euclaise/mathqa_programs huggingface dataset:
Problem: a man purchased 3 blankets @ rs . 100 each , 3 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) 750 , b ) 277 , c ) 878 , d ) 450 , e ) 272
Rationale: "10 * 150 = 1500 3 * 100 + 3 * 150 = 750 1500 – 750 = 750 answer : a"
Answer: a
Python program:
a = 10 * 150
b = 3 * 100
c = 3 * 150
d = b + c 
e = a - d
Problem: an amount at compound interest sums to rs . 17640 / - in 2 years and to rs . 18522 / - in 3 years at the same rate of interest . find the rate percentage ?
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "the difference of two successive amounts must be the simple interest in 1 year on the lower amount of money . s . i = 18522 / - - 17640 / - = rs . 882 / - rate of interest = ( 882 / 17640 ) × ( 100 / 1 ) = > 8820 / 1764 = 5 % principal = amount / ( 1 + r / 100 ) n = 17640 / ( 1 + 5 / 100 ) 2 = 17640 / ( 21 / 20 × 21 / 20 ) = 17640 / ( 1.05 × 1.05 ) = 17640 / 1.1025 = 16000 thus the principal is rs . 16000 / - and the rate of interest is 5 % a"
Answer: a
Python program:
a = 18522 - 17640
b = a / 17640
c = b * 100
Problem: how many integers from 101 to 1000 , inclusive , remains the value unchanged when the digits were reversed ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "question is asking for palindrome first digit possibilities - 1 through 9 = 9 second digit possibilities - 0 though 9 = 10 third digit is same as first digit = > total possible number meeting the given conditions = 9 * 10 = 90 answer is e ."
Answer: e
Python program:
a = 1000 / 10
Problem: when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 37 ?
Options: a ) 3 , b ) 4 , c ) 12 , d ) 6 , e ) 35
Rationale: "n = 5 p + 1 = 6,11 , 16,21 , 26,31 n = 7 q + 3 = 3 , 10,17 , 24,31 = > n = 37 m + 31 to get this , we need to take lcm of co - efficients of p and q and first common number in series . so we need to add 6 more to make it 37 m + 36 answer - d"
Answer: d
Python program:
a = 37 - reminder
Problem: a train covers a distance of 12 km in 10 min . if it takes 2 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 40 , b ) 80 , c ) 20 , d ) 100 , e ) 60
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 2 = 40 m . answer : option a"
Answer: a
Python program:
a = 12 / 10
b = a - 2
c = 12 / b
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 49 hours respectively . the ratio of their speeds is ?
Options: a ) 4 : 7 , b ) 7 : 3 , c ) 4 : 9 , d ) 4 : 4 , e ) 4 : 2
Rationale: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 49 : â ˆ š 9 = 7 : 3 . answer : b"
Answer: b
Python program:
a = math.sqrt(49)
b = math.sqrt(9)
c = a / b
Problem: at what price must an article costing rs . 47.50 be marked in order that after deducting 10 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 65.9 , b ) 62.3 , c ) 62.7 , d ) 62.2 , e ) 62.9
Rationale: "cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 90 / 100 ) = 59.375 mp = 65.9 answer : a"
Answer: a
Python program:
a = 47 * 50
b = a / 100
c = 47 + 50 
d = c * 100
e = 100 - 10
f = d / e
Problem: two vessels having volumes in the ratio 3 : 5 are filled with water and milk solutions . the ratio of milk and water in the two vessels are 1 : 2 and 6 : 4 respectively . if the contents of both the vessel are empties into a larger vessel , find the ratio of milk and water in the larger vessel .
Options: a ) 1 : 1 , b ) 2 : 1 , c ) 3 : 1 , d ) 5 : 1 , e ) 6 : 1
Rationale: "vessel a = 300 gallons - - > milk = 100 , water = 200 ; vessel b = 500 gallons - - > milk = 300 , water = 200 ; vessel a + b = 800 gallons - - > milk = 400 , water 400 the ratio = 400 / 400 - - > 1 : 1 answer : a"
Answer: a
Python program:
a = 1 ** 3
Problem: the price of a jacket is reduced by 10 % . during a special sale the price of the jacket is reduced another 30 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ?
