euclaise/mathqa_programs huggingface dataset:
Problem: a tank is filled in sixteen hours by 3 pipes a , b and c . pipe a is twice as fast as pipe b , and b is twice as fast as c . how much time will pipe b alone take to fill the tank ?
Options: a ) 56 hours , b ) 28 hours , c ) 55 hours , d ) 66 hours , e ) 47 hours
Rationale: 1 / a + 1 / b + 1 / c = 1 / 16 ( given ) also given that a = 2 b and b = 2 c = > 1 / 2 b + 1 / b + 2 / b = 1 / 16 = > ( 1 + 2 + 4 ) / 2 b = 1 / 16 = > 2 b / 7 = 16 = > b = 56 hours . answer : a
Answer: a
Python program:
a = 4 + 2 
b = a + 1 
c = b / 2
d = 3 * 4
e = d + 4 
f = c * e
Problem: two numbers n and 16 have lcm = 48 and gcf = 18 . find n .
Options: a ) 24 , b ) 34 , c ) 44 , d ) 54 , e ) 64
Rationale: "the product of two integers is equal to the product of their lcm and gcf . hence . 16 × n = 48 × 18 n = 48 × 18 / 16 = 54 correct answer d"
Answer: d
Python program:
a = 48 * 18
b = a / 16
Problem: when n is divided by 20 , the remainder is 5 . what is the remainder when n + 16 is divided by 5 ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "assume n = 15 remainder ( n / 20 ) = 5 n + 16 = 31 remainder ( 31 / 5 ) = 1 option a"
Answer: a
Python program:
a = 5 - reminder
Problem: if a = { 10 , 15 , 18 , 22 , 36 , 44 } , what is the product of mean and median of the numbers in a ?
Options: a ) 105 , b ) 245 , c ) 360 , d ) 480 , e ) 542
Rationale: "mean = ( 10 + 15 + 18 + 22 + 36 + 43 ) / 6 = 24 median = ( 18 + 22 ) / 2 = 20 product = 24 * 20 = 480 option d"
Answer: d
Python program:
a = 10 + 15 
b = a + 18 
c = b + 22 
d = c + 36 
e = 4 + 1 
f = d / e
g = f + 18
Problem: of the 3,600 employees of company x , 1 / 6 are clerical . if the clerical staff were to be reduced by 1 / 3 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 25 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.7 %
Rationale: "welcome , just post the question and the choices let ' s see , the way i did it was 1 / 6 are clerical out of 3600 so 600 are clerical 600 reduced by 1 / 3 is 600 * 1 / 3 so it reduced 200 people , so there is 400 clerical people left but since 200 people left , it also reduced from the total of 3600 so there are 3400 people total since 400 clerical left / 3400 people total you get ( a ) 11.7 % answer : e"
Answer: e
Python program:
a = 1 / 6
b = 1 / 3
c = 1 - b
d = a * c
e = 1 / 6
f = 1 / 3
g = 1 - f
h = e * g
i = 1 / 6
j = 1 - i
k = h + j 
l = d / k
m = l * 100
Problem: two trains leave a station traveling in the same direction . train a leaves traveling at a constant speed of 50 mph , while train b leaves traveling at a constant speed of 80 mph . if train b left the station 30 minutes after train a left , in how many minutes will train b overtake train a ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: we can use a form of the equation d = rt [ distance = rate * time ] train a will have traveled for 30 minutes longer when train b overtakes it so time of train a : t + 30 minutes = t + 1 / 2 hours ( switch to hours since the rates are in hours ) time of train b : t rate of train a : 50 mph rate of train b : 80 mph the distance traveled by each will be the same when b overtakes a so set the right side of d = rt equal to each other for the two trains 50 * ( t + 1 / 2 ) = 80 * t 50 t + 25 = 80 t 25 = 30 t 25 / 30 = t 5 / 6 hours = t which is 5 / 6 * 60 = 50 minutes c
Answer: c
Python program:
a = 50 * 30
b = a / const_60
c = 80 - 50
d = b / c
e = d * const_60
Problem: if 4 : 6 : : x : 36 , then find the value of x
Options: a ) 24 , b ) 22 , c ) 28 , d ) 30 , e ) 18
Rationale: explanation : treat 4 : 6 as 4 / 6 and x : 36 as x / 36 , treat : : as = so we get 4 / 6 = x / 36 = > 6 x = 144 = > x = 24 option a
Answer: a
Python program:
a = 6 * 4
b = a + 6 
c = b / 36
Problem: what is the value of 4 ^ 6 + 4 ^ 8 ?
