euclaise/mathqa_programs huggingface dataset:
Problem: what is the value of x ^ 2 yz − xyz ^ 2 , if x = - 1 , y = 1 , and z = 3 ?
Options: a ) 20 , b ) 24 , c ) 30 , d ) 12 , e ) 48
Rationale: "1 * 1 * 3 - ( - 1 * 1 * 9 ) = 3 + 9 = 12 ans : d"
Answer: d
Python program:
a = negate * (
b = a * 1
c = b * 1
Problem: a batsman in his 19 th inning makes a score of 100 and their by increasing his average by 2 . what is his average after the 19 th inning ?
Options: a ) 58 , b ) 60 , c ) 62 , d ) 64 , e ) 66
Rationale: "18 x + 100 = 19 ( x + 2 ) x = 62 + 2 = 64 answer : d"
Answer: d
Python program:
a = 2 * 19
b = 100 - a
c = b + 2
Problem: b takes 12 more days than a to finish a task . b and a start this task and a leaves the task 12 days before the task is finished . b completes 60 % of the overall task . how long would b have taken to finish the task if he had worked independently ?
Options: a ) 48 days , b ) 36 days , c ) 28 days , d ) 32 days , e ) 22 days
Rationale: detailed solution let us say a and b split their share of the task and started doing their respective shares simultaneously . let ’ s say a takes a days to finish the task . therefore , b takes a + 12 days to finish the entire task . a has to finish 40 % of the task , since b is doing the rest . so a will only take 2 a / 5 number of days . b only has to finish 60 % of the task , so b will take ( 3 ( a + 12 ) / 5 ) number of days . but as we know , b starts working along with a and finishes 12 days after a stops working . so , ( 3 ( a + 12 ) / 5 ) = ( ( 2 a ) / 5 + 12 ) 3 a + 36 = 2 a + 60 a = 24 ; b = 36 days . answer choice b
Answer: b
Python program:
a = 12 * 10
b = 4 + 1 
c = a / b
d = c + 12
Problem: a train 100 m long is running with a speed of 68 kmph . in what time will it pass a man who is running at 8 kmph in the same direction in which the train is going ?
Options: a ) 6 sec . , b ) 7 sec . , c ) 9 sec . , d ) 11 sec . , e ) none
Rationale: "solution speed of the train relative to man = ( 68 - 8 ) = 60 kmph = 60 x 5 / 18 = 50 / 3 m / sec . time taken by it to cover 100 m at ( 50 / 3 ) m / sec = ( 100 x 3 / 50 ) sec = 6 sec . answer a"
Answer: a
Python program:
a = 68 + 8 
b = a * const_0_2778
c = 100 / b
Problem: with a uniform speed a car covers the distance in 8 hours . had the speed been increased by 4 km / hr , the same distance could have been covered in 7 1 / 2 hours . what is the distance covered ?
Options: a ) 347 , b ) 480 , c ) 288 , d ) 278 , e ) 131
Rationale: "let the distance be x km . then , x / ( 7 1 / 2 ) - x / 8 = 4 2 x / 15 - x / 8 = 4 = > x = 480 km . answer : b"
Answer: b
Python program:
a = 1 / 2
Problem: in the first 20 overs of a cricket game , the run rate was only 4.2 . what should be the run rate in the remaining 30 overs to reach the target of 324 runs ?
Options: a ) 7.25 , b ) 8.5 , c ) 8 , d ) 9.15 , e ) 10
Rationale: "explanation : required run rate = ( 324 - 4.2 20 ) = 240 / 30 = 8 . answer : c"
Answer: c
Python program:
a = 20 * 4
b = 324 - a
c = b / 30
Problem: x and y are integers . a + b < 11 , and a > 6 . what is the smallest possible value of a - b ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) - 2 , e ) - 4
Rationale: focus on the transition points and plug in the values . a > 6 so a could be 7 , 8 , 9 , 10 , 11 etc look at a = 7 7 + b < 11 b < 4 b could be 3 , 2 , 1 , 0 , - 1 etc when b is 3 , we get a - b = 4 this must be the smallest value because as a increases , b reduces so a - b increases . take another example . a = 11 so b < 0 . a - b will give a value greater than 11 . answer ( c ) .