Options: a ) 32.5 , b ) 58.7 , c ) 48 , d ) 65 , e ) 67.5
Rationale: "1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 10 % , therefore bringing down the price to $ 90 . 3 ) again it is further discounted by 30 % , therefore bringing down the price to $ 63 . 4 ) now 67.5 has to be added byx % in order to equal the original price . 63 + ( x % ) 63 = 100 . solving this eq for x , we get x = 58.7 ans is b"
Answer: b
Python program:
a = 100 - 10
b = 100 - 10
c = 30 / 100
d = b * c
e = a - d
f = 100 - e
g = 100 - 10
h = 100 - 10
i = 30 / 100
j = h * i
k = g - j
l = f / k
m = 100 * l
Problem: the ratio between the sale price and the cost price of an article is 7 : 5 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 8 , b ) 2 : 1 , c ) 2 : 2 , d ) 2 : 4 , e ) 2 : 5
Rationale: "explanation : let c . p . = rs . 5 x and s . p . = rs . 7 x . then , gain = rs . 2 x required ratio = 2 x : 5 x = 2 : 5 answer : e"
Answer: e
Python program:
a = 7 - 5
b = a / 5
Problem: two trains 110 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.9 , b ) 10.7 , c ) 10.3 , d ) 10.8 , e ) 9.72
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 110 + 160 = 270 m . required time = 270 * 9 / 250 = 243 / 25 = 9.72 sec . ' answer : e"
Answer: e
Python program:
a = 110 + 160 
b = 60 + 40 
c = b * const_0_2778
d = a / c
Problem: thomas ' s age and matt ' s age are in the ratio 3 : 5 . two years ago the ratio of their ages was 5 : 9 . find the ratio of their ages 4 years hence ?
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) 5 : 6
Rationale: let ages of thomas and matt be x and y respectively . x / y = 3 / 5 = > x = 3 / 5 y ( x - 2 ) / ( y - 2 ) = 5 / 9 = > 9 x - 18 = 5 y - 10 = > 9 x = 5 y + 8 but x = 3 / 5 y 9 * 3 / 5 y = 5 y + 8 27 y = 25 y + 40 = > y = 20 years = > x = 3 * 20 / 5 = > 12 years ratio of their ages four years hence , ( 12 + 4 ) / ( 20 + 4 ) = 16 / 24 . = > 2 : 3 answer : b
Answer: b
Python program:
a = 5 + 3 
b = a * 5
c = b / 2
d = c * 3
e = d / 5
f = e + 4 
g = 5 + 3 
h = g * 5
i = h / 2
j = i + 4 
k = f / j
Problem: dan ' s age after 16 years will be 4 times his age 8 years ago . what is the present age of dan ?
Options: a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 28
Rationale: let dan ' s present age be x . x + 16 = 4 ( x - 8 ) 3 x = 48 x = 16 the answer is b .
Answer: b
Python program:
a = 8 * 4
b = 16 + a 
c = 4 - 1
d = b / c
Problem: how much space , in cubic units , is left vacant when maximum number of 6 x 6 x 6 cubes are fitted in a rectangular box measuring 12 x 18 x 14 ?
Options: a ) 428 , b ) 429 , c ) 430 , d ) 431 , e ) 432
Rationale: "no of cubes that can be accommodated in box = ( 12 * 18 * 14 ) / ( 6 * 6 * 6 ) 12 * 16 in numerator can be perfectly divided by 6 * 6 in denominator . side with length 14 ca n ' t be perfectly divided by 6 and hence is the limiting factor . closet multiple of 6 less that 14 is 12 . so vacant area in cube = = 18 * 12 * ( 14 - 12 ) = 18 * 12 * 2 = 432 ans - e"
Answer: e
Python program:
a = 6 * 2
b = 12 - a
c = 18 * 14
d = b * c
Problem: a work as fast as b . if b can complete a work in 16 days independently , the number of days in which a and b can together finish the work in ?