Options: a ) 4 ^ 12 , b ) 4 ^ 35 , c ) 17 ( 4 ^ 6 ) , d ) 8 ^ 12 , e ) 7 ( 4 ^ 5 )
Rationale: "4 ^ 6 + 4 ^ 8 = 4 ^ 6 ( 1 + 4 ^ 2 ) = 4 ^ 6 * 17 answer c"
Answer: c
Python program:
a = 100 + const_60 
b = a + 1 
c = b * 4
d = c / 100
Problem: let the least number of 6 digits , which when divided by 4 , 610 and 15 leaves in each case the same remainder of 2 , be n . the sum of the digits in n is :
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: solution least number of 6 digital is 100000 . l . c . m . of 4 , 610 and 15 = 60 . on dividing 100000 by 60 , the remainder obtained is 40 . so , least number of 6 digits divisible by 4 , 610 and 15 = 100000 + ( 60 - 40 ) = 100020 . so , n = ( 100020 + 2 ) = 100022 . sum of digits in n = ( 1 + 2 + 2 ) = 5 . answer c
Answer: c
Python program:
a = 1 + 2 
b = a + 1 
c = b + 1
Problem: if a = 105 and a ^ 3 = 21 * 25 * 35 * b , what is the value of b ?
Options: a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 63
Rationale: "first step will be to break down all the numbers into their prime factors . 105 = 3 * 5 * 7 21 = 7 * 3 25 = 5 * 5 35 = 7 * 5 so , ( 105 ) ^ 3 = 3 * 7 * 5 * 5 * 7 * 5 * b therefore ( 3 * 5 * 7 ) ^ 3 = 3 * 5 ^ 3 * 7 ^ 2 * b therefore , b = 3 ^ 3 * 5 ^ 3 * 7 ^ 3 / 3 * 5 ^ 3 * 7 ^ 2 b = 3 ^ 2 * 7 = 9 * 7 = 63 correct answer e ."
Answer: e
Python program:
a = 105 ** 3
b = 21 * 25
c = b * 35
d = a / c
Problem: what is the maximum number of pieces of birthday cake of size 2 ” by 2 ” that can be cut from a cake 20 ” by 20 ” ?
Options: a ) 5 , b ) 100 , c ) 16 , d ) 20 , e ) 25
Rationale: the prompt is essentially asking for the maximum number of 2 x 2 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 10 ' pieces ' each , we have ( 10 ) ( 10 ) = 100 total smaller squares ( at maximum ) . b
Answer: b
Python program:
a = 20 * 20
b = 2 * 2
c = a / b
Problem: how many positive integers less than 50 are multiples of 2 but not multiples of 5 ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 20
Rationale: "imo the answer is c ( 8 numbers ) the lcm of 2 and 5 is 10 . if x < 50 and x is divisible by 2 not by 5 - - > x is not divisible by 10 . from 1 - - > 50 , we have 5 numbers which is divisible by 10 : 10 , 20 , 30 , 40 , 50 . from 1 - - > 50 , we have ( 50 - 2 ) / 2 + 1 = 25 numbers divisible by 2 . therefore , our answer is 25 - 5 = 20 numbers . e"
Answer: e
Python program:
a = 4 + 2 
b = a - 1
c = math.factorial(b)
d = math.factorial(2)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: if | 4 x + 14 | = 46 , what is the sum of all the possible values of x ?