Answer: c
Python program:
a = 11 + 6 
b = a - 4
c = b + 1 
d = c / 2
e = d - 3
Problem: a mobile battery in 1 hour charges to 20 percent . how much time ( in minute ) will it require more to charge to 65 percent .
Options: a ) 145 , b ) 150 , c ) 195 , d ) 160 , e ) 130
Rationale: 1 hr = 20 percent . thus 15 min = 5 percent . now to charge 65 percent 195 min . answer : c
Answer: c
Python program:
a = 65 / 20
b = a * const_60
Problem: if x is the product of the positive integers from 1 to 8 , inclusive , and if i , k , m , and p are positive integers such that x = 2 ^ i * 3 ^ k * 5 ^ m * 7 ^ p , then i + k + m + p =
Options: a ) 4 , b ) 7 , c ) 8 , d ) 11 , e ) 12
Rationale: given that x = 8 ! = 2 ^ 7 ∗ 3 ^ 2 ∗ 5 ∗ 7 x . hence , x = 2 ^ 7 ∗ 3 ^ 2 ∗ 5 ^ 1 ∗ 7 ^ 1 = 2 ^ i ∗ 3 ^ k ∗ 5 ^ m ∗ 7 p , since i , k , m , and p are positive integers , then we can equate the exponents , so we have that i = 7 , k = 2 , m = 1 , and p = 1 therefore , i + k + m + p = 7 + 2 + 1 + 1 = 11 answer : d .
Answer: d
Python program:
a = 7 + 2 
b = 5 / 5
c = a + b 
d = 3 / 3
e = c + d
Problem: find the base k of the number system , if ( 524 ) 8 = ( 664 ) k ?
Options: a ) 4
b ) 5
c ) 6
d ) 7
e ) 8
Rationale: 5 * 8 ^ 2 + 2 * 8 ^ 1 + 4 * 8 ^ 0 = 6 * k ^ 2 + 6 * k ^ 1 + 4 * k ^ 0 320 + 16 + 4 = 6 ( k ^ 2 ) + 6 k + 4 340 = 6 ( k ^ 2 ) + 6 k + 4 6 ( k ^ 2 ) + 6 k + 4 - 340 = 0 6 ( k ^ 2 ) + 6 k - 336 = 0 dividing by 6 ; ( k ^ 2 ) + k - 56 = 0 solving this quadratic equation we get , k = 7 and k = - 8 thus k = 7 answer : d
Answer: d
Python program:
a = 2 * 8
b = 8 ** 2
c = 10 / 2
d = b * c
e = a + d 
f = 4 + e 
g = 4 - f
h = g / 3
i = h / 2
j = 4 * i
k = 1 - j
l = math.sqrt(k)
m = l - 1
n = m / 2
Problem: an area of a circularplace is 17 hectares . find the cost of fencing it at the rate of rs . 3 permeter approximately .
Options: a ) rs . 4000
b ) rs . 4450
c ) rs . 4457
d ) rs . 4560
e ) rs . 5457
Rationale: area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 3 ) = rs . 4457 . c
Answer: c
Python program:
a = 17 / math.pi
b = math.sqrt(a)
c = b * 100
d = circumface * (
Problem: having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.90 at the candy store . what is john ’ s weekly allowance ?
Options: a ) $ 2.40 , b ) $ 3.00 , c ) $ 3.40 , d ) $ 3.60 , e ) $ 4.80
Rationale: "total allowance = x amount spent at the arcade = 3 / 5 x amount remaining = 2 / 5 x amount spent at the toy store = 2 / 5 * 1 / 3 x = 2 / 15 x amount remaining = 2 / 5 x - 2 / 15 x = 4 / 15 x now , 4 / 15 x = $ 0.9 therefore , x = $ 3.40 . answer c"
Answer: c
Python program:
a = 3 / 5
b = 1 / 3
c = 3 / 5
d = 1 - c
e = b * d
f = a + e 
g = 1 - f
h = 0 / 90
Problem: if a tire rotates at 400 revolutions per minute when the car is traveling 96 km / h , what is the circumference of the tire ?
