euclaise/mathqa_programs huggingface dataset:
Problem: stacy and heather are 5 miles apart and walk towards each other along the same route . stacy walks at constant rate that is 1 mile per hour fast than heather ' s constant rate of 5 miles / hour . if heather starts her journey 24 minutes after stacy , how far from the original destination has heather walked when the two meet ? .
Options: a ) 2.5 mile , b ) 1.9 mile , c ) 1.7 mile , d ) 1.5 mile , e ) 1.18 mile
Rationale: "ss - stacy ' s speed = 6 m / hr sh - heather ' s speed = 5 m / hr in 24 minutes stacy will cover = ( 24 / 60 ) * 6 = 2.4 miles now since both are walking in opposite directions , add their speeds - 6 + 5 = 11 m / hr and distance to cover is 5 - 2.4 = 2.6 time taken = distance / speed = 2.6 / 11 = 0.23 hrs heather will cover = 5 * 0.23 = 1.18 miles . answer e"
Answer: e
Python program:
a = 1 + 5 
b = a / const_60
c = 24 * b
d = 5 - c
e = 1 + 5 
f = 5 + e 
g = d / f
h = g * 5
Problem: a train crosses a platform of 180 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 ) 30 , b ) 887 , c ) 167 , d ) 197 , e ) 161
Rationale: "length of the train be ‘ x ’ x + 180 / 15 = x + 250 / 20 20 x + 3600 = 15 x + 3750 5 x = 150 x = 30 m answer : a"
Answer: a
Python program:
a = 15 / 3
b = 15 / a
c = 250 * b
d = 15 / 3
e = 20 / d
f = 180 * e
g = c - f
Problem: 2 + 2 + 2 ² + 2 ³ . . . + 2 ^ 7
Options: a ) 2 ^ 9 , b ) 2 ^ 10 , c ) 2 ^ 16 , d ) 2 ^ 35 , e ) 2 ^ 8
Rationale: "2 + 2 = 2 ^ 2 2 ^ 2 + 2 ^ 2 = ( 2 ^ 2 ) * ( 1 + 1 ) = 2 ^ 3 2 ^ 3 + 2 ^ 3 = ( 2 ^ 3 ) * ( 1 + 1 ) = 2 ^ 4 so you can notice the pattern . . . in the end you will have 2 ^ 7 + 2 ^ 7 , which will give you 2 ^ 8 answer e"
Answer: e
Python program:
a = 2 + 2 
b = 2 * a
c = b / 2
Problem: what will be the difference between simple interest and compound interest @ 10 % per annum on a sum of rs . 1000 after 4 years ?
Options: a ) rs . 31 , b ) rs . 32.10 , c ) rs . 40.40 , d ) rs . 64.10 , e ) none
Rationale: solution s . i . = rs ( 1000 x 10 x 4 / 100 ) = rs . 400 . c . i . = rs . [ 1000 x ( 1 x 10 / 100 ) 4 - 1000 ] = rs . 464.10 ∴ difference = rs . ( 464.10 - 400 ) = rs . 64.10 answer d
Answer: d
Python program:
a = 10 / 100
b = a + 1 
c = b ** 4
d = c * 1000
e = d - 1000
f = 10 * 1000
g = 4 * f
h = g / 100
i = e - h
Problem: two men start together to walk a certain distance , one at 4 kmph and another at 3 kmph . the former arrives half an hour before the latter . find the distance .
Options: a ) 6 km , b ) 7 km , c ) 8 km , d ) 9 km , e ) none of these
Rationale: let the distance be x km . then , x / 3 - x / 4 = 1 / 2 ( 4 x - 3 x ) / 12 = 1 / 2 x = 6 km answer : a
Answer: a
Python program:
a = 3 * 4
b = a / 2
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 . 25 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 ) 100
Rationale: "use the options . the options which after getting added to 25 shows a cube of a number could be right . here 64 + 25 = 89 72 + 25 = 97 86 + 25 = 111 98 + 25 = 123 100 + 25 = 125 - - - ( 5 * 5 * 5 ) so we have 100 as the answer ! e"
Answer: e
Python program:
a = 1 + 3 
b = 1 + a 
c = b ** 3
d = c - 25
Problem: there are 35 kids in a play school . 26 kids play with white color balls and some kids play with yellow color balls and 19 kids play with both color balls . how many kids use yellow color balls ?
