: if the largest 3 digit number is subtracted from the smallest 5 digit number , then the remainder is
Options: a ) 1 , b ) 9000 , c ) 9001 , d ) 90001 , e ) none
Rationale: solution required remainder = ( 10000 - 999 ) = 9001 answer c
Answer: c
Python program:
a = 5 * 100
b = 5 * 100
c = a + b 
d = c * 10
e = 5 * 100
f = 5 * 100
g = e + f 
h = g - 1
i = d - h
Problem: x and y started a business investing rs . 50000 and rs 40000 respectively . in what ratio the profit earned after 2 years be divided between x and y respectively ?
Options: a ) 3 : 2 , b ) 9 : 2 , c ) 5 : 4 , d ) 1 : 4 , e ) 18 : 4
Rationale: x : y = 50000 : 40000 = 5 : 4 answer : c
Answer: c
Python program:
a = 50000 / 40000
Problem: a man can row downstream at 26 kmph and upstream at 10 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 2 , 9 , b ) 4 , 9 , c ) 8 , 9 , d ) 18 , 8 , e ) 7 , 9
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 26 - - - ( 1 ) and x - y = 10 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 36 = > x = 18 , y = 8 . answer : d"
Answer: d
Python program:
a = 26 + 10 
b = a / 2
c = b / 2
Problem: if log 1087.5 = 3.9421 , then the number of digits in ( 875 ) 10 is ?
Options: a ) 30 , b ) 28 , c ) 27 , d ) 50 , e ) 25
Rationale: "x = ( 875 ) 10 = ( 87.5 x 10 ) 10 therefore , log 10 x = 10 ( log 1087.5 + 1 ) = 10 ( 3.9421 + 1 ) = 10 ( 4.9421 ) = 49.421 x = antilog ( 49.421 ) therefore , number of digits in x = 50 . answer : d"
Answer: d
Python program:
a = 4 * 3
b = math.log(100)
c = math.log(10)
d = b / c
e = a + d
Problem: if $ 5,000 is invested in an account that earns 12 % interest compounded semi - annually , then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8 % simple yearly interest ?
Options: a ) $ 4 , b ) $ 8 , c ) $ 12 , d ) $ 16 , e ) $ 432
Rationale: "solution amount ( ci ) = p + ( 1 + r / n ) ^ nt = 5000 + ( 1 + 0.12 / 2 ) ^ 2 = 5412 amount ( si ) = p + ptr / 100 = 5000 + ( 5000 * 1 * 12 / 100 ) = 5400 difference = 5412 - 5400 = 12 $ c"
Answer: c
Python program:
a = 12 * 1
Problem: the sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 180 m , its area is ?
Options: a ) 90 , b ) 882 , c ) 277 , d ) 261 , e ) 281
Rationale: "5 x + 12 x + 13 x = 180 = > x = 6 a = 30 , b = 72 , c = 78 s = ( 30 + 72 + 78 ) / 2 = 90 answer : a"
Answer: a
Python program:
a = 5 + 12 
b = a + 13 
c = 180 / b
d = 180 * c
Problem: if 2 ^ 4 , 2 ^ 3 , and 11 ^ 3 are factors of the product of 1,452 and w , where w is a positive integer , what is the smallest possible value of w ?
Options: a ) 176 , b ) 288 , c ) 363 , d ) 396 , e ) 484
Rationale: i will go with a ( pending elements to match is 2 ^ 2 * 2 ^ 2 * 11 ^ 1 = 176
Answer: a
Python program:
a = 2 ** 2
b = a * 2
c = 11 / 2
d = b * c
e = d * 2
Problem: what is the sum of 80 consecutive integers from - 39 inclusive , in a increasing order ?
Options: a ) - 29 , b ) 39 , c ) - 30 , d ) 40 , e ) 60
Rationale: "from - 39 to - 1 - - > 39 nos . zero - - > 1 number from + 1 to + 39 - - > 39 nos . when we add up nos . from - 39 to + 39 sum will be zero . total 79 nos will be added . 80 th number will be 40 . sum of these 80 nos . = 40 . d is the answer ."