Options: a ) 2 , b ) - 7 , c ) 4 , d ) - 5 , e ) 6
Rationale: "there will be two cases 4 x + 14 = 46 or 4 x + 14 = - 46 = > x = 8 or x = - 15 sum of both the values will be - 15 + 8 = - 7 answer is b"
Answer: b
Python program:
a = 46 - 14
b = a / 4
Problem: what is the least number . which should be added to 0.0282 to make it a perfect square ?
Options: a ) 0.0007 , b ) 0.0042 , c ) 0.0002 , d ) 0.0003 , e ) 0.0004
Rationale: "0.0282 + 0.0007 = 0.0289 ( 0.17 ) ^ 2 answer : a"
Answer: a
Python program:
a = 12 + 4 
b = a + 2 
c = b / 100
d = 12 + 4 
e = d + 2 
f = e / 100
g = c * f
h = g - 0
Problem: at the faculty of aerospace engineering , 302 students study random - processing methods , 232 students study scramjet rocket engines and 112 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ?
Options: a ) 444 , b ) 432 , c ) 346 , d ) 422 , e ) 448
Rationale: "302 + 232 - 112 ( since 112 is counted twice ) = 422 d is the answer"
Answer: d
Python program:
a = 112 / 2
b = 302 - a
c = 112 / 2
d = 232 - c
e = b + d
Problem: in a group of 100 people , 55 have visited iceland and 43 have visited norway . if 61 people have visited both iceland and norway , how many people have visited neither country ?
Options: a ) 60 , b ) 61 , c ) 62 , d ) 63 , e ) 64
Rationale: "this is an example of a standard overlapping sets question . it has no ' twists ' to it , so you ' ll likely find using the overlapping sets formula to be a fairly easy approach . if you ' re not familiar with it , then here is the formula : 100 = 55 + 43 - 61 + ( # in neither group ) = 63 the prompt gives you all of the numbers you need to get to the correct answer . just plug in and solve . d"
Answer: d
Python program:
a = 55 + 43 
b = a - 61
c = 100 - b
Problem: a car was driving at 60 km / h for 20 minutes , and then at 90 km / h for another 40 minutes . what was its average speed ?
Options: a ) 80 . , b ) 75 , c ) 70 , d ) 65 . , e ) 54 .
Rationale: "driving at 60 km / h for 20 minutes , distance covered = 60 * 1 / 3 = 20 km driving at 90 km / h for 40 minutes , distance covered = 90 * 2 / 3 = 60 km average speed = total distance / total time = 80 / 1 = 80 km / h answer : a"
Answer: a
Python program:
a = 20 + 40 
b = 20 / a
c = b * 60
d = 20 + 40 
e = 40 / d
f = e * 90
g = c + f 
h = 20 + 40 
i = h / const_60
j = g / i
Problem: if ( a + b ) = 5 , ( b + c ) = 9 and ( c + d ) = 3 , what is the value of ( a + d ) ?
Options: a ) 16 . , b ) 8 . , c ) 7 . , d ) 2 . , e ) - 1 .
Rationale: given a + b = 5 b + c = 9 c + d = 3 ( a + b ) - ( b + c ) + ( c + d ) = ( a + d ) = > 5 - 9 + 3 = - 1 . option e . . .
Answer: e
Python program:
a = 5 + 3 
b = a - 9
Problem: in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 13 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 104 %
Rationale: x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,13 = 13 / 100 x = 80 * 13 / 100 x = 10.4 10.4 / 10 = 1,04 = 104 % , answer e
Answer: e
Python program:
a = 20 / 100
b = 1 - a
c = 13 * b
d = c / 10
e = d * 100
Problem: 150 ml of 30 % sulphuric acid was added to approximate 400 ml of 12 % sulphuric acid solution . find the approximate concentration c of the acid in the mixture ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 5
Rationale: "do not need any computation 30 % - - - - - - - - - - - 21 % - - - - - - - - - 12 % if volume of both sol . were equal the concentration c would be 21 % = 1 / 5 , but 12 % is more than 3 times only possibility is 1 / 6 d"
Answer: d
Python program:
a = 150 * 30
b = a / 100
c = 400 * 12
d = c / 100
e = b + d 
f = 150 + 400 
g = e / f
Problem: a , b and c invests rs . 2000 , rs . 3000 and rs . 4000 in a business . after one year a removed his money ; b and c continued the business for one more year . if the net profit after 2 years be rs . 3200 , then a ' s share in the profit is ?