Options: a ) 12 , b ) 32 , c ) 5 , d ) 28 , e ) 35
Rationale: explanation : n ( aub ) = n ( a ) + n ( b ) - n ( anb ) . . . . ( 1 ) n ( a ) = number of kids playing with white color balls = 26 n ( aub ) = total number of kids in the play school = 35 n ( anb ) = number of kids playing with both white and yellow color balls = 19 we have to find , n ( b ) = number of kids playing with yellow color balls from ( 1 ) , 35 = 26 + n ( b ) - 19 n ( b ) = 35 + 19 - 26 = 28 hence , answer is 28 kids play with yellow color balls . answer : d
Answer: d
Python program:
a = 26 - 19
b = 35 - a
Problem: in a certain boys camp , 20 % of the total boys are from school a and 30 % of those study science . if there are 21 boys in the camp that are from school a but do not study science then what is the total number of boys in the camp ?
Options: a ) 70 , b ) 245 , c ) 150 , d ) 35 , e ) 350
Rationale: "since 30 % of the boys from school a study science , then 70 % of the boys from school a do not study science and since 20 % of the total number of boys are from school a , then 0.2 * 0.7 = 0.14 , or 14 % of the boys in the camp are from school a and do not study science . we are told that this number equals to 21 , so 0.14 * { total } = 21 - - > { total } = 150 . answer : c ."
Answer: c
Python program:
a = 100 - 30
b = a / 100
c = 20 / 100
d = b * c
e = 21 / d
Problem: a train 110 m long is running with a speed of 80 km / hr . in what time will it pass a man who is running at 8 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 5 , b ) 6 , c ) 4.5 , d ) 8 , e ) 9
Rationale: "speed of train relative to man = 80 + 8 = 88 km / hr . = 88 * 5 / 18 = 220 / 9 m / sec . time taken to pass the men = 110 * 9 / 220 = 4.5 sec . answer : option c"
Answer: c
Python program:
a = 80 + 8 
b = a * const_0_2778
c = 110 / b
Problem: tickets numbered 1 to 10 are mixed up and then a ticket is drawn at random . what is the probability that the ticket drawn bears a number which is a multiple of 2 ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 1 / 2 , d ) 2 / 3 , e ) 1 / 4
Rationale: "here , s = { 1 , 2,3 , . . . . . . , 9,10 } e = event getting a multiple of 3 = { 2 , 4,6 , 8,10 } probability = 5 / 10 = 1 / 2 correct option is c"
Answer: c
Python program:
a = 2 / 10
Problem: set a contains all the even numbers between 6 and 50 inclusive . set b contains all the even numbers between 106 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 ) 2300 , b ) 2550 , c ) 5050 , d ) 6275 , e ) 11325
Rationale: "set a contains 6 , 8 , . . . 50 set b contains 102 , 104 , 106 . . . 150 number of terms in each set = 23 difference between corresponding terms in set a and b = 100 difference between sum of set b and set a = 100 * 23 = 2300 answer a"
Answer: a
Python program:
a = 106 - 6
b = 50 - 6
c = b / 2
d = c + 1 
e = a * d
Problem: david completes a piece of work in 5 days , john completes the same work in 9 days . if both of them work together , then the number of days required to complete the work is ?