Options: a ) 7 meters , b ) 9 meters , c ) 4 meters , d ) 5 meters , e ) 3 meters
Rationale: "400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 96,000 m : c is the circumference c = 4 meters correct answer c"
Answer: c
Python program:
a = 2 * 3
b = a * 10
c = b * 400
d = 96 / c
e = d * 1000
Problem: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 % of the distribution lies one standard deviation f of the mean , what percent of the distribution is less than m + f ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "16 % ________________________________________________ m + f 34 % ________________________________________________ m 34 % ________________________________________________ m - f 16 % since 68 % lies one standard deviation from mean m , = > 50 % of 68 % lies on either side as it is symmetric about m . thus 16 % lie below m - f and 16 % lie above m + f now below m + f = 16 + 34 + 34 = 84 % hence d"
Answer: d
Python program:
a = 100 - 68
b = a / 2
c = 100 - b
Problem: the result when a number subtracted from 100 is the same as the number added to 40 . what is the number ?
Options: a ) 70 , b ) 65 , c ) 80 , d ) 140 , e ) 60
Rationale: "answer let the number be x . then , x - 40 = 100 - x â ‡ ’ 2 x = 100 + 40 = 140 â ‡ ’ 2 x = 140 â ˆ ´ x = 70 correct option : a"
Answer: a
Python program:
a = 100 - 40
b = a / 2
c = b + 40
Problem: if a / b = 6 / 5 , then ( 5 a + 4 b ) / ( 5 a - 4 b ) = ?
Options: a ) 4 , b ) 7 , c ) 5 , d ) 3 , e ) 6
Rationale: "answer dividing numerator as well as denominator by b , we get given exp . = ( 5 a + 4 b ) / ( 5 a - 4 b ) = ( 5 a / b + 4 ) / ( 5 a / b - 4 ) since a / b = 6 / 5 this implies that = [ ( 5 * 6 ) / 5 + 4 ] / [ ( 5 * 6 ) / 5 - 4 ) ] = ( 6 + 4 ) / ( 6 - 4 ) = 5 option : c"
Answer: c
Python program:
a = 5 * 6
b = 4 * 5
c = a + b 
d = 5 * 6
e = 4 * 5
f = d - e
g = c / f
Problem: running at their respective constant rate , machine x takes 2 days longer to produce w widgets than machines y . at these rates , if the two machines together produce 5 w / 4 widgets in 3 days , how many days would it take machine x alone to produce 1 w widgets .
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "i am getting 12 . e . hope havent done any calculation errors . . approach . . let y = no . of days taken by y to do w widgets . then x will take y + 2 days . 1 / ( y + 2 ) + 1 / y = 5 / 12 ( 5 / 12 is because ( 5 / 4 ) w widgets are done in 3 days . so , x widgets will be done in 12 / 5 days or 5 / 12 th of a widget in a day ) solving , we have y = 4 = > x takes 6 days to doing x widgets . answer : b"
Answer: b
Python program:
a = 1 * 2
b = a * 3
Problem: if the number 761 * 829 is completely divisible by 9 , then the smallest whole number in place of * will b
Options: a ) 4 , b ) 5 , c ) 3 , d ) 8 , e ) 9
Rationale: sum of digits = ( 7 + 6 + 1 + x + 8 + 2 + 9 ) = ( 33 + x ) , which must be divisible by 9 . x = 3 . c )
Answer: c
Python program:
a = 4 + 3 
b = 3 + 3 
c = a + b 
d = c + 1 
e = 4 + 4 
f = d + e 
g = f + 2 
h = g + 9 
i = h + 3 
j = 4 + 3 
k = 3 + 3 
l = j + k 
m = l + 1 
n = 4 + 4 
o = m + n 
p = o + 2 
q = p + 9 
r = i - q
Problem: teas worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs 157 per kg , the price of the third variety per kg will be ?