Answer: d
Python program:
a = 39 + 1
Problem: the profit earned by selling an article for rs . 832 is equal to the loss incurred when the same article is sold for rs . 448 . what should be the sale price for making 70 % profit ?
Options: a ) 277 , b ) 1088 , c ) 277 , d ) 266 , e ) 121
Rationale: "let c . p . = rs . x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 170 % of rs . 640 = 170 / 100 * 640 = rs . 1088 . answer : b"
Answer: b
Python program:
a = 832 - 448
b = a / 2
c = 832 - b
d = 70 / 100
e = 1 + d 
f = c * e
Problem: a man has some hens and cows . if the number of heads be 46 and the number of feet equals 136 , then the number of hens will be
Options: a ) 22 , b ) 24 , c ) 26 , d ) 20 , e ) 28
Rationale: "explanation : let number of hens = h and number of cows = c number of heads = 46 = > h + c = 46 - - - ( equation 1 ) number of feet = 136 = > 2 h + 4 c = 136 = > h + 2 c = 68 - - - ( equation 2 ) ( equation 2 ) - ( equation 1 ) gives 2 c - c = 68 - 46 = > c = 22 substituting the value of c in equation 1 , we get h + 22 = 46 = > h = 46 - 22 = 24 i . e . , number of hens = 24 answer : b"
Answer: b
Python program:
a = 46 * 4
b = a - 136
c = b / 2
Problem: find the smallest number which when divided by 13 and 17 leaves respective remainders of 3 and 7 .
Options: a ) 187 , b ) 211 , c ) 207 , d ) 219 , e ) 227
Rationale: "let ' n ' is the smallest number which divided by 13 and 17 leaves respective remainders of 3 and 7 . required number = ( lcm of 13 and 17 ) - ( common difference of divisors and remainders ) = ( 221 ) - ( 10 ) = 211 . answer : b"
Answer: b
Python program:
a = 13 * 17
b = 10 + 1 
c = a - b
Problem: a ' s speed is 20 / 13 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that b beats a by 25 % of the length of the race ?
Options: a ) 44 % , b ) 48 % , c ) 52 % , d ) 42 % , e ) 61 %
Rationale: "first calculate the distance , b has covered with his speed in the time , in which a reached 60 % of the race . then add the remaining distance as head start for b to win the race . its best to apply ratios concept here . since a ' s speed is 20 / 13 of b , therefore , b ' s speed is 13 / 20 of a distance covered by b = speed x time = ( 13 / 20 ) x ( 0.6 ) = 0.39 % ( which means b would have covered 0.39 of the race length during the time in which a has covered 0.6 of the race length . therefore to win , b needs a headstart of ( 1 - 0.39 = ) 0.61 of the race length . so the answer is e"
Answer: e
Python program:
a = 100 - 25
b = a / 100
c = 13 / 20
d = b * c
e = 1 - d
f = e * 100
Problem: find the constant k so that : - x 2 - ( k + 11 ) x - 8 = - ( x - 2 ) ( x - 4 )
Options: a ) 11 , b ) 12 , c ) 17 , d ) 14 , e ) 15
Rationale: "- x 2 - ( k + 11 ) x - 8 = - ( x - 2 ) ( x - 4 ) : given - x 2 - ( k + 11 ) x - 8 = - x 2 + 6 x - 8 - ( k + 11 ) = 6 : two polynomials are equal if their corresponding coefficients are equal . k = - 17 : solve the above for k correct answer c"
Answer: c
Python program:
a = 4 + 2 
b = 11 + a
Problem: what is the maximum number of pieces of birthday cake of size 10 ” by 10 ” that can be cut from a cake 20 ” by 20 ” ?
Options: a ) 4 , b ) 10 , c ) 16 , d ) 20 , e ) 25
Rationale: "the prompt is essentially asking for the maximum number of 10 x 10 squares that can be cut from a larger 20 by 20 square . since each ' row ' and each ' column ' of the larger square can be sub - divided into 2 ' pieces ' each , we have ( 2 ) ( 2 ) = 4 total smaller squares ( at maximum ) . a"
Answer: a
Python program:
a = 20 * 20
b = 10 * 10
c = a / b
Problem: if the sides of a triangle are 65 cm , 60 cm and 25 cm , what is its area ?