Options: a ) 3.2 days , b ) 8 days , c ) 10 days , d ) 12 days , e ) 14 days
Rationale: ifa can complete a work in x days and b can complete the same work in y days , then , both of them together can complete the work in x y / x + y days . that is , the required no . of days = 5 × 9 / 14 = 3.2 days answer : a
Answer: a
Python program:
a = 1/(9)
b = 1/(5)
c = a + b 
d = 1/(c)
Problem: the citizens of planet nigiet are 8 fingered and have thus developed their decimal system in base 8 . a certain street in nigiet contains 1000 buildings numbered 1 to 1000 in base 8 . how many 3 s are used in numbering these buildings ? express your answer in base 10
Options: a ) 192 , b ) 200 , c ) 196 , d ) 198 , e ) none
Rationale: "explanation : number 3 in 1 - 100 comes 20 times . 101 - 200 - > 20 times 201 - 300 - > 20 times 301 - 400 - > 120 times 401 - 500 - > 20 times 501 - 600 - > 20 times 601 - 700 - > 20 times 701 - 800 - > 20 times 801 - 900 - > 20 times 901 - 1000 - > 20 times total times : 300 times ( any no . from 1 to 9 except 0 will occur 300 times ) 8 based planet . . then 3 * 8 ( 2 ) + 0 * 8 ( 1 ) + 0 * 8 ( 0 ) = 192 answer : a"
Answer: a
Python program:
a = 8 ** 2
b = 3 * a
Problem: mixture a is 30 percent alcohol , and mixture b is 60 percent alcohol . if the two are poured together to create a 4 - gallon mixture that contains 40 percent alcohol , approximately how many gallons of mixture a are in the mixture ?
Options: a ) 0.8 , b ) 0.7 , c ) 0.6 , d ) 0.5 , e ) 0.4
Rationale: "( 60 - 50 ) / ( 50 - 30 ) = qa / qb 10 / 20 = qa / qb 1 / 2 = qa / qb qa = ( 1 / 6 ) * 4 = 4 / 6 = 1 / 2 = 0.50 answer : d"
Answer: d
Python program:
a = 30 * 60
b = a / 60
c = b / 2
Problem: 12 men work 8 hours per day to complete the work in 10 days . to complete the same work in 4 days , working 15 hours a day , the number of men required ?
Options: a ) 15 days , b ) 12 days , c ) 16 days , d ) 18 days , e ) 20 days
Rationale: that is , 1 work done = 12 × 8 × 10 then , 12 8 × 10 = ? × 15 × 6 ? ( i . e . no . of men required ) = 12 × 8 × 10 / 15 × 6 = 16 days c )
Answer: c
Python program:
a = 12 * 10
b = a * 8
c = 4 * 15
d = b / c
Problem: due to construction , the speed limit along an 4 - mile section of highway is reduced from 55 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 15 , e ) 2
Rationale: "4 / 35 - 4 / 55 = 4 / 5 * ( 11 - 7 ) / 77 = 4 / 5 * 4 / 77 * 60 min = 4 * 12 * 4 / 77 = 192 / 77 ~ 2.4 answer - e"
Answer: e
Python program:
a = 55 + 4 
b = a - 1
c = 4 / 35
d = 4 / 55
e = c - d
f = b * e
g = max(f)
Problem: if k ^ 3 is divisible by 162 , what is the least possible value of integer k ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 24 , e ) 36
Rationale: "k ^ 3 = 162 * x = 2 * 3 ^ 4 * x the factors of k must at minimum include 2 * 3 ^ 2 = 18 . the answer is c ."
Answer: c
Python program:
a = 162 / 2
b = a / 2
Problem: when positive integer x is divided by 11 , the quotient is y and the remainder is 4 . when 2 x is divided by 8 , the quotient is 3 y and the remainder is 3 . what is the value of 13 y – x ?
Options: a ) 1 , b ) 0 , c ) - 1 , d ) - 2 , e ) - 4
Rationale: "( 1 ) x = 11 y + 4 ( 2 ) 2 x = 24 y + 3 let ' s subtract equation ( 1 ) from equation ( 2 ) . 13 y - 1 = x 13 y - x = 1 the answer is a ."