Options: a ) 299 , b ) 267 , c ) 269 , d ) 400 , e ) 276
Rationale: "2 * 12 : 3 * 12 : 4 * 24 1 : 3 : 4 1 / 8 * 3200 = 400 answer : d"
Answer: d
Python program:
a = 3000 * 2
b = 4000 * 2
c = a + b 
d = 2000 + c 
e = 2000 / d
f = e * 2000
Problem: a train is moving at a speed of 100 km / hour . the length of the train is 100 metre . in how much time will it cross a pole ?
Options: a ) 1 second , b ) 2.5 second , c ) 4 second , d ) 3.6 second , e ) 4.5 second
Rationale: in order to cross the pole , the train will need to cover its own length of 100 meter . to cover 100 x 1000 meter , train takes 60 minutes or 60 x 60 = 3600 second . so , to cover 100 meter , train would take 3600 x 100 / 100 x 1000 = 3.6 second . answer : d .
Answer: d
Python program:
a = 100 * const_0_2778
b = 100 / a
Problem: a ladder 14 feet long is leaning against a wall that is perpendicular to level ground . the bottom of the ladder is 9 feet from the base of the wall . if the top of the ladder slips down 1 feet , how many feet will the bottom of the ladder slip ?
Options: a ) 4 , b ) 10 , c ) 18 , d ) 19 , e ) 25
Rationale: "14 ^ 2 - 9 ^ 2 = 115 it means that the height is equal to 10.72 . since the top of the ladder slips down 1 feet , then the height of the wall = 10.72 - 1 = 9.72 the bottom = sqrt ( 14 ^ 2 - 9.72 ^ 2 ) = sqrt ( 196 - 94.47 ) = 10.07 ~ = 10 ans is b"
Answer: b
Python program:
a = 14 ** 2
b = 14 ** 2
c = 9 ** 2
d = b - c
e = math.sqrt(d)
f = e - 1
g = f ** 2
h = a - g
i = math.sqrt(h)
Problem: a trader sells 40 metres of cloth for rs . 8200 at a profit of rs . 30 per metre of cloth . how much profit will the trder earn on 40 metres of cloth ?
Options: a ) rs . 950 , b ) rs . 1500 , c ) rs . 1000 , d ) rs . 1200 , e ) none of these
Rationale: "explanation : sp of 1 metre cloth = 8200 / 40 = rs . 205 . cp of 1 metre cloth = rs . 205 – 30 = rs . 175 cp on 40 metres = 175 x 40 = rs . 7000 profit earned on 40 metres cloth = rs . 8200 – rs . 7000 = rs . 1200 . answer : option d"
Answer: d
Python program:
a = 30 * 40
Problem: a train 330 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 18 , e ) 9
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 330 * 3 / 55 = 18 sec . answer : option d"
Answer: d
Python program:
a = 60 + 6 
b = a * const_0_2778
c = 330 / b
Problem: a completes 80 % of a work in 20 days . then b also joins and a and b together finish the remaining work in 3 days . how long does it need for b if he alone completes the work ?
Options: a ) 37 1 / 2 days , b ) 22 days , c ) 31 days , d ) 22 days , e ) 25 1 / 2 days
Rationale: work done by a in 20 days = 80 / 100 = 8 / 10 = 4 / 5 work done by a in 1 day = ( 4 / 5 ) / 20 = 4 / 100 = 1 / 25 - - - ( 1 ) work done by a and b in 3 days = 20 / 100 = 1 / 5 ( because remaining 20 % is done in 3 days by a and b ) work done by a and b in 1 day = 1 / 15 - - - ( 2 ) work done by b in 1 day = 1 / 15 – 1 / 25 = 2 / 75 = > b can complete the work in 75 / 2 days = 37 ½ days option a
Answer: a
Python program:
a = 80 + 100
Problem: if - 3 / ( a - 3 ) = 3 / ( a + 2 ) , then a = ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
Rationale: multiply all terms of the given equation by ( a - 3 ) ( a + 2 ) , simplify and solve ( a - 3 ) ( a + 2 ) [ - 3 / ( a - 3 ) ] = ( a - 3 ) ( a + 2 ) [ 3 / ( a + 2 ) ] - 3 ( a + 2 ) = 3 ( a - 3 ) a = 1 / 2 correct answer a
Answer: a
Python program:
a = 3 * 2
b = 3 / a
Problem: company p had 15 percent more employees in december than it had in january . if company p had 460 employees in december , how many employees did it have in january ?