Options: a ) rs . 147.50 , b ) rs . 785.50 , c ) rs . 179.50 , d ) rs . 258.50 , e ) none of these
Rationale: explanation : since first and second varieties are mixed in equal proportions . so , their average price = rs . ( 126 + 135 ) / 2 . = > rs . 130.50 . so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . by the rule of alligation , we have : cost of 1 kg cost of 1 kg of 1 st kind of 2 nd kind ( rs . 130.50 ) ( rs . x ) \ / mean price ( rs . 157 ) / \ x â ˆ ’ 157 22.50 = > x â ˆ ’ ( 157 / 22.50 ) = 1 . = > x â ˆ ’ 157 = 22.50 . = > x = 179.50 rs . answer : c
Answer: c
Python program:
a = 1 + 1 
b = a + 2 
c = 157 * b
d = 126 + 135 
e = c - d
f = e / 2
Problem: the sub - duplicate ratio of 9 : 25 is
Options: a ) 4 : 3 , b ) 1 : 2 , c ) 3 : 5 , d ) 1 : 4 , e ) 2 : 3
Rationale: root ( 9 ) : root ( 25 ) = 3 : 5 answer : c
Answer: c
Python program:
a = math.sqrt(9)
b = math.sqrt(25)
c = a / b
Problem: sushil got thrice as many marks in english as in science . his total marks in english , science and maths are 162 . if the ratio of his marks in english and maths is 3 : 5 , find his marks in science ?
Options: a ) 18 , b ) 68 , c ) 67 , d ) 55 , e ) 56
Rationale: "s : e = 1 : 3 e : m = 3 : 5 - - - - - - - - - - - - s : e : m = 3 : 9 : 15 3 / 27 * 162 = 18 answer : a"
Answer: a
Python program:
a = 3 * 3
b = a + 3 
c = 3 * 3
d = 3 * 3
e = d + 3 
f = c * e
g = b + f 
h = g + 3
Problem: a train moves past a post and a platform 264 m long in 8 seconds and 20 seconds respectively . what is the speed of the train ?
Options: a ) 79.2 km / hr , b ) 69 km / hr , c ) 74 km / hr , d ) 61 km / hr , e ) none of these
Rationale: let x is the length of the train and v is the speed time taken to move the post = 8 s = > x / v = 8 = > x = 8 v - - - ( 1 ) time taken to cross the platform 264 m long = 20 s ( x + 264 ) / v = 20 = > x + 264 = 20 v - - - ( 2 ) substituting equation 1 in equation 2 , we get 8 v + 264 = 20 v = > v = 264 / 12 = 22 m / s = 22 × 36 / 10 km / hr = 79.2 km / hr answer : b
Answer: b
Python program:
a = speed * (
Problem: of 120 applicants for a job , 56 had at least 4 years ' experience , 72 had degrees , and 12 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 10 , b ) 15 , c ) 22 , d ) 20 , e ) 24
Rationale: "120 - 12 = 108 108 - 56 - 72 = - 20 then 20 are in the intersection between 4 years experience and degree . answer : d"
Answer: d
Python program:
a = 56 + 72 
b = 120 - 12
c = a - b
d = 72 - 56
e = c + d
Problem: a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 39000 , then the share of b is ?
Options: a ) a ) 34500 , b ) b ) 24000 , c ) c ) 24098 , d ) d ) 19007 , e ) e ) 18000
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 39000 share of b = 6 / 13 ( 39000 ) = rs . 18000 answer : e"
Answer: e
Python program:
a = const_60 * 100
b = 39000 - a
Problem: divide rs . 32000 in the ratio 3 : 5 ?
Options: a ) 12000 , 20000 , b ) 12000 , 200098 , c ) 12000 , 20007 , d ) 12000 , 20006 , e ) 12000 , 20001
Rationale: "3 / 8 * 32000 = 12000 5 / 8 * 32000 = 20000 answer : a"
Answer: a
Python program:
a = 5 - 2
b = 5 - 2
c = 3 + b 
d = 32000 / c
e = a * d
Problem: what is the hcf of 2 / 3 , 4 / 15 and 6 / 5
Options: a ) 7 / 45 , b ) 2 / 45 , c ) 4 / 15 , d ) 8 / 45 , e ) 2 / 15
Rationale: "explanation : hcf of fractions = hcf of numerators / lcm of denominators = ( hcf of 2 , 4 , 6 ) / ( lcm of 3 , 15 , 5 ) = 2 / 15 answer : option e"
Answer: e
Python program:
a = 2 / 5
Problem: n a race of 1000 m , a can beat by 100 m , in a race of 800 m , b can beat c by 100 m . by how many meters will a beat c in a race of 600 m ?