Answer: a
Python program:
a = 2 * 4
b = a - 3
c = 8 * 3
d = 2 * 11
e = c - d
f = b / e
g = 13 * f
h = 2 * 4
i = h - 3
j = 8 * 3
k = 2 * 11
l = j - k
m = i / l
n = 11 * m
o = n + 4 
p = g - o
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 12 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 , b ) 4 , c ) 6 , d ) 9 / 2 , 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 12 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 / 12 lets say x machines are used to attain the desired rate , thus x / 36 + x / 12 = 1 / 2 ( desired r = 1 / 2 i . e . to complete the job in 2 hours ) ( x + 3 x ) / 36 = 1 / 2 4 x / 36 = 1 / 2 x = 9 / 2 . qa = 9 / 2 ( answer d )"
Answer: d
Python program:
a = 1 / 36
b = 1 / 2
c = a + b 
d = 12 * c
e = 1 / d
Problem: a can do a piece of work in 20 days ; b can do the same in 30 days . a started alone but left the work after 10 days , then b worked at it for 10 days . c finished the remaining work in 10 days . c alone can do the whole work in ?
Options: a ) 24 days , b ) 60 days , c ) 86 days , d ) 45 days , e ) 17 days
Rationale: "10 / 20 + 10 / 30 + 10 / x = 1 x = 60 days answer : b"
Answer: b
Python program:
a = 10 + 10 
b = a / 20
c = 1 - b
d = 10 / c
Problem: a money lender lent rs . 800 at 3 % per year and rs . 1400 at 5 % per year . the amount should be returned to him when the total interest comes to rs . 350 . find the number of years .
Options: a ) 3.5 , b ) 3.72 , c ) 4 , d ) 4.25 , e ) 4.5
Rationale: ( 800 xtx 3 / 100 ) + ( 1400 xtx 5 / 100 ) = 350 â † ’ t = 3.72 answer b
Answer: b
Python program:
a = 3 * 800
b = a / 100
c = 1400 * 5
d = c / 100
e = b + d 
f = 350 / e
Problem: two watches are set for an alarm at 10 0 ' clock in the night . one watch gains 2 minutes per hour . when the faster watch shows 4 : 12 in the morning when the alarm rings what does the correct watch show ?
Options: a ) 5 : 00 , b ) 4 : 00 , c ) 4 : 10 , d ) 5 : 20 , e ) 6 : 00
Rationale: the faster watch gains 2 minutes per hour the two watches show 10 : 00 at 10 0 ' clock at 11 0 ' clock - the correct watch is at 11 : 00 the faster watch is at 11 : 02 ( 1 hour + gains 2 minutes per hour ) at 12 midnight - the correct watch is at 12 : 00 the faster watch is at 12 : 04 ( 2 hours + gains 4 minutes per 2 hours ) in 6 hours the faster watch gains 6 * 2 = 12 minutes and is at 4 : 12 and the correct watch is at 4 : 00 answer is b
Answer: b
Python program:
a = 4 + 12 
b = 4 + 12 
c = b - 10
d = c * 2
e = a - d
Problem: if 3 x – 5 y = 5 and x / x + y = 5 / 7 , then what is the value of x – y ?
Options: a ) 9 , b ) 6 , c ) 4 , d ) 3 , e ) none of these
Rationale: 3 x – 5 y = 5 . . . ( i ) and xx + y = 57 xx + y = 57 ⇒ 7 x = 5 x + 5 y ⇒ 2 x = 5 y . . . ( ii ) from ( i ) and ( ii ) , x = 5 and y = 2 ∴ x – y = 3 answer d
Answer: d
Python program:
a = 5 / 7
b = 1/(a)
c = b - 1
d = c * 5
e = 3 - d
f = 5 / e
g = 5 / 7
h = 1/(g)
i = h - 1
j = 5 / 7
k = 1/(j)
l = k - 1
m = l * 5
n = 3 - m
o = 5 / n
p = i * o
q = f - p
Problem: a , b and c are partners . a receives 2 / 3 of profits , b and c dividing the remainder equally . a ' s income is increased by rs . 300 when the rate to profit rises from 5 to 7 percent . find the capital of b ?
Options: a ) 3750 , b ) 7799 , c ) 2500 , d ) 2772 , e ) 2912
Rationale: "a : b : c = 2 / 3 : 1 / 6 : 1 / 6 = 4 : 1 : 1 x * 2 / 100 * 2 / 3 = 300 b capital = 22500 * 1 / 6 = 3750 . answer : a"
Answer: a
Python program:
a = 300 * 100
b = a / 2
Problem: john borrowed 3 soccer boots from jake , and forgot them on the field , if peter came across a total of 15 boots on the field jake ' s boots inclusive , and he took 4 boots at random , what is the probability that jake ' s boots were not amongst the 4 taken ? .