Options: a ) 2 days , b ) 3 days , c ) 4 days , d ) 5 1 / 3 days , e ) 6 days
Rationale: "ratio of rates of working of a and b = 2 : 1 ratio of times taken = 1 : 2 a ' s 1 day work = 1 / 8 b ' s 1 day work = 1 / 16 a + b 1 day work = 1 / 8 + 1 / 16 = 3 / 16 = > 16 / 3 = 5 1 / 3 a and b can finish the work in 5 1 / 3 days answer is d"
Answer: d
Python program:
a = 1/(16)
b = 1/(16)
c = 2 * b
d = a + c 
e = 1/(d)
Problem: the sum of 11 consecutive integers is 1111 . what is the greatest integer in the set ?
Options: a ) 100 , b ) 102 , c ) 104 , d ) 106 , e ) 108
Rationale: "let x be the first integer in the set , then x + 10 is the largest integer . the sum is : x + ( x + 1 ) + ( x + 2 ) + . . . + ( x + 10 ) = 11 x + 10 * 11 / 2 = 11 ( x + 5 ) then x + 5 = 101 x = 96 the largest integer in the set is 96 + 10 = 106 the answer is d ."
Answer: d
Python program:
a = 11 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 11 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 11 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 11 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: for any integer n greater than 1 , n * denotes the product of all the integers from 1 to n , inclusive . how many prime numbers q are there between 6 * + 2 and 6 * + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: given that n * denotes the product of all the integers from 1 to n , inclusive so , 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 . now , notice that we can factor out 2 our of 6 ! + 2 so it can not be a prime number , we can factor out 3 our of 6 ! + 3 so it can not be a prime number , we can factor out 4 our of 6 ! + 4 so it can not be a prime number , . . . the same way for all numbers between 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 , inclusive . which means that there are no primes q in this range . answer : a .
Answer: a
Python program:
a = math.factorial(6)
b = a + 6 
c = math.factorial(6)
d = c + 6 
e = b / d
Problem: 5020 − ( 1004 ÷ 20.08 ) = ?
Options: a ) 4520 , b ) 4350 , c ) 4210 , d ) 4100 , e ) 4970
Rationale: "explanation : = 5020 − ( 1004 / 2008 × 100 ) = 5020 − 50 = 4970 option e"
Answer: e
Python program:
a = 1004 / 20
b = 5020 - a
Problem: it takes 60 identical printing machines 2 hours to print 300 cards . how much more time would it take 50 of these machines to print the same total ?
Options: a ) 20 min , b ) 25 min , c ) 26 min , d ) 36 min , e ) 30 min
Rationale: 50 % of 60 = 30 % or 0.30 2 hr x 60 min = 120 min 120 min x 0.30 = 36 min it will take 36 min longer to print them with only 50 printers . answer is d
Answer: d
Python program:
a = 60 / 2
b = 300 / 50
c = a + b
Problem: a 18 % stock yielding 12 % is quoted at :
Options: a ) s . 83.33 , b ) s . 110 , c ) s . 112 , d ) s . 120 , e ) s . 150
Rationale: "income of rs 12 on investment of rs 100 income of rs 18 on investment of ? = ( 18 * 100 ) / 12 = 150 answer : e"
Answer: e
Python program:
a = 100 / 12
b = a * 18
Problem: ( 23341379 × 72 ) = ?
Options: a ) 1223441288 , b ) 2142579288 , c ) 2142339288 , d ) 2142339277 , e ) 1680579288
Rationale: "23341379 × 72 = 23341379 ( 70 + 2 ) = ( 23341379 × 70 ) + ( 23341379 × 2 ) = 1633896530 + 46682758 = 1680579288 answer is e ."
Answer: e
Python program:
a = 4 + 1 
b = a ** 4
c = 23341379 * b
Problem: the maximum number of student amoung them 1802 pens and 1203 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Options: a ) 1 , b ) 10 , c ) 11 , d ) 19 , e ) none of these
Rationale: solution required number of student = h . c . f of 1802 and 1203 = 1 . answer a
Answer: a
Python program:
a = math.gcd(1802, 1203)
Problem: how many of the positive factors of 25 , 150 and how many common factors are there in numbers ?
