euclaise/mathqa_programs huggingface dataset:
Problem: a , b , c subscribe rs . 50,000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 30,000 , a receives :
Options: a ) s . 12,000 , b ) s . 12,200 , c ) s . 12,400 , d ) s . 12,600 , e ) s . 12,800
Rationale: "let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 3 x = 36000 x = 12000 a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . a ' s share = rs . ( 30000 x 21 / 50 ) = rs . 12,600 . d"
Answer: d
Python program:
a = 10 * 5000
b = a - 5000
c = 4000 + 5000 
d = b - c
e = d / 3
f = 4000 + 5000 
g = e + f 
h = 10 * 5000
i = g / h
j = 3 + 4 
k = j * 5000
l = i * k
m = l / 1000
n = math.floor(m)
o = n - 1
Problem: if the simple interest on a certain amount in at 4 % rate 5 years amounted to rs . 2080 less than the principal . what was the principal ?
Options: a ) 1500 , b ) 2600 , c ) 2507 , d ) 3200 , e ) 11500
Rationale: "p - 2080 = ( p * 5 * 4 ) / 100 p = 2600 answer : b"
Answer: b
Python program:
a = 4 * 5
b = a / 100
c = 1 - b
d = 2080 / c
Problem: a small pool filled only with water will require an additional 600 gallons of water in order to be filled to 80 % of its capacity . if pumping in these additional 600 gallons of water will increase the amount of water in the pool by 30 % , what is the total capacity of the pool in gallons ?
Options: a ) 1000 , b ) 1250 , c ) 1300 , d ) 1600 , e ) 2000
Rationale: "since pumping in additional 600 gallons of water will increase the amount of water in the pool by 30 % , then initially the pool is filled with 1,000 gallons of water . so , we have that 1,000 + 600 = 0.8 * { total } - - > { total } = 2,000 . answer : e ."
Answer: e
Python program:
a = 600 * 100
b = a / 30
c = b + 600 
d = 80 / 100
e = c / d
Problem: the compound ratio of 2 : 3 , 3 : 2 and 4 : 5 ?
Options: a ) 1 : 9 , b ) 1 : 7 , c ) 1 : 2 , d ) 4 : 5 , e ) 1 : 4
Rationale: "2 / 3 * 3 / 2 * 4 / 5 = 4 / 5 = 4 : 5 answer : d"
Answer: d
Python program:
a = 2 * 3
b = 3 * 2
c = a / b
d = 3 * 4
e = 2 * 5
f = d / e
g = c / f
Problem: the h . c . f . of two numbers is 12 and their l . c . m . is 600 . if one of the numbers is 720 , then the other is :
Options: a ) 8 , b ) 10 , c ) 12 , d ) 4 , e ) 6
Rationale: "other number = ( 12 x 600 ) / 720 = 10 . answer : c"
Answer: c
Python program:
a = 12 * 720
Problem: david obtained 76 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 75 , d ) none of these , e ) can not be determined
Rationale: "solution : average = ( 76 + 65 + 82 + 67 + 85 ) / 5 = 375 / 5 = 75 . hence , average = 75 . answer : option c"
Answer: c
Python program:
a = 76 + 65 
b = a + 82 
c = b + 67 
d = c + 85 
e = 2 + 3 
f = d / e
Problem: if the ratio of s . i earned on certain amount on same rate is 4 : 5 . what is the ratio of time ?
Options: a ) 1 : 2 , b ) 6 : 9 , c ) 4 : 5 , d ) 2 : 3 , e ) not possible to calculate
Rationale: s . i 1 / s . i 2 = [ ( p * r * t 1 ) / 100 ] / [ ( p * r * t 2 ) / 100 ] 4 / 5 = t 1 / t 2 ratio = 4 : 5 answer c
Answer: c
Python program:
a = 4 / 5
Problem: dick and jane each saved $ 2,000 in 1989 . in 1990 dick saved 10 percent more than in 1989 , and together he and jane saved a total of $ 4,000 . approximately what percent less did jane save in 1990 than in 1989 ?