Options: a ) 12 / 91 , b ) 3 / 15 , c ) 12 / 15 , d ) 33 / 91 , e ) 3 / 91
Rationale: since jake owns 3 of the boots , the subset from which the 4 boots should be chosen are the 12 boots not owned by jake from the universe of 15 . the first boot can be one of the 12 from the 15 with probability 12 / 15 . the second boot can be one of the 11 from the 14 remaining with probability 11 / 14 . the third boot can be one of the 10 from the 13 remaining with probability 10 / 13 . the fourth boot can be one of the 9 from the 12 remaining with probability 9 / 12 . the total probability will be 12 / 15 × 11 / 14 × 10 / 13 × 9 / 12 . on cancellation , this comes to 33 / 91 . thus , the answer is d - 33 / 91
Answer: d
Python program:
a = 15 - 3
b = math.comb(a, 4)
c = math.comb(15, 4)
d = b / c
Problem: a student needs 30 % of the marks on a test to pass the test . if the student gets 80 marks and fails the test by 40 marks , find the maximum marks set for the test .
Options: a ) 400 , b ) 500 , c ) 600 , d ) 700 , e ) 800
Rationale: 30 % = 120 marks 1 % = 4 marks 100 % = 400 marks the answer is a .
Answer: a
Python program:
a = 80 + 40 
b = 30 / 100
c = a / b
Problem: set a consists of the integers from 5 to 10 , inclusive , while set b consists of the integers from 1 to 8 , inclusive . how many distinct integers do belong to the both sets at the same time ?
Options: a ) 5 , b ) 10 , c ) 8 , d ) 2 , e ) 4
Rationale: "a = { 5,6 , 7 , 8 , 9 , 10 } b = { 1,2 , 3,4 , 5,6 , 7,8 } common elements = { 5,6 , 7 , 8 } = 4 elements answer : option e ."
Answer: e
Python program:
a = 1 + 5
Problem: he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 75 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 95 kg , c ) 45 kg , d ) 85 kg , e ) 25 kg
Rationale: "explanation : total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 75 + 20 ) kg = 95 kg . answer : b"
Answer: b
Python program:
a = 2 * 5
b = a + 75
Problem: a garden center sells a certain grass seed in 5 - pound bags at $ 13.85 per bag , 10 - pound bags at $ 20.40 per bag , and 25 - pound bags $ 32.25 per bag . if a customer is to buy at least 65 pounds of the grass seed , but no more than 80 pounds , what is the least possible cost of the grass seed that the customer will buy ?
Options: a ) $ 94.03 , b ) $ 96.75 , c ) $ 98.75 , d ) $ 102.07 , e ) $ 105.3
Rationale: "there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.75 or 2 ) 25 + 25 + 25 = $ 96.75 c"
Answer: c
Python program:
a = 2 * 32
b = 1 * 20
c = a + b 
d = 1 * 13
e = c + d
Problem: the difference between compound interest and simple interest on a certain amount of money at 5 % per annum for 2 years is 20 . find the sum :
Options: a ) 4500 , b ) 7500 , c ) 5000 , d ) 8000 , e ) none of these
Rationale: "sol . ( d ) let the sum be 100 . therefore , si = 100 × 5 × 2100 = 10100 × 5 × 2100 = 10 and ci = 100 ( 1 + 5100 ) 2 − 100100 ( 1 + 5100 ) 2 − 100 ∴ = 100 × 21 × 2120 × 20 − 100 = 414 = 100 × 21 × 2120 × 20 − 100 = 414 difference of ci and si = 41 ⁄ 4 - 10 = 1 ⁄ 4 if the difference is 1 ⁄ 4 , the sum = 100 = > if the difference is 20 , the sum = 400 × 20 = 8000 answer d"
Answer: d
Python program:
a = 5 / 100
b = 1 + a 
c = b ** 2
d = 5 / 100
e = 2 * d
f = 1 + e 
g = c - f
h = 20 / g
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 . 8400 ?