Options: a ) 391 , b ) 400 , c ) 410 , d ) 423 , e ) 445
Rationale: given : january * 1.15 = december - - > january * 1.15 = 460 - - > january = 460 / 1.15 = 400 . answer : b .
Answer: b
Python program:
a = 15 / 100
b = 1 + a 
c = 460 / b
Problem: if rs . 782 be divided into 3 parts , proportional to 1 / 2 : 1 / 3 : 3 / 4 , then the second part is ?
Options: a ) a ) 426 , b ) b ) 526 , c ) c ) 207 , d ) d ) 165 , e ) e ) 297
Rationale: given ratio = 1 / 2 : 2 / 3 : 3 / 4 = 6 : 4 : 9 1 st part = 782 * 4 / 19 = rs . 165 answer : d
Answer: d
Python program:
a = 3 / 4
b = 1 / 2
c = 1 / 3
d = b + c 
e = a + d 
f = 782 / e
g = 1 / 3
h = f * g
Problem: a number is doubled and 5 is added . if the resultant is trebled , it becomes 117 . what is that number ?
Options: a ) 12 , b ) 29 , c ) 27 , d ) 17 , e ) 99
Rationale: "explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 117 6 x + 15 = 117 6 x = 102 x = 17 answer : d"
Answer: d
Python program:
a = 3 * 5
b = 117 - a
c = 3 * 2
d = b / c
Problem: find out the c . i on rs . 5000 at 4 % p . a . compound half - yearly for 1 1 / 2 years .
Options: a ) 306.05 , b ) 306.00 , c ) 306.04 , d ) 306.05 , e ) 306.01
Rationale: "a = 5000 ( 51 / 50 ) 3 = 5306.04 5000 - - - - - - - - - - - 306.04 answer : a"
Answer: a
Python program:
a = 4 / 100
b = 1 + a 
c = 3 / 2
d = b ** c
e = 5000 * d
f = e - 5000
Problem: what is the greatest of 3 consecutive integers whose sum is 24 ?
Options: a ) 3 , b ) 76 , c ) 8 , d ) 9 , e ) 10
Rationale: explanation : the sum of three consecutive integers can be written as n + ( n + 1 ) + ( n + 2 ) = 3 n + 3 if the sum is 24 , we need to solve the equation 3 n + 3 = 24 ; = > 3 n = 21 ; = > n = 7 the greatest of the three numbers is therefore 7 + 2 = 9 answer : d ) 9
Answer: d
Python program:
a = 24 - 3
b = a / 3
c = b + 2
Problem: i sold a book at a profit of 10 % . had i sold it for $ 120 more , 15 % would have been gained . find the cost price ?
Options: a ) $ 2000 , b ) $ 2500 , c ) $ 2400 , d ) $ 3120 , e ) $ 1540
Rationale: "115 % of cost - 110 % of cost = $ 120 5 % of cost = $ 120 cost = 120 * 100 / 5 = $ 2400 answer is c"
Answer: c
Python program:
a = 120 * 10
b = 15 - 10
c = a / b
d = c * 100
e = d / 10
Problem: how much is 25 % of 40 is greater than 4 / 5 of 25 ?