Options: a ) 10 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 35 %
Rationale: "1990 dick saved = $ 2200 jane saved = $ 1800 ( jane saved $ 200 less than she did the prior year ) jane saved approximately $ 200 / 2000 $ ( 10 % ) less in 1990 answer : a"
Answer: a
Python program:
a = 10 / 100
b = a + 1 
c = 2 - b
d = 1 - c
e = d * 100
Problem: tough and tricky questions : exponents . if 7 ^ ( 3 x - 1 ) * 3 ^ ( 4 y - 3 ) = 49 ^ x * 27 ^ y , then x + y =
Options: a ) 3 , b ) 4 , c ) 2 , d ) 1 , e ) 5
Rationale: here is my solution . 7 ^ ( 3 x - 1 ) * 3 ^ ( 4 y - 3 ) = 49 ^ x * 27 ^ y here rhs 49 ^ x * 27 ^ y = 7 ^ ( 2 x ) * 3 ^ ( 3 y ) equating powers on both sides - - > 3 x - 1 = 2 x , thus x = 1 and 4 y - 3 = 3 y giving y = 3 so , x + y = 4 option : b
Answer: b
Python program:
a = 1 + 3
Problem: a candidate got 35 % of the votes polled and he lost to his rival by 2250 votes . how many votes were cast ?
Options: a ) 7500 , b ) 3388 , c ) 2665 , d ) 2888 , e ) 2661
Rationale: 35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % - - - - - - - - - - 2250 100 % - - - - - - - - - ? = > 7500 answer : a
Answer: a
Python program:
a = 35 / 100
b = 1 - a
c = 35 / 100
d = b - c
e = 2250 / d
Problem: find the ratio in which rice at rs . 7.20 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg .
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 3 : 5 , e ) 4 : 5
Rationale: "req = 60 : 90 = 2 : 3 answer b"
Answer: b
Python program:
a = 6 - 30
b = 7 - 20
c = a / b
Problem: a volume of 11248 l water is in a container of sphere . how many hemisphere of volume 4 l each will be required to transfer all the water into the small hemispheres ?
Options: a ) 2812 , b ) 8231 , c ) 2734 , d ) 4222 , e ) 4254
Rationale: "a volume of 4 l can be kept in 1 hemisphere therefore , a volume of 11248 l can be kept in ( 11248 / 4 ) hemispheres ans . 2812 answer : a"
Answer: a
Python program:
a = 11248 / 4
Problem: b completes a work in 6 days . a alone can do it in 10 days . if both work together , the work can be completed in how many days ?
Options: a ) 3.33 days , b ) 4.33 days , c ) 5.33 days , d ) 6.33 days , e ) 7.33 days
Rationale: "1 / 5 + 1 / 10 = 3 / 10 10 / 3 = 3.33 days answer : a"
Answer: a
Python program:
a = 10 * 6
b = 6 + 10 
c = a / b
Problem: a man can row upstream at 20 kmph and downstream at 28 kmph , and then find the speed of the man in still water ?
Options: a ) 24 , b ) 37 , c ) 30 , d ) 27 , e ) 18
Rationale: "us = 20 ds = 28 m = ( 28 + 20 ) / 2 = 24 answer : a"
Answer: a
Python program:
a = 20 + 28 
b = a / 2
Problem: if x and y are integers such that x ^ 2 = 2 y and xy = 256 , then x – y = ?
Options: a ) - 30 , b ) - 24 , c ) - 5 , d ) 5 , e ) 20
Rationale: "here x and y are integers . x ^ 2 = 2 y , xy = 256 . substitute ( x ^ 2 ) / 2 = y in xy = > x ^ 3 = 256 * 2 = > x ^ 3 = 512 . here x ^ 3 is positive , x is also positive . x = 8 then y = 32 . x - y = - 24 so option b is correct"
Answer: b
Python program:
a = 256 * 2
b = a ** const_0_33
c = 256 * 2
d = c ** const_0_33
e = 256 / d
f = b - e
Problem: if a tire rotates at 400 revolutions per minute when the car is traveling 144 km / h , what is the circumference of the tire ?