Options: a ) rs . 12 , b ) rs . 16 , c ) rs . 14 , d ) rs . 10 , e ) rs . 18
Rationale: "required difference = [ 3 ½ % of rs . 8400 ] – [ 3 1 / 3 % of rs . 8400 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 8400 = 1 / 6 % of rs . 8400 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 8400 ] = rs . 14 . answer is c ."
Answer: c
Python program:
a = 1 / 2
b = a + 3 
c = 1 / 3
d = c + 3 
e = b - d
f = e * 8400
g = f / 100
Problem: how many two - digit whole numbers yield a remainder of 2 when divided by 12 and also yield a remainder of 2 when divided by 6 ?
Options: a ) none , b ) five , c ) six , d ) seven , e ) eight
Rationale: "the possible number n can be written as follow : n = multiple of lcm ( 12,6 ) + 1 st such number n = 12 x + 2 possible values = 2 , 26,38 , 50,62 , 86,98 answer : 6 such 2 digit number . c ."
Answer: c
Python program:
a = 2 + 2 
b = a + 2
Problem: find ( 7 x + 8 y ) / ( x - 2 y ) if x / 2 y = 3 / 2 ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 29
Rationale: x / 2 y = 3 / 2 = > x = 6 y / 2 = 3 y = > ( 7 x + 8 y ) / ( x - 2 y ) = ( ( 7 * ( 3 y ) ) + 8 y ) / ( 3 y - 2 y ) = > 29 y / y = 29 answer : e
Answer: e
Python program:
a = 3 / 2
b = a * 2
c = b * 7
d = c + 8 
e = 3 / 2
f = e * 2
g = f - 2
h = d / g
Problem: kramer can pack 10 boxes of cigarettes per minute . if there are 5 boxes of cigarettes in one case , how many cases can kramer pack in 2 hours ?
Options: a ) 100 , b ) 120 , c ) 240 , d ) 150 , e ) 200
Rationale: kramer can pack 10 boxes per min . therefore in 2 hrs ( 120 mins ) he can pack 120 * 10 = 1200 boxes . if there are 5 boxes in one case then then the total number of cases packed by kramer = 1200 / 5 = 240 answer is c
Answer: c
Python program:
a = const_60 * 2
b = a * 10
c = b / 5
Problem: what number should replace the question mark ? 11 , 15 , 16 , 12 , 21 , 9 , - - - ?
Options: a ) 21 , b ) 29 , c ) 28 , d ) 27 , e ) 26
Rationale: "answer : e 11 , 15 , 16 , 12 , 21 , 9 , - - - ? there are two alternate sequences : + 5 and - 3 ."
Answer: e
Python program:
a = 2 + 0 
b = a + 11 
c = b + 11
Problem: list d consists of 12 consecutive integers . if - 4 is the least integer in list d , what is the range of positive integers in list d ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 12
Rationale: since - 4 is the least integer in list d , then 7 is the largest integer in that list . thus the range of the positive integers in the list is 7 - 1 = 6 . answer : b .
Answer: b
Python program:
a = 12 - 1
b = a - 4
c = b - 1
Problem: a train 125 m long passes a man , running at 15 km / hr in the same direction in which the train is going , in 10 sec . the speed of the train is ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 79 , e ) 80
Rationale: "speed of the train relative to man = 125 / 10 = 25 / 2 m / sec . = 25 / 2 * 18 / 5 = 45 km / hr let the speed of the train be x km / hr . then , relative speed = ( x - 15 ) km / hr . x - 15 = 45 = > x = 60 km / hr . answer : option c"
Answer: c
Python program:
a = 15 * const_0_2778
b = a * 15
c = 125 - b
d = c / 15
e = d / const_0_2778
Problem: the ratio of the volumes of two cubes is 729 : 1000 . what is the ratio of their total surface areas ?