Options: a ) 127.6 , b ) 127.5 , c ) 127.0 , d ) 127.2 , e ) 127.3
Rationale: when a runs 1000 m , b runs 900 m and when b runs 800 m , c runs 700 m . when b runs 900 m , distance that c runs = ( 900 * 700 ) / 800 = 6300 / 8 = 787.5 m . in a race of 1000 m , a beats c by ( 1000 - 787.5 ) = 212.5 m to c . in a race of 600 m , the number of meters by which a beats c = ( 600 * 212.5 ) / 1000 = 127.5 m . answer : ob
Answer: b
Python program:
a = 1000 - 100
b = a * 600
c = b / 1000
d = 800 - 100
e = c * d
f = e / 800
g = 600 - f
Problem: 3 , 14,39 , _ ?
Options: a ) 81 , b ) 82 , c ) 83 , d ) 84 , e ) 85
Rationale: "n ^ 3 + n ^ 2 + n soln : 1 ^ 3 + 1 ^ 2 + 1 = 3 2 ^ 3 + 2 ^ 2 + 2 = 8 + 4 + 2 = 14 3 ^ 3 + 3 ^ 2 + 3 = 27 + 9 + 3 = 39 4 ^ 3 + 4 ^ 2 + 4 = 64 + 16 + 4 = 84 answer : d"
Answer: d
Python program:
a = 3 / 14
b = a * 100
Problem: if x : y = 3 : 5 , find the value of ( 2 x + 4 y ) : ( 4 x – y )
Options: a ) 29 : 7 , b ) 22 : 7 , c ) 26 : 7 , d ) 20 : 7 , e ) 26 : 5
Rationale: "explanation : given : a / b = 3 / 5 ( 2 * 3 + 4 * 5 ) : ( 4 * 3 – 5 ) = 26 : 7 answer : c"
Answer: c
Python program:
a = 2 ** 4
b = a + 4 
c = 3 + 5 
d = c + 4 
e = b / d
Problem: nd the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 14 cm ?
Options: a ) 235 cm 2 , b ) 260 cm 2 , c ) 266 cm 2 , d ) 270 cm 2 , e ) 280 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 14 ) = 266 cm 2 answer : c"
Answer: c
Python program:
a = 20 + 18 
b = 14 * a
c = b / 2
Problem: a “ palindromic integer ” is an integer that remains the same when its digits are reversed . so , for example , 43334 and 516615 are both examples of palindromic integers . how many 6 - digit palindromic integers are both even and greater than 600,000 ?
Options: a ) 150 , b ) 200 , c ) 240 , d ) 300 , e ) 480
Rationale: "the first digit and last digit are the same so the 2 possibilities are 6 or 8 . the second and third digits can be any number from 0 to 9 . the total number of palindromic integers is 2 * 10 * 10 = 200 the answer is b ."
Answer: b
Python program:
a = 6 - 4
b = a * 10
c = b * 10
Problem: a reduction of 20 % in the price of salt enables a lady to obtain 4 kgs more for rs . 100 , find the original price per kg ?
Options: a ) 6.16 , b ) 6.21 , c ) 6.25 , d ) 2.4 , e ) 2.7
Rationale: "100 * ( 20 / 100 ) = 20 - - - 4 ? - - - 1 = > rs . 5 100 - - - 80 ? - - - 5 = > rs . 6.25 answer : c"
Answer: c
Python program:
a = 20 / 100
b = a * 100
c = b / 4
d = 20 / 100
e = d * 100
f = c / e
g = f * 100
Problem: kyle , david , and catherine each try independently to solve a problem . if their individual probabilities for success are 1 / 8 , 1 / 4 and 3 / 5 , respectively , what is the probability no one will solve the problem ?
Options: a ) 3 / 80 , b ) 21 / 80 , c ) 5 / 16 , d ) 25 / 76 , e ) 9 / 80
Rationale: "p ( kyle will not solve ) = 1 - 1 / 8 = 7 / 8 p ( david will not solve ) = 1 - 1 / 4 = 3 / 4 p ( catherine will not solve ) = 1 - 3 / 5 = 2 / 5 p = ( 7 / 8 ) * ( 3 / 4 ) * ( 2 / 5 ) = 42 / 160 = 21 / 80 answer : b"
Answer: b
Python program:
a = 3 * 3
b = const_60 * 8
c = 8 * 8
d = b + c 
e = a / d
Problem: if p and q are prime numbers , how many divisors does the product p ^ 6 * q ^ 7 have ?