Options: a ) 2 meters , b ) 6 meters , c ) 5 meters , d ) 3 meters , e ) 7 meters
Rationale: "400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 144,000 m : c is the circumference c = 6 meters correct answer b"
Answer: b
Python program:
a = 2 * 3
b = a * 10
c = b * 400
d = 144 / c
e = d * 1000
Problem: the average of runs of a cricket player of 10 innings was 18 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 87 , b ) 16 , c ) 62 , d ) 76 , e ) 17
Rationale: "average after 11 innings = 22 required number of runs = ( 33 * 11 ) - ( 18 * 10 ) = 242 - 180 = 62 . answer : c"
Answer: c
Python program:
a = 10 + 1 
b = 4 + 18 
c = a * b
d = 10 * 18
e = c - d
Problem: if a = 105 and a ^ 3 = 21 * 25 * 15 * b , what is the value of b ?
Options: a ) 35 , b ) 42 , c ) 45 , d ) 147 , e ) 54
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 15 = 3 * 5 so , ( 105 ) ^ 3 = 3 * 7 * 5 * 5 * 3 * 5 * b therefore ( 3 * 5 * 7 ) ^ 3 = 3 ^ 2 * 5 ^ 3 * 7 * b therefore , b = 3 ^ 3 * 5 ^ 3 * 7 ^ 3 / 3 ^ 2 * 5 ^ 3 * 7 b = 3 * 7 ^ 2 = 3 * 49 = 147 correct answer d ."
Answer: d
Python program:
a = 105 ** 3
b = 21 * 25
c = b * 15
d = a / c
Problem: if the difference of two numbers is 3 and the difference of their square is 39 , then the larger number is :
Options: a ) 9 , b ) 2 , c ) 12 , d ) 14 , e ) 8
Rationale: let the numbers be x and y then x 2 - y 2 = 39 and x - y = 3 we get x + y = 13 solving x - y = 3 , x + y = 13 x = 8 , y = 5 larger number 8 answer e
Answer: e
Python program:
a = 39 / 3
b = a - 3
c = b / 2
d = c + 3
Problem: the ratio of two numbers is 3 : 4 and their sum is 21 . the greater of the two numbers is ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 17 , e ) 19
Rationale: 3 : 4 total parts = 7 = 7 parts - - > 21 ( 7 ã — 3 = 21 ) = 1 part - - - - > 3 ( 1 ã — 3 = 4 ) = the greater of the two number is = 4 = 4 parts - - - - > 12 ( 4 ã — 3 = 12 ) a
Answer: a
Python program:
a = 21 * 3
b = 3 + 4 
c = a / b
d = 21 - c
Problem: working alone at its constant rate , machine a produces x boxes in 10 minutes and working alone at its constant rate , machine b produces 2 x boxes in 5 minutes . how many minutes does it take machines a and b , working simultaneously at their respective constant rates , to produce 6 x boxes ?
Options: a ) 3 minutes , b ) 4 minutes , c ) 5 minutes , d ) 6 minutes , e ) 12 minutes
Rationale: "rate = work / time given rate of machine a = x / 10 min machine b produces 2 x boxes in 5 min hence , machine b produces 4 x boxes in 10 min . rate of machine b = 4 x / 10 we need tofind the combined time that machines a and b , working simultaneouslytakeat their respective constant rates let ' s first find the combined rate of machine a and b rate of machine a = x / 10 min + rate of machine b = 4 x / 10 = 5 x / 10 now combine time = combine work needs to be done / combine rate = 6 x / 5 x * 10 = 12 min ans : e"
Answer: e
Python program:
a = 6 * 10
b = speed + ( 
c = 2 * 10
d = a / b
Problem: a light flashes every 15 seconds , how many times will it flash in ? of an hour ?