Options: a ) 2 , b ) 4 , c ) 3 , d ) 5 , e ) 1
Rationale: "factors of 25 - 1 , 5 , 25 factors of 150 - 1 , 2 , 3 , 5 , 6 , 10 , 15 , 25 , 30 , 50 , 75 , 150 comparing both , we have three common factors of 25 and 150 - 1 , 5,25 answer ( c )"
Answer: c
Python program:
a = 150 / 25
Problem: if the cost price of 35 chocolates is equal to the selling price of 21 chocolates , the gain percent is :
Options: a ) 66.55 % , b ) 66.66 % , c ) 66 % , d ) 55 % , e ) 66.33 %
Rationale: "explanation : solution : let c . p . of each chocolate be re . 1 . then , c . p . of 21 chocolates = rs . 21 ; s . p . of 21 chocolates = rs . 35 . . ' . gain % = 14 * 100 / 21 = 66.66 % answer : b"
Answer: b
Python program:
a = 35 - 21
b = 21 / a
c = 100 / b
Problem: nd the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 15 cm ?
Options: a ) 766 cm 2
b ) 535 cm 2
c ) 285 cm 2
d ) 324 cm 2
e ) 235 cm 2
Rationale: area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 15 ) = 285 cm 2 answer : c
Answer: c
Python program:
a = 20 + 18 
b = 15 * a
c = b / 2
Problem: if ( 10 ^ 4 * 3.456789 ) ^ 11 is written as a single term , how many digits would be to the right of the decimal place ?
Options: a ) 12 , b ) 18 , c ) 22 , d ) 28 , e ) 36
Rationale: "3.456789 ^ 11 has 6 * 11 = 66 decimal places . 10 ^ 44 moves the decimal place to the right 44 places . ( 10 ^ 4 * 3.456789 ) ^ 11 has 66 - 44 = 22 digits after the decimal point . the answer is c ."
Answer: c
Python program:
a = 11 * 2
Problem: a 300 m long train crosses a platform in 36 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 288 , b ) 300 , c ) 889 , d ) 276 , e ) 234
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 36 = 50 / 3 3 x + 900 = 1800 = > x = 300 m . answer : b"
Answer: b
Python program:
a = speed * (
b = a - 36
Problem: the average expenditure of a labourer for 3 months was 85 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income is
Options: a ) 70.2 , b ) 50.1 , c ) 75.2 , d ) 78.4 , e ) 52.5
Rationale: "income of 3 months = ( 3 × 85 ) – debt = 255 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 525 average monthly income = 525 ÷ 10 = 52.5 answer e"
Answer: e
Python program:
a = 85 * 3
b = 60 * 4
c = a + b 
d = c + 30 
e = 3 + 4 
f = d / e
Problem: the average ( arithmetic mean ) of 16 students first quiz scores in a difficult english class is 62.5 . when one student dropped the class , the average of the remaining scores increased to 63.0 . what is the quiz score of the student who dropped the class ?
Options: a ) a ) 10 , b ) b ) 25 , c ) c ) 40 , d ) d ) 55 , e ) e ) 70
Rationale: total score of 16 students is 16 * 62.50 = 1000 total score of 15 students is 15 * 63 = 945 so , the score of the person who left is 55 ( 1000 - 945 ) answer will be ( d )
Answer: d
Python program:
a = 16 * 62
b = 16 - 1
c = b * 63
d = a - c
Problem: how many positive integers w between 200 and 300 ( both inclusive ) are not divisible by 2 , 3 or 5 ?
Options: a ) 3 , b ) 16 , c ) 75 , d ) 24 , e ) 26
Rationale: 1 ) i figured there are 101 integers ( 300 - 200 + 1 = 101 ) . since the set begins with an even and ends with an even , there are 51 evens . 2 ) question says integers are not divisible by 2 , leaving all of the odds ( 101 - 51 = 50 integers ) . 3 ) question says integers are not divisible by 5 , removing all the integers ending in 5 ( already took out those ending in 0 ) . take out 10 integers ( 2 ? 5 , ? = 0 to 9 ) , leaving us with 40 integers . 4 ) now the painstaking part . we have to remove the remaining numbers that are multiples of 3 . those are 201 , 207 , 213 , 219 , 231 , 237 , 243 , 249 , 261 , 267 , 273 , 279 , 291 , and 297 . . . a total of 14 numbers . 26 numbers left ! 6 ) answer choice e .