Options: a ) 120 cm 2 , b ) 750 cm 2 , c ) 216 cm 2 , d ) 197 cm 2 , e ) 275 cm 2
Rationale: "the triangle with sides 65 cm , 60 cm and 25 cm is right angled , where the hypotenuse is 65 cm . area of the triangle = 1 / 2 * 60 * 25 = 750 cm 2 answer : b"
Answer: b
Python program:
a = 60 * 25
b = a / 2
Problem: a man walking at a rate of 15 km / hr crosses a bridge in 30 minutes . the length of the bridge is ?
Options: a ) 1250 m , b ) 1110 m , c ) 950 m , d ) 1500 m , e ) 1300 m
Rationale: "speed = 15 * 5 / 18 = 15 / 18 m / sec distance covered in 30 minutes = 15 / 18 * 30 * 60 = 1500 m answer is d"
Answer: d
Python program:
a = 15 * 1000
b = a / const_60
c = b * 30
Problem: the population of a city increases by 7 % per year but due to migration it decrease by 1 % per years . what will be the percentage increase in population in 3 years ?
Options: a ) 9 % , b ) 9.10 % , c ) 27 % , d ) 12 % , e ) none of these
Rationale: "actual increase in population = 6 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 6 / 100 ) ^ 3 = 119.1016 ∴ required percentage = 9.1016 % answer : b"
Answer: b
Python program:
a = 7 - 1
b = 100 + a 
c = 7 - 1
d = b * c
e = d / 100
f = 7 - 1
g = e + f 
h = 100 + g 
i = 7 - 1
j = h * i
k = j / 100
l = 7 - 1
m = 100 + l 
n = 7 - 1
o = m * n
p = o / 100
q = 7 - 1
r = p + q 
s = k + r
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 r at the restaurant ? ( assume that all boxes are filled to capacity . )
Options: a ) 96 , b ) 240 , c ) r = 256 , d ) r = 384 , e ) r = 480
Rationale: most test takers would recognize thesystemof 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 factory has three types of machines , each of which works at its own constant rate . if 7 machine as and 11 machine bs can produce 360 widgets per hour , and if 8 machine as and 22 machine cs can produce 600 widgets per hour , how many widgets could one machine a , one machine b , and one machine c produce in one 8 - hour day ?
Options: a ) 400 , b ) 475 , c ) 480 , d ) 625 , e ) 700
Rationale: "let machine a produce a widgets per hour . b produce b widgets per hour and c produce c widgets per hour . 7 a + 11 b = 360 - - - ( 1 ) 8 a + 22 c = 600 - - - ( 2 ) dividing ( 2 ) by 2 4 a + 11 c = 300 . . . . . ( 3 ) adding ( 1 ) ( 3 ) 11 a + 11 b + 11 c = 660 a + b + c = 60 per hour so for eight hrs = 60 * 8 = 480 = answer = c"
Answer: c
Python program:
a = 600 / 11
b = a * 8
Problem: on increasing the number of lines in a page by 60 , they become 240 . what is the % of increase in the no . of lines in the page ?
Options: a ) 33.3 % , b ) 305 , c ) 50 % , d ) 55 % , e ) 60 %
Rationale: "explanation : number of pages increased = 60 now , the number of pages of book = 240 number of pages of the books before increase = 240 – 60 = 180 % increase in the number of pages in the book = 60 / 180 x 100 % = 33.3 % a"
Answer: a
Python program:
a = 240 - 60
b = 240 / a
c = b * 100
d = c - 100
Problem: if ( 2 ^ 14 ) ( 25 ^ s ) = 5 ( 10 ^ m ) what is the value of m ?
Options: a ) 7 , b ) 8 , c ) 15 , d ) 16 , e ) 14
Rationale: "given 2 ^ 14 * 25 ^ s = 5 * 10 ^ 2 = > 2 ^ 14 * 5 ^ ( 2 s ) = 2 ^ m * 5 ^ ( m + 1 ) ans e on comparing the power of 2 = > m = 14"
Answer: e
Python program:
a = 10 / 5
b = a ** 4
Problem: in a box carrying one dozen of oranges , one - third have become bad . if 3 oranges are taken out from the box at random , what is the probability that at least one orange out of the 3 oranges picked up is good ?