Options: a ) 550 , b ) 600 , c ) 240 , d ) 700 , e ) 750
Rationale: "1 flash = 15 sec for 1 min = 4 flashes so for 1 hour = 4 * 60 = 240 flashes . answer : c"
Answer: c
Python program:
a = 3600 / 15
Problem: a train running at the speed of 60 km / hr crosses a pole in 7 seconds . find the length of the train .
Options: a ) 116.67 , b ) 882 , c ) 772 , d ) 252 , e ) 121
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 7 = 116.67 meter . answer : a"
Answer: a
Python program:
a = 60 * 1000
b = a / 3600
c = b * 7
Problem: in what time will a train 40 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 1.0 sec , c ) 7.5 sec , d ) 2.3 sec , e ) 1.5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 40 / 40 = 1.0 sec . answer : b"
Answer: b
Python program:
a = 144 * const_0_2778
b = 40 / a
Problem: a certain country had a total annual expenditure of $ 1.2 x 10 ^ 12 . if the population of the country was 240 million last year , what was the per capita expenditure ?
Options: a ) $ 500 , b ) $ 1000 , c ) $ 2000 , d ) $ 3000 , e ) $ 5000
Rationale: "explanation : in scientific notation 240 million is 2.4 x 10 ^ 8 . so the per capita expenditure was : ( $ 1.2 x 10 ^ 12 ) / ( 2.4 x 10 ^ 8 ) = ( $ 1.2 ) / ( 2.4 ) x 10 ^ 12 - 8 = $ 0.5 x 10 ^ 4 = $ 5000 answer : option e"
Answer: e
Python program:
a = 10 ** 12
b = 1 * 2
c = 4 + 2 
d = 10 ** c
e = 240 * d
f = b / e
Problem: in a dairy farm , 50 cows eat 50 bags of husk in 50 days . in how many days one cow will eat one bag of husk ?
Options: a ) 34 days , b ) 40 days , c ) 46 days , d ) 50 days , e ) none of these
Rationale: "explanation : less cows , more days ( indirect proportion ) less bags , less days ( direct proportion ) [ cows 1 50 bags 50 1 ] : : 50 : x = > x ∗ 50 ∗ 1 = 50 ∗ 1 ∗ 50 = > x = 50 option d"
Answer: d
Python program:
a = 50 / 50
b = a * 50
Problem: what is the range of all the roots of | x ^ 2 - 1 | = x ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: we get 2 quadratic equations here . . 1 ) x ^ 2 - x - 1 = 0 . . . . . . . roots 2 , - 1 2 ) x ^ 2 + x - 1 = 0 . . . . . . . . roots - 2 , 1 inserting each root in given equation , it can be seen that - 1 and - 2 do not satisfy the equations . so value of x for given equation . . . . x = 2 or x = 1 i guess range is 2 - 1 = 1 d
Answer: d
Python program:
a = math.sqrt(1)
Problem: one - third of rahul ’ s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 2 , 50000 as total savings , how much has he saved in public provident fund ?
Options: a ) rs . 30,000 , b ) rs . 50,000 , c ) rs . 60,000 , d ) rs . 100,000 , e ) none
Rationale: explanation let savings in n . s . c and p . p . f . be rs . x and rs . ( 250000 – x ) respectively . then , 1 / 3 x = 1 / 2 ( 250000 - x ) = > x / 3 + x / 2 = 125000 = > 5 x / 6 = 125000 = > x = 125000 x 6 / 5 = 150000 savings in public provident fund = rs . ( 250000 – 150000 ) = rs . 100000 answer d
Answer: d
Python program:
a = 100 * 1000
b = 2 * a
c = b + 50000 
d = 100 * 1000
e = 2 * d
f = e + 50000 
g = 2 + 3 
h = f / g
i = c - h
Problem: roja and pooja start moving in the opposite directions from a pole . they are moving at the speeds of 2 km / hr and 3 km / hr respectively . after 4 hours what will be the distance between them ?