Options: a ) 10 , b ) 776 , c ) 66 , d ) 12 , e ) 99
Rationale: "( 25 / 100 ) * 40 – ( 4 / 5 ) * 25 10 - 20 = 10 answer : a"
Answer: a
Python program:
a = 25 / 100
b = 40 * a
c = 4 / 5
d = c * 25
e = b - d
Problem: a certain car uses 12 gallons of gasoline in traveling 360 miles . in order for the car to travel the same distance using 10 gallons of gasoline , by how many miles per gallon must the car ’ s gas mileage be increased ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "360 / 10 = 36 . the difference is 36 - 30 = 6 . answer c"
Answer: c
Python program:
a = 360 / 10
b = 360 / 12
c = a - b
Problem: in an election between two candidates - lange and sobel - 70 % of the voters voted for sobel . of the election ` s voters , 60 % were male . if 35 % of the female voters voted for lange , what percentage of the male voters voted for sobel ?
Options: a ) 14 , b ) 16 , c ) 26 , d ) 44 , e ) 65
Rationale: m f total l 16 14 30 s 44 70 tot 60 40 100 35 % of 40 = 14 - - - - - - female voters that means 16 male voted for l so 60 - 16 = 44 d is correct
Answer: d
Python program:
a = 100 - 60
b = 100 - 60
c = b * 35
d = c / 100
e = a - d
f = 70 - e
Problem: a 100 - litre mixture of milk and water contains 49 litres of milk . ' x ' litres of this mixture is removed and replaced with an equal quantum of water . if the process is repeated once , then the concentration of the milk stands reduced at 25 % . what is the value of x ?
Options: a ) 27.5 litres , b ) 26.67 litres , c ) 27.67 litres , d ) 28.57 litres , e ) 26 litres
Rationale: "working formula . . . initial concentration * initial volume = final concentration * final volume . let x is the part removed from 100 lts . 49 % ( 1 - x / 100 ) ^ 2 = 25 % * 100 % ( 1 - x / 100 ) ^ 2 = 25 / 49 - - - - - - > ( 1 - x / 100 ) ^ 2 = ( 5 / 7 ) ^ 2 100 - x = 500 / 7 x = 28.57 . . . ans d"
Answer: d
Python program:
a = 25 / 49
b = math.sqrt(a)
c = 1 - b
d = 100 * c
Problem: the standard deviation of a normal distribution of data is 2 , and 3 standard deviations below the mean is greater than 46 . what is a possible value for the mean of the distribution ?
Options: a ) 46 , b ) 52 , c ) 48 , d ) 49 , e ) 50
Rationale: "the standard deviation ( { sd } ) = 2 ; 3 standard deviations below the mean is greater than 46 : { mean } - 3 * { sd } > 46 ; { mean } - 6 > 46 ; { mean } > 52 . answer : b ."
Answer: b
Python program:
a = 3 * 2
b = 46 + a 
c = b + 1
Problem: 4 friends a , b , c and d decided to share a lot of apples . each of them had half of the total plus half an apple in order . after each of them took their share 3 time , no apples were left . how many apples were there ?
Options: a ) 4096 , b ) 4055 , c ) 4092 , d ) 4085 , e ) 4095
Rationale: whenever the rate of reduction is ' half of the total and half of it ' , the answer is always ( 2 ^ n ) - 1 , where ' n ' is the number of times the process is repeated . here , the process is repeated 12 times . so answer is ( 2 ^ 12 ) - 1 = 4095 answer e
Answer: e
Python program:
a = 4 * 1000
b = 10 * 10
c = a + b 
d = 3 + 2 
e = c - d
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 16 hours and 4 hours respectively . the ratio of their speeds is :
Options: a ) 2 : 4 , b ) 4 : 3 , c ) 6 : 7 , d ) 9 : 16 , e ) none of these
Rationale: "let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 4 : â ˆ š 16 = 2 : 4 . answer a"
Answer: a
Python program:
a = math.sqrt(4)
b = math.sqrt(16)
c = a / b
Problem: a certain family has 3 sons : richard is 6 years older than david , and david is 8 years older than scott . if in 8 years , richard will be twice as old as scott , then how old was david 2 years ago ?