Answer: e
Python program:
a = 300 - 200
b = a + 1 
c = 300 / 2
d = 200 / 2
e = c - d
f = e + 1 
g = b - f
h = 300 / 3
i = 200 / 3
j = h - i
k = j + 1 
l = 3 + 4 
m = 10 + l 
n = k - m
o = g - n
p = 300 / 5
q = 200 / 5
r = p - q
s = r + 1 
t = 10 + 5 
u = s - t
v = o - u
Problem: the cost price of an article is 64 % of the marked price . calculate the gain percent after allowing a discount of 25 % ?
Options: a ) 37.5 % , b ) 37.6 % , c ) 38.5 % , d ) 17.1 % , e ) 37.2 %
Rationale: "let marked price = rs . 100 . then , c . p . = rs . 64 , s . p . = rs . 75 gain % = 11 / 64 * 100 = 17.1 % . answer : d"
Answer: d
Python program:
a = 100 - 25
b = a / 64
c = b - 1
d = c * 100
Problem: one - fourth of the workers in palabras bookstore have read the latest book by j . saramago , and 5 / 8 of the workers have read the latest book by h . kureishi . the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book . if there are 40 workers in the palabras bookstore , how many of them have read both books ?
Options: a ) 3 , b ) 2 , c ) 9 , d ) 8 , e ) 7
Rationale: there are total 40 workers . one - fourth of the workers in palabras bookstore have read the latest book by j . saramago , so 10 have read saramago . 5 / 8 of the workers have read the latest book by h . kureishi . so ( 5 / 8 ) * 40 = 25 have read kureishi the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book if b workers have read both books , 20 - b have read saramago but not kureishi . so , ( 10 - b - 1 ) have read neither . total = n ( a ) + n ( b ) - both + neither 40 = 10 + 25 - b + ( 10 - b - 1 ) b = 2 answer ( b )
Answer: b
Python program:
a = 40 / 4
b = 40 / 4
c = a + b 
d = 40 / 8
e = d * 5
f = c + e 
g = f - 40
h = g - 1
i = h / 2
Problem: a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 70 percent of books that were loaned out are returned and there are 57 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 20 , b ) 30 , c ) 35 , d ) 40 , e ) 60
Rationale: "i did n ' t understand how did we get 100 ? total = 75 books . 65 % of books that were loaned out are returned - - > 100 % - 70 % = 30 % of books that were loaned out are not returned . now , there are 57 books , thus 76 - 68 = 7 books are not returned . { loaned out } * 0.30 = 18 - - > { loaned out } = 60 . answer : e ."
Answer: e
Python program:
a = 75 - 57
b = 70 / 100
c = 1 - b
d = a / c
Problem: a train 330 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 18 sec , b ) 15 sec , c ) 4 sec , d ) 16 sec , e ) 12 sec
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 330 * 3 / 55 ] sec = 18 sec answer : a"
Answer: a
Python program:
a = 330 / 1000
b = 60 + 6 
c = a / b
d = 3600 * c
Problem: if the selling price of 50 articles is equal to the cost price of 40 articles , then the loss or gain percent is :
Options: a ) 45 % , b ) 23 % , c ) 20 % , d ) 60 % , e ) 56 %
Rationale: "c c . p . of each article be re . 1 . then , c . p . of 50 articles = rs . 50 ; s . p . of 50 articles = rs . 40 . loss % = 10 / 50 * 100 = 20 %"
Answer: c
Python program:
a = 50 - 40
Problem: a shopkeeper loses 15 % , if an article is sold for rs . 136 . what should be the selling price of the article to gain 20 % ?
Options: a ) s . 147 , b ) s . 148 , c ) s . 144 , d ) s . 189 , e ) s . 192
Rationale: "given that sp = rs . 136 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 136 ) / 85 = rs . 160 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 160 * 120 ) / 100 = rs . 192 answer : e"
Answer: e
Python program:
a = 15 / 100
b = 1 - a
c = 136 / b
d = 15 / 100
e = 1 - d
f = 136 / e
g = 20 / 100
h = f * g
i = c + h
Problem: what two - digit number is less than the sum of the square of its digits by 15 and exceeds their doubled product by 5 ?