Options: a ) 11 , b ) 20 , c ) 77 , d ) 26 , e ) 12
Rationale: "distance = relative speed * time = ( 2 + 3 ) * 4 = 20 km [ they are travelling in the opposite direction , relative speed = sum of the speeds ] . answer : b"
Answer: b
Python program:
a = 2 + 3 
b = a * 4
Problem: the proportion of water to alcohol in solution a is 4 : 1 and the proportion of water to alcohol in solution b is 3 : 1 . if an equal amount of each solution is mixed together , what is the concentration of alcohol in the new solution ?
Options: a ) 16.5 % , b ) 18.5 % , c ) 20.5 % , d ) 22.5 % , e ) 24.5 %
Rationale: "let v be the total volume of the new solution . then a volume of v / 2 was added from each solution a and b . the amount of alcohol added to the new solution was : ( 1 / 5 ) ( v / 2 ) + ( 1 / 4 ) ( v / 2 ) = v / 10 + v / 8 = 9 v / 40 . the concentration of alcohol is 9 / 40 = 22.5 % the answer is d ."
Answer: d
Python program:
a = 1 + 1 
b = 4 + 3 
c = 1 + 1 
d = b + c 
e = a / d
f = e * 100
Problem: find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm ?
Options: a ) 188 cm 2 , b ) 150 cm 2 , c ) 168 cm 2 , d ) 198 cm 2 , e ) 987 cm 2
Rationale: "1 / 2 * 20 ( 9 + 6 ) = 150 cm 2 answer : b"
Answer: b
Python program:
a = 1 / 2
b = 6 + 9 
c = a * b
d = c * 20
Problem: how many integers between 0 and 1000 do not contain the integer 1
Options: a ) 727 , b ) 728 , c ) 758 , d ) 748 , e ) 792
Rationale: from 1 to 99 = 19 integers having 1 from 101 to 199 = all are having 1 similarly 201 - 299 , 301 - 399 , 401 - 499 , . . . . . so on , will have 19 integers having 1 answer = 1000 - ( 19 * 9 + 99 + 2 ) / / 2 is added for 100 and 1000 = 728 answer : b
Answer: b
Python program:
a = 2 * 100
b = 3 + 4 
c = b * 10
d = a + c 
e = d + 2 
f = 1000 - e
Problem: working simultaneously and independently at an identical constant rate , 4 machines of a certain type can produce a total of x units of product p in 6 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 3 x units of product p in 6 days ?
Options: a ) 24 , b ) 18 , c ) 16 , d ) 12 , e ) 8
Rationale: "4 machines do x units in 6 days we have x / 6 = > rate of the 4 machines we know that we need to have 4 x units in 6 days therefore , we need to get to 4 x / 6 rate of the machines . rate of one machine is x / 6 * 1 / 4 = x / 24 . now , we need to know how many machines need to work simultaneously , to get 3 x done in 6 days . 3 x / 6 work needs to be done by machines that work at x / 24 rate . let ' s assign a constant y for the number of machines : ( x / 24 ) * y = 3 x / 6 y = 3 x / 6 * 24 / x cancel 6 with 24 , and x with x and get - > 12 . answer choice d"
Answer: d
Python program:
a = 4 * 3
b = 6 / 6
c = a * b
Problem: how many factors of 270 are odd numbers greater than 1 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 9
Rationale: "prime factors of 810 are 2 ^ 1,3 ^ 4,5 ^ 1 total divisors = ( power if a prime factor + 1 ) total no . of odd factors ( 3,5 , ) = ( 4 + 1 ) ( 1 + 1 ) = 10 since we need odd divisors other than 1 = > 10 - 1 = 9 odd divisors e is the answer"
Answer: e
Python program:
a = 10 * 2
b = 270 / a
Problem: a batsman in his 12 th innings makes a score of 65 and thereby increases his average by 2 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ?