Options: a ) 40 , b ) 56 , c ) 60 , d ) 62 , e ) 70
Rationale: "when a number n = a ^ x * b ^ y , where a and b are prime numbers , and x , y are positive integers , the number of divisors of n = ( x + 1 ) ( y + 1 ) therefore , the answer is b . 7 * 8 = 56"
Answer: b
Python program:
a = 6 + 1 
b = 7 + 1 
c = a * b
Problem: if there is an equal probability of a child being born a boy or a girl , what is the probability that a couple who have 4 children have two children of the same sex and one of the opposite sex ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 4 , d ) 1 / 2 , e ) 3 / 5
Rationale: no of ways of selecting a gender - 2 c 1 no of ways of selecting any 2 children out of 4 = 4 c 2 total possible outcomes - 2 ^ 4 ( each child can be either a girl or a boy ) probability = 2 c 1 * 4 c 2 / 2 ^ 4 = 2 * 4 / 2 * 2 * 2 * 2 = 8 / 16 = 1 / 2 ans = d
Answer: d
Python program:
a = 2 / 4
Problem: the measurement of a rectangular box with lid is 25 cmx 12 cmx 18 cm . find the volume of the largest sphere that can be inscribed in the box ( in terms of π cm 3 ) . ( hint : the lowest measure of rectangular box represents the diameter of the largest sphere )
Options: a ) 288 , b ) 48 , c ) 72 , d ) 864 , e ) 964
Rationale: "d = 12 , r = 6 ; volume of the largest sphere = 4 / 3 π r 3 = 4 / 3 * π * 6 * 6 * 6 = 288 π cm 3 answer : a"
Answer: a
Python program:
a = 4 / 3
b = 3 ** 3
c = a * b
Problem: in a tournament prize of 1 st , 2 nd , and 3 rd is given in same interval . if total amount of prize rs 4800 and prize of 1 st is rs 2000 , find the interval ? ?
Options: a ) 600 , b ) 450 , c ) 350 , d ) 550 , e ) 400
Rationale: let the interval is x . prize of 2 nd and 3 rd is 2000 - x and 2000 - 2 x 2000 + 2000 - x + 2000 - 2 x = 4800 x = 400 answer : e
Answer: e
Python program:
a = 2000 * 3
b = a - 4800
c = b / 3
Problem: if n = 8 ^ 11 – 1 , what is the units digit of n ?
Options: a ) 3 , b ) 1 , c ) 0 , d ) 6 , e ) 4
Rationale: "8 ^ 11 - 8 = 8 ( 8 ^ 10 - 1 ) = = > 8 ( 2 ^ 30 - 1 ) last digit of 2 ^ 30 is 4 based on what explanation livestronger is saying . 2 ^ 30 - 1 yields 4 - 1 = 3 as the unit digit . now on multiply this with 1 , we get unit digit as 3 . answer : a"
Answer: a
Python program:
a = math.log(1)
b = 8 ** 11
c = math.log(b)
d = a / c
Problem: $ 600 will become $ 720 in 4 years find the rate of interest ?
Options: a ) 10 % , b ) 15 % , c ) 5 % , d ) 7 % , e ) 20 %
Rationale: "si = simple interest = a - p = 720 - 600 = $ 120 r = 100 si / pt = 100 * 120 / 600 * 4 = 5 % answer is c"
Answer: c
Python program:
a = 720 - 600
b = 4 / 100
c = 600 * b
d = a / c
Problem: the area of a circle is increased by 300 % . by what percent has the diameter of the circle increased ?
Options: a ) 400 %
b ) 200 %
c ) 300 %
d ) 100 %
e ) 800 %
Rationale: the area of the circle is increased by 300 % , thus the area is increased 4 times . the area of a circle it proportional to the square of the diameter ( area = π d ^ 2 / 4 ) , therefore the diameter must increase 2 times ( diameter increase 2 times = area increase 4 times ) , which is increase by 100 % . answer : d .