Options: a ) 8 , b ) 12 , c ) 12 , d ) 14 , e ) 16
Rationale: let ' s say age of richard is ` ` r ' ' age of david is ` ` d ' ' age of scott is ` ` s ' ' now richard is 6 years older than david , i . e . r = d + 6 david is 8 years older than scott i . e . d = s + 8 if in 8 years , richard will be twice as old as scott i . e . r + 8 = 2 x ( s + 8 ) i . e . r + 8 = 2 s + 16 i . e . r = 2 s + 8 but r = d + 6 = ( s + 8 ) + 6 = s + 14 therefore , 2 s + 8 = s + 14 i . e . s = 6 i . e . r = 20 i . e . d = 14 now , how old was david 2 years ago ? i . e . d - 2 = 14 - 2 = 12 years answer : b
Answer: b
Python program:
a = 6 + 8 
b = a - 2
Problem: a river 4 m deep and 22 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 4500 , b ) 2678 , c ) 2933 , d ) 2761 , e ) 2882
Rationale: ( 2000 * 4 * 22 ) / 60 = 2933 m 3 answer : c
Answer: c
Python program:
a = 4 * 22
b = 2 * 1000
c = a * b
d = 1 * const_60
e = c / d
Problem: a drink vendor has 40 liters of maaza , 144 liters of pepsi and 368 liters of sprite . he wants to pack them in cans , so that each can contains the same number of liters of a drink , and does n ' t want to mix any two drinks in a can . what is the least number of cans required ?
Options: a ) 35 , b ) 37 , c ) 42 , d ) 50 , e ) 69
Rationale: the number of liters in each can = hcf of 40 , 144 and 368 = 8 liters . number of cans of maaza = 40 / 8 = 5 number of cans of pepsi = 144 / 8 = 18 number of cans of sprite = 368 / 8 = 46 the total number of cans required = 5 + 18 + 46 = 69 cans . answer : e
Answer: e
Python program:
a = math.gcd(40, 144)
b = math.gcd(a, 368)
c = 368 / b
d = math.gcd(40, 144)
e = math.gcd(d, 368)
f = 40 / e
g = math.gcd(40, 144)
h = math.gcd(g, 368)
i = 144 / h
j = f + i 
k = c + j
Problem: if x is 3 times larger than n , and if 2 n + 3 is 20 % of 25 , what is the value of ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 6 , e ) 12
Rationale: then the wordings of question are misleading . moreover , it ' d also be a bad way to convey x = 4 n , if it really wanted to convey so . from other questions that i have seen , proper wordings could be : if x is three times as large as n or simply , if x is three times n . c
Answer: c
Python program:
a = 25 * 20
b = a / 100
c = b - 3
d = c / 2
e = d * 3
Problem: a one - foot stick is marked in 1 / 3 and 1 / 5 portion . how many total markings will there be , including the end points ?
Options: a ) 10 , b ) 7 , c ) 6 , d ) 5 , e ) 8
Rationale: "lcm of 15 = 15 1 / 3 marking are ( table of 5 ) 0 . . . . . . 5 . . . . . . 10 . . . . . 15 ( total = 4 ) 1 / 5 marking are ( table of 3 ) 0 . . . . . . . 3 . . . . . . 6 . . . . . . 9 . . . . . . . . 12 . . . . . . 15 ( total = 6 ) overlapping markings are 0 . . . . . . . . 15 ( total = 2 ) total markings = 4 + 6 - 2 = 8 answer = e"
Answer: e
Python program:
a = 3 + 5
Problem: sachin is younger than rahul by 6 years . if their ages are in the respective ratio of 7 : 9 , how old is sachin ?
Options: a ) 16 , b ) 18 , c ) 28 , d ) 30 , e ) 34
Rationale: "let rahul ' s age be x years . then , sachin ' s age = ( x - 6 ) years . ( x - 6 ) / x = 7 / 9 9 x - 54 = 7 x 2 x = 54 x = 27 hence , sachin ' s age = ( x - 7 ) = 34 years . ans - e"
Answer: e
Python program:
a = 9 - 7
b = 6 / a
c = b * 7