Options: a ) 42 , b ) 43 , c ) 44 , d ) 45 , e ) 46
Rationale: "let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 2 ) + 65 ∴ x = 43 answer b"
Answer: b
Python program:
a = 12 * 2
b = 65 - a
c = b + 2
Problem: if the number is decreased by 5 and divided by 7 the result is 7 . what would be the result if 14 is subtracted and divided by 10 ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 5 , e ) 3
Rationale: "explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 14 ) / 10 = ( 54 - 14 ) / 10 = 4 answer : option a"
Answer: a
Python program:
a = 7 * 7
b = a + 5 
c = b - 14
d = c / 10
Problem: when the number 1 y 92355 is exactly divisible by 11 , then the smallest whole number in place of y is ?
Options: a ) 1 , b ) 3 , c ) 7 , d ) 9 , e ) 0
Rationale: the given number = 1 y 92355 sum of the odd places = 5 + 3 + 9 + 1 = 18 sum of the even places = 5 + 2 + y ( sum of the odd places ) - ( sum of even places ) = number ( exactly divisible by 11 ) 18 - ( 7 + y ) = divisible by 11 11 � y = divisible by 11 . y must be 0 , to make given number divisible by 11 . e
Answer: e
Python program:
a = 1 - 1
Problem: how many liters of oil at rs . 40 per liter should be mixed with 240 liters of a second variety of oil at rs . 60 per liter so as to get a mixture whose cost is rs . 52 per liter ?
Options: a ) 120 , b ) 150 , c ) 160 , d ) 180 , e ) 200
Rationale: 8 : 12 = 2 : 3 if 240 lrs of the 2 nd variety taken then the 1 st variety should be taken as 160 lr answer c
Answer: c
Python program:
a = 240 * 60
b = 52 * 240
c = a - b
d = 52 - 40
e = c / d
Problem: if w / x = 1 / 3 and w / y = 2 / 3 , then ( x + y ) / y =
Options: a ) 2 , b ) 4 , c ) 5 , d ) 3 , e ) 7
Rationale: "ratio 1 : 3 w = x ratio 2 : 3 w = 2 y x = 2 y ( x + y ) / y = ( 2 y + y ) / y = y ( 2 + 1 ) / y = 3 answer is d"
Answer: d
Python program:
a = 2 / 1
b = 3 / 3
c = a / b
d = c + 1
Problem: two trains running in opposite directions cross a man standing on the platform in 25 seconds and 18 seconds respectively and they cross each other in 20 seconds . the ratio of their speeds is :
Options: a ) 3 : 1 , b ) 3 : 2 , c ) 3 : 8 , d ) 2 : 5 , e ) 3 : 4
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 25 x meters , and length of the second train = 18 y meters . ( 25 x + 18 y ) / ( x + y ) = 20 = = > 25 x + 18 y = 20 x + 20 y = = > 5 x = 2 y = = > x / y = 2 / 5 answer : option d"
Answer: d
Python program:
a = 25 - 20
b = 20 - 18
c = a / b
Problem: in how many no . between 100 and 1000 at least one of their digits is 7 ?
Options: a ) 900 , b ) 648 , c ) 720 , d ) 252 , e ) 729
Rationale: "let ' s count the number of occurrences with only one 7 : ( 1 ) 7 xx : 1 * 9 * 9 = 81 ( 2 ) x 7 x : 8 * 1 * 9 = 72 ( 3 ) xx 7 : 8 * 9 * 1 = 72 81 + 72 + 72 = 225 at this point we can already see that the answer must be d since the choice are very dispersed . anyways , let ' s count number of occurrences with two 7 s : ( 1 ) 77 x : 1 * 1 * 9 = 9 ( 2 ) x 77 : 8 * 1 * 1 = 8 ( 3 ) 7 x 7 : 1 * 9 * 1 = 9 9 + 8 + 9 = 26 number 777 is missing . so the total becomes 225 + 26 + 1 = 252 d is the correct answer ."
Answer: d
Python program:
a = 1000 / 100
b = a / 7
Problem: the charge for a single room at hotel p is 25 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?
Options: a ) 15 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 150 %
Rationale: "let rate in r = 100 x then p = 75 x g = 100 y p = 90 y thus 75 x = 90 y or x = 1.20 y ans r = 120 y so increase = 20 % answer : b ."