Options: a ) 1 ⁄ 55 , b ) 54 ⁄ 55 , c ) 45 ⁄ 55 , d ) 3 ⁄ 55 , e ) none of these
Rationale: n ( s ) = 12 c 3 = 12 × 11 × 10 / 3 × 2 = 2 × 11 × 10 = 220 no . of selection of 3 oranges out of the total 12 oranges = 12 c 3 = 2 × 11 × 10 = 220 no . of selection of 3 bad oranges out of the total 4 bad oranges = 4 c 3 = 4 \ n ( e ) = no . of desired selection of oranges = 220 – 4 = 216 \ p ( e ) = n ( e ) / n ( s ) = 216 / 220 = 54 / 55 answer b
Answer: b
Python program:
a = 10 + 1 
b = a * 12
c = b * 10
d = 3 * 2
e = c / d
f = e - 4
g = 10 + 1 
h = g * 12
i = h * 10
j = 3 * 2
k = i / j
l = f / k
Problem: a goods train runs at the speed of 72 km / hr and crosses a 220 m long platform in 26 sec . what is the length of the goods train ?
Options: a ) 382 , b ) 782 , c ) 300 , d ) 270 , e ) 881
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 220 ) / 26 = 20 x = 300 m . answer : c"
Answer: c
Python program:
a = 72 / 3600
b = a * 1000
c = b * 26
d = c - 220
Problem: a and b are two partially filled buckets of water . if 5 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 3 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?
Options: a ) 11 , b ) 13 , c ) 17 , d ) 49 / 5 , e ) 23
Rationale: "let a contains a , b contains b liters so , ( a - 5 ) / ( b + 5 ) = 1 / 3 . . . . . . . ( 1 ) again , ( b - 3 ) / ( a + 3 ) = 1 / 2 . . . . . . . . . . ( 2 ) from ( 1 ) ( 2 ) we find a = 49 / 5 ans : ( d )"
Answer: d
Python program:
a = 5 + 3 
b = a + 2 
c = 5 / 2
d = b * c
e = 1 / 2
f = 2 + e 
g = d / f
Problem: two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 10 % and 35 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
Options: a ) 18 % , b ) 20 % , c ) 21 % , d ) 35 % , e ) can not be determined
Rationale: answer : d .
Answer: d
Python program:
a = 10 * 4
b = a / 2
c = 10 + 5 
d = b + c
Problem: of 60 children , 30 are happy , 10 are sad , and 20 are neither happy nor sad . there are 18 boys and 42 girls . if there are 6 happy boys and 4 sad girls , how many boys are neither happy nor sad ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "venn diagrams are useful for multiple values of a single variable e . g . state of mind - happy / sad / neither . when you have two or more variables such as here where you have gender - boy / girl too , it becomes unwieldy . in this case , either use the table or logic . table method is shown above ; here is how you will use logic : there are 6 happy boys . there are 4 sad girls but total 10 sad children . so rest 6 sad children must be sad boys . we have 6 happy boys and 6 sad boys . total we have 18 boys . so 18 - 6 - 6 = 6 boys must be neither happy nor sad . answer ( c )"
Answer: c
Python program:
a = 10 - 4
b = 18 - a
c = b - 6
Problem: the sum of all the integers k such that − 26 < k < 24 is
Options: a ) 0 , b ) − 2 , c ) − 25 , d ) − 49 , e ) − 51
Rationale: "since k defines a range between − 26 < k < 24 we can set 0 as the reference point for the negative values and positive values . the negative values will range from - 25 to 0 whereas the positive values will range from 0 - 23 . we can conclude that for all but - 25 and - 24 the number pairs will add to 0 . so we have left - 25 - 24 = - 49 . answer d ."