Options: a ) 1 : 12 , b ) 81 : 13 , c ) 46 : 51 , d ) 86 : 16 , e ) 56 : 13
Rationale: "ratio of the sides = ³ √ 729 : ³ √ 1000 = 9 : 10 ratio of surface areas = 92 : 102 = 46 : 51 answer : c"
Answer: c
Python program:
a = 729 / 1000
b = 1 / 3
c = a ** b
Problem: the average weight of 9 person ' s increases by 5.5 kg when a new person comes in place of one of them weighing 86 kg . what might be the weight of the new person ?
Options: a ) 72 kg , b ) 77.5 kg , c ) 135.5 kg , d ) data inadequate , e ) none of these
Rationale: "total weight increased = ( 9 x 5.5 ) kg = 49.5 kg . weight of new person = ( 86 + 49.5 ) kg = 135.5 kg . answer : option c"
Answer: c
Python program:
a = 9 * 5
b = a + 86
Problem: in a maths test , students were asked to find 5 / 16 of a certain number . one of the students by mistake found 5 / 6 th of that number and his answer was 50 more than the correct answer . find the number .
Options: a ) 96 , b ) 280 , c ) 384 , d ) 400 , e ) 500
Rationale: "explanation : let the number be x . 5 * x / 6 = 5 * x / 16 + 50 25 * x / 48 = 50 x = 96 answer a"
Answer: a
Python program:
a = 50 * 16
b = a * 6
c = 5 * 16
d = 5 * 6
e = c - d
f = b / e
Problem: a rectangle having length 150 cm and width 40 cm . if the length of the rectangle is increased by fifteen percent then how much percent the breadth should be decreased so as to maintain the same area .
Options: a ) 25 % , b ) 9.09 % , c ) 40 % , d ) 75 % , e ) none of these
Rationale: "explanation : solution : ( 15 / ( 150 + 15 ) * 100 ) % = 9.09 % answer : b"
Answer: b
Python program:
a = 150 * 40
b = 3 * 10
c = b * 150
d = c / 100
e = 150 + d 
f = a / e
g = f / 40
h = 1 + g 
i = h * 10
Problem: two numbers n and 12 have lcm = 42 and gcf = 6 . find n .
Options: a ) 35 , b ) 56 , c ) 21 , d ) 87 , e ) 24
Rationale: "the product of two integers is equal to the product of their lcm and gcf . hence . 12 * n = 42 * 6 n = 42 * 6 / 12 = 21 correct answer c"
Answer: c
Python program:
a = 42 * 6
b = a / 12
Problem: ajay spends 45 % of his monthly income on household items , 25 % of his monthly income on buying cloths , 7.5 % of his monthly income on medicines and saves the remaining amount which is rs . 9000 . find his monthly income .
Options: a ) rs . 40000 , b ) rs . 36000 , c ) rs . 50000 , d ) rs . 45000 , e ) none of these
Rationale: "let the monthly income of ajay be rs . x savings of ajay = x - ( 45 + 25 + 7.5 ) / 100 * x = 22.5 / 100 x 22.5 / 100 x = 9000 x = 40000 . answer : a"
Answer: a
Python program:
a = 45 + 25 
b = a + 7 
c = 100 - b
d = c / 100
e = 9000 / d
Problem: the average of numbers 0.44204 , 0.44203 , 0.44202 and 0.44201 is ?
Options: a ) 0.44202 , b ) 0.44204 , c ) 0.442022 , d ) 0.442025 , e ) none
Rationale: "answer average = ( 0.44204 + 0.44203 + 0.44202 + 0.44201 ) / 4 = 1.7681 / 4 = 0.442025 correct option : d"
Answer: d
Python program:
a = 0 * 44204
b = 0 * 44204
c = a + b 
d = c / 0
Problem: how many diagonals does a polygon with 19 sides have , if one of its vertices does not connect to any diagonal ?
Options: a ) 135 , b ) 125 , c ) 120 , d ) 110 , e ) 140
Rationale: "if i calculate it using the formulae , # diagonals = n ( n - 3 ) / 2 each vertex sends of n - 3 diagonals n = 19 - 1 then 18 * ( 18 - 3 ) / 2 = 135 correct option : a"
Answer: a
Python program:
a = 19 - 1
b = 19 - 1
c = b - 3
d = a * c
e = d / 2