Options: a ) 95 , b ) 99 , c ) 26 , d ) 73 , e ) none of the above
Rationale: "let the digits be x and y . the number would be 10 x + y . we are given that 2 xy + 5 = 10 x + y = x ^ 2 y ^ 2 - 15 thus 2 xy + 5 = x ^ 2 + y ^ 2 - 15 x ^ 2 + y ^ 2 - 2 xy = 16 ( x - y ) ^ 2 = 16 ( x - y ) = 4 or - 4 substituting the values of ( x - y ) in the equation 2 xy + 5 = 10 x + y x comes out to be 1 or 9 . . . thus the two numbers can be 15 or 73 thus the answer is d"
Answer: d
Python program:
a = 15 - 5
b = a + 1 
c = 10 * b
d = c + 5
Problem: on a map , 1.5 inches represent 24 miles . how many miles approximately is the distance if you measured 47 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 174.2 , b ) 212 , c ) 288.1 , d ) 296 , e ) 282.4
Rationale: 1.5 inch = 2.54 * 1.5 cm . so , 2.54 * 1.5 represents 24 miles . so for 47 cm . : 47 / ( 2.54 * 1.5 ) = x / 24 - - - > x = 24 * 47 / ( 4.81 ) = 296 answer will be d .
Answer: d
Python program:
a = 47 / 2
b = 24 / 1
c = a * b
Problem: a train 800 m long can cross an electric pole in 20 sec and then find the speed of the train ?
Options: a ) 87 kmph , b ) 97 kmph , c ) 72 kmph , d ) 144 kmph , e ) 120 kmph
Rationale: "length = speed * time speed = l / t s = 800 / 20 s = 40 m / sec speed = 40 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 144 kmph answer : d"
Answer: d
Python program:
a = 800 / 1000
b = 20 / 3600
c = a / b
Problem: 4 weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 14 weavers in 14 days ?
Options: a ) 40 , b ) 45 , c ) 49 , d ) 53 , e ) 58
Rationale: "1 weaver can weave 1 mat in 4 days . 14 weavers can weave 14 mats in 4 days . 14 weavers can weave 49 mats in 14 days . the answer is c ."
Answer: c
Python program:
a = 4 * 4
b = 4 / a
c = 14 * b
d = 14 * c
Problem: diana is painting statues . she has 7 / 8 of a gallon of paint remaining . each statue requires 1 / 16 gallon of paint . how many statues can she paint ?
Options: a ) 10 , b ) 20 , c ) 28 , d ) 14 , e ) 19
Rationale: number of statues = all the paint ÷ amount used per statue = 7 / 8 ÷ 1 / 16 = 7 / 8 * 16 / 1 = 112 / 8 = 14 . answer is d .
Answer: d
Python program:
a = 7 / 8
b = 1 / 16
c = a / b
Problem: when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 12 - inch boxes . if the university pays $ 0.40 for every box , and if the university needs 2.4 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?
Options: a ) $ 200 , b ) $ 275 , c ) $ 510 , d ) $ 1,250 , e ) $ 2,550
Rationale: "the volume of each box is 20 * 20 * 12 = 4800 cubic inches . number of boxes = 2 , 400,000 / 4800 = 500 boxes total cost = 500 × $ 0.4 = $ 200 the answer is a ."
Answer: a
Python program:
a = 1000 * 1000
b = 2 * 4
c = 20 * 20
d = c * 12
e = b / d
f = e * 0
Problem: if pintu is coded as 79523 in a certain code language , how would you code jumbo in the same language ?
Options: a ) 13426 , b ) 14236 , c ) 13436 , d ) 14263 , e ) 15263
Rationale: 1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z sooo . . . jumbo is 13426 . . . answer : a
Answer: a
Python program:
a = 3 + 3 
b = 79523 / a
Problem: suresh can complete a job in 15 hours . ashutosh alone can complete the same job in 10 hours . suresh works for 9 hours and then the remaining job is completed by ashutosh . how many hours will it take ashutosh to complete the remaining job alone ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 12 , e ) none of these
Rationale: "the part of job that suresh completes in 9 hours = 9 ⁄ 15 = 3 ⁄ 5 remaining job = 1 - 3 ⁄ 5 = 2 ⁄ 5 remaining job can be done by ashutosh in 2 ⁄ 5 × 10 = 4 hours answer a"
Answer: a
Python program:
a = 9 / 15
b = 1 - a
c = b * 10