Answer: d
Python program:
a = negate + ( 
b = a + 1
Problem: evaluate 75 / . 05
Options: a ) 1400 , b ) 1500 , c ) 1505 , d ) none of these , e ) 1506
Rationale: "explanation : 75 / . 05 = 7500 / 5 = 1500 option b"
Answer: b
Python program:
a = 5 / 75
b = 100 / 0
Problem: the length of a rectangle is three times of its width . if the length of the diagonal is 8 √ 10 then find the perimeter of the rectangle .
Options: a ) 77 cm
b ) 88 cm
c ) 64 cm
d ) 11 cm
e ) 18 cm
Rationale: let breadth = x cm , then , length = 3 x cm x 2 + ( 3 x ) 2 = ( 810 − − √ ) 2 = > 10 x 2 = 640 = > x = 8 x 2 + ( 3 x ) 2 = ( 810 ) 2 = > 10 x 2 = 640 = > x = 8 so , length = 24 cm and breadth = 8 cm perimeter = 2 ( l + b ) = 2 ( 24 + 8 ) = 64 cm answer : c
Answer: c
Python program:
a = 8 ** 2
b = math.sqrt(a)
c = 8 ** 2
d = math.sqrt(c)
e = d * 3
f = b + e 
g = f * 2
Problem: 225 metres long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 17
Rationale: "26 trees have 25 gaps between them , required distance ( 225 / 25 ) = 10 a"
Answer: a
Python program:
a = 26 - 2
b = a + 1 
c = 225 / b
Problem: car a runs at the speed of 60 km / hr and reaches its destination in 8 hours . car b runs at the speed of 70 km / h and reaches its destination in 4 hours . what is the ratio of distances covered by car a and car b ?
Options: a ) 3 : 7 , b ) 4 : 9 , c ) 12 : 7 , d ) 5 : 7 , e ) 6 : 11
Rationale: car a travels 60 × 8 = 480 km car b travels 70 × 4 = 280 km the ratio is 480 : 280 = 48 : 28 = 12 : 7 the answer is c .
Answer: c
Python program:
a = 60 * 8
b = 70 * 4
c = a / b
Problem: if an object travels at five feet per second , how many feet does it travel in one hour ?
Options: a ) 3488 , b ) 3778 , c ) 12788 , d ) 1800 , e ) 2881
Rationale: "explanation : if an object travels at 5 feet per second it covers 5 x 60 feet in one minute , and 5 x 60 x 60 feet in one hour . answer = 1800 answer : d ) 1800"
Answer: d
Python program:
a = 3 * const_60
b = a * const_60
Problem: a house wife saved $ 4 in buying an item on sale . if she spent $ 29 for the item , approximately how much percent she saved in the transaction ?
Options: a ) 8 % , b ) 9 % , c ) 10 % , d ) 11 % , e ) 12 %
Rationale: "actual price = 29 + 4 = $ 33 saving = 4 / 33 * 100 = 12 % approximately answer is e"
Answer: e
Python program:
a = 29 + 4 
b = 4 / a
c = b * 100
Problem: tough and tricky questions : exponents . if 2 ^ ( 3 x + 2 ) * 3 ^ ( 2 y - 3 ) = 32 ^ x * 9 ^ y , then x + y =
Options: a ) - 3 , b ) - 1 , c ) 0 , d ) - 5 , e ) - 2
Rationale: here is my solution . 2 ^ ( 3 x + 2 ) * 3 ^ ( y - 3 ) = 32 ^ x * 9 ^ y here rhs 32 ^ x * 9 ^ y = 2 ^ ( 5 x ) * 3 ^ ( 2 y ) equating powers on both sides - - > 3 x + 2 = 5 x , thus x = 1 and y - 3 = 2 y giving y = - 3 so , x + y = - 2 option : e
Answer: e
Python program:
a = 2 - 3
b = 3 / 2
c = b * 3
d = a * c
e = 3 / 2
f = d + e 
g = f + 1
Problem: what is the units digit of ( 147 ^ 25 ) ^ 49 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: the units digit of the exponents of 7 repeat in a cycle of four , which is { 7,9 , 3,1 } . the number 25 has the form 4 n + 1 so the units digit is 7 inside the bracket . the exponent 49 has the form 4 n + 1 , so the units digit is 7 . the answer is d .
Answer: d
Python program:
a = 4 + 3 
b = a + 2