Answer: d
Python program:
a = 2 / 2
b = 100 * a
Problem: 18 men take 21 days of 8 hours each to do a piece of work . how many days of 6 hours each would 21 women take to do the same . if 3 women do as much work as 2 men ?
Options: a ) 32 , b ) 87 , c ) 36 , d ) 99 , e ) 77
Rationale: "3 w = 2 m 18 m - - - - - - 21 * 8 hours 21 w - - - - - - x * 6 hours 14 m - - - - - - x * 6 18 * 21 * 8 = 14 * x * 6 x = 36 answer : c"
Answer: c
Python program:
a = 21 * 8
b = 18 * 3
c = a * b
d = 21 * 2
e = d * 6
f = c / e
g = math.floor(f)
h = g + 1
Problem: find the simple interest on rs 7000 at 50 / 3 % for 9 months
Options: a ) rs . 1075 , b ) rs . 975 , c ) rs . 875 , d ) rs . 775 , e ) none of these
Rationale: "explanation : s . i . = p × r × t 100 so , by pu ƫ ing the values in the above formula , our result will be . required result = 7000 × 50 × 93 × 12 × 100 = 875 [ please note that we have divided by 12 as we converted 9 months in a year format ] answer : c"
Answer: c
Python program:
a = 50 / 100
b = 7000 * a
Problem: what is the area of a square with perimeter 4 p ?
Options: a ) p ^ 2 , b ) 4 p , c ) p ^ 2 / 4 , d ) p / 16 , e ) p ^ 2 / 16
Rationale: "each side is p a = ( p ) ^ 2 answer a"
Answer: a
Python program:
a = math.sqrt(4)
b = a * 4
c = b / math.pi
d = c / 2
e = math.sqrt(4)
f = e * 4
g = f / math.pi
h = g / 2
i = d * h
j = i * math.pi
k = j * 2
Problem: a school has 9 english 7 history and 6 geography teachers each teacher can teach 2 subjects max what is he minimum number of teachers required
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: total subjects = 9 + 7 + 6 = 22 max subjects by 1 teacher = 2 so , min of teachers required = 22 / 2 = 11 answer : e
Answer: e
Python program:
a = 9 + 7 
b = a + 6 
c = b / 2
Problem: a goods train runs at the speed of 72 kmph and crosses a 230 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 270 m , c ) 643 m , d ) 832 m , e ) 290 m
Rationale: "speed = ( 72 x 5 / 18 ) m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , x + 230 / 26 = 20 x + 230 = 520 x = 290 . answer : e"
Answer: e
Python program:
a = const_0_2778 * 72
b = 230 / a
c = 26 - b
d = const_0_2778 * 72
e = c * d
Problem: it takes joey the postman 1 hours to run a 2 mile long route every day . he delivers packages and then returns to the post office along the same path . if the average speed of the round trip is 6 mile / hour , what is the speed with which joey returns ?
Options: a ) 9 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "let his speed for one half of the journey be 3 miles an hour let the other half be x miles an hour now , avg speed = 5 mile an hour 2 * 2 * x / 3 + x = 6 4 x = 6 x + 18 = > 2 x = 18 x = 9 a"
Answer: a
Python program:
a = 2 * 2
b = a / 6
c = b - 1
d = 2 / c
Problem: the distance from the x - axis to point p is half the distance from the y - axis to point p . if the coordinates of p are ( x , - 9 ) , how many units is p from the y - axis ?
Options: a ) 18 , b ) 12 , c ) 9 , d ) 4.5 , e ) 3
Rationale: "the x - axis is 9 units from the point p . thus the y - axis is 18 units from the point p . the answer is a ."
Answer: a
Python program:
a = 9 * 2
Problem: if a ' s height is 45 % less than that of b , how much percent b ' s height is more than that of a ?
Options: a ) 66.66 % , b ) 81.81 % , c ) 66.766 % , d ) 86.66 % , e ) 66.65 %
Rationale: "excess of b ' s height over a ' s = [ ( 45 / ( 100 - 45 ) ] x 100 % = 81.81 % answer : b )"
Answer: b
Python program:
a = 100 - 45
b = 45 / a
c = b * 100