Answer: b
Python program:
a = 100 - 25
b = 100 - 10
c = a / b
d = c * 100
e = 100 - d
f = 100 - 25
g = 100 - 10
h = f / g
i = h * 100
j = e / i
k = j * 100
Problem: farm tax is levied on the 60 % of the cultivated land . the tax department collected total $ 4000 through the farm tax from the village of mr . willam . mr . willam paid only $ 500 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 15 % , b ) 25 % , c ) 12.5 % , d ) 20.83 % , e ) none
Rationale: "only trick n this question is to ignore 60 % information as farm tax is levied uniformly in the village and that includes mr william ' s land . what percentage of tax mr william paid ? this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 500 / 4000 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 60 ) = 20.833 % and the answer is not there in the options . the correct answer is ( d ) ."
Answer: d
Python program:
a = 500 / 4000
b = a * 100
c = b * 100
d = c / 60
Problem: the s . i . on a certain sum of money for 2 years at 6 % per annum is half the c . i . on rs . 4000 for 2 years at 10 % per annum . the sum placed on s . i . is ?
Options: a ) 2197 , b ) 1267 , c ) 3500 , d ) 2267 , e ) 1262
Rationale: "explanation : c . i . = [ 4000 * ( 1 + 10 / 100 ) 2 - 4000 ] = ( 4000 * 11 / 10 * 11 / 10 - 4000 ) = rs . 840 . sum = ( 420 * 100 ) / ( 2 * 6 ) = rs . 3500 answer : c"
Answer: c
Python program:
a = 10 / 100
b = 1 + a 
c = b ** 2
d = 4000 * c
e = d - 4000
f = e / 2
g = 6 / 100
h = 2 * g
i = f / h
Problem: the avg weight of a , b & c is 60 kg . if d joins the group , the avg weight of the group becomes 65 kg . if another man e who weights is 3 kg more than d replaces a , then the avgof b , c , d & e becomes 64 kg . what is the weight of a ?
Options: a ) 56 , b ) 65 , c ) 75 , d ) 89 , e ) 87
Rationale: "a + b + c = 3 * 60 = 180 a + b + c + d = 4 * 65 = 260 - - - - ( i ) so , d = 80 & e = 80 + 3 = 83 b + c + d + e = 64 * 4 = 256 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 260 – 256 = 4 a = e + 4 = 83 + 4 = 87 answer : e"
Answer: e
Python program:
a = 65 * 4
b = 64 * 4
c = 65 * 4
d = 60 * 3
e = c - d
f = 3 + e 
g = b - f
h = a - g
Problem: a reduction of 40 % in the price of bananas would enable a man to obtain 66 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 1.91 , b ) 2.91 , c ) 4.91 , d ) 3.91 , e ) 5.91
Rationale: "40 * ( 40 / 100 ) = 16 - - - 66 ? - - - 12 = > rs . 2.91 answer : b"
Answer: b
Python program:
a = 40 / 100
b = 40 * a
c = b / 66
d = 12 * c
Problem: a car travels uphill at 30 km / hr and downhill at 80 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ?
Options: a ) 38 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 36 kmph
Rationale: "avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 80 = 5 / 8 ; avg speed = 150 / ( 10 / 3 + 5 / 8 ) = 38 kmph answer : a"
Answer: a
Python program:
a = 100 + 50 
b = 100 / 30
c = 50 / 80
d = b + c 
e = a / d
Problem: convert the 8 / 26 m / s into kilometers per hour ?
Options: a ) 3.5 kmph . , b ) 2.5 kmph . , c ) 1.2 kmph . , d ) 1.1 kmph . , e ) 1.9 kmph .
Rationale: "8 / 26 m / s = 8 / 26 * 18 / 5 = 1 ( 1 / 10 ) = 1.1 kmph . answer : d"
Answer: d
Python program:
a = 8 / 26
b = const_3_6 * a