euclaise/mathqa_programs huggingface dataset:
Problem: a box measuring 90 inches long by 45 inches wide by 9 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
Options: a ) 17 , b ) 18 , c ) 50 , d ) 108 , e ) 864
Rationale: "least number of cubes will be required when the cubes that could fit in are biggest . 9 is the biggest number that could divide all three , 90 , 45 and 9 . thus side of cube must be 9 , and total number of cubes = 90 / 9 * 45 / 9 * 9 / 9 = 50 ans c it is ."
Answer: c
Python program:
a = 90 * 45
b = a * 9
c = 9 / 2
d = b / volume_cube
Problem: you collect baseball cards . suppose you start out with 11 . maria takes half of one more than the number of baseball cards you have . since you ' re nice , you give peter 1 baseball card . since his father makes baseball cards , paul decides to triple your baseball cards . how many baseball cards do you have at the end ?
Options: a ) 12 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: "solution start with 11 baseball cards . maria takes half of one more than the number of baseball cards you have . so maria takes half of 11 + 1 which is 6 , so you ' re left with 11 - 6 = 5 . peter takes 1 baseball card from you : 5 - 1 = 4 baseball cards . paul triples the number of baseball cards you have : 4 ã — 3 = 12 baseball cards . so you have 12 at the end . correct answer : a"
Answer: a
Python program:
a = 11 - 4
b = a - 4
c = b - 1
d = c * 3
Problem: a bullet train 130 m long is running with a speed of 50 kmph . in what time will it pass a man who is running at 10 kmph in the direction opposite to that in which the bullet train is going ?
Options: a ) 23 sec , b ) 13 sec , c ) 12 sec , d ) 11 sec , e ) 16 sec
Rationale: "b 13 sec speed of the bullet train relative to man = ( 50 + 10 ) kmph = 60 * 5 / 18 m / sec = 30 / 3 m / sec . time taken by the bullet train to cross the man = time taken by it to cover 130 m at ( 30 / 3 ) m / sec = ( 130 * 3 / 30 ) sec = 13 sec"
Answer: b
Python program:
a = 50 + 10 
b = a * 1000
c = b / 3600
d = 130 / c
Problem: find the smallest number of five digits exactly divisible by 22 , 33,66 and 44 .
Options: a ) 10101 , b ) 11000 , c ) 10110 , d ) 10111 , e ) 10100
Rationale: "smallest number of five digits is 10000 . required number must be divisible by l . c . m . of 22,33 , 66,44 i . e 132 , on dividing 10000 by 132 , we get 32 as remainder . therefore , required number = 10000 + ( 132 â € “ 32 ) = 10100 . answer is e ."
Answer: e
Python program:
a = 100 * 100
b = 10 * a
c = b - 100
d = c + 33
Problem: a man walking at a constant rate of 5 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 25 miles per hour . the woman stops to wait for the man 5 minutes after passing him , while the man continues to walk at his constant rate . how many minutes must the woman wait until the man catches up ?
Options: a ) 16 , b ) 20 , c ) 24 , d ) 25 , e ) 28
Rationale: "when the woman passes the man , they are aligned ( m and w ) . they are moving in the same direction . after 5 minutes , the woman ( w ) will be ahead the man ( m ) : m - - - - - - m - - - - - - - - - - - - - - - w w in the 5 minutes , after passing the man , the woman walks the distance mw = ww , which is 5 * 25 / 60 = 25 / 12 miles and the man walks the distance mm , which is 5 * 5 / 60 = 5 / 12 mile . the difference of 25 / 12 - 5 / 12 = 1 / 3 miles ( mw ) will be covered by the man in ( 4 / 3 ) / 4 = 1 / 3 of an hour , which is 20 minutes . answer b ."
Answer: b
Python program:
a = 5 / const_60
b = 25 - 5
c = a * b
d = c / 5
e = const_60 * d
Problem: the ages of two persons differ by 20 years . if 5 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 20,20 , b ) 20,10 , c ) 25,15 , d ) 30,10 , e ) none of these
Rationale: explanation : let their ages be x and ( x + 20 ) years . 5 ( x - 5 ) = ( x + 20 - 5 ) or 4 x = 40 or x = 10 . their present ages are 30 years and 10 years option d
Answer: d
Python program:
a = 20 * 5
b = 5 - 1
c = a / b
d = c + 5 
e = d - 20
Problem: p and q are the only two applicants qualified for a short - term research project that pays 300 dollars in total . candidate p has more experience and , if hired , would be paid 50 percent more per hour than candidate q would be paid . candidate q , if hired , would require 10 hours more than candidate p to do the job . candidate p ’ s hourly wage is how many dollars greater than candidate q ’ s hourly wage ?
Options: a ) $ 5 , b ) $ 10 , c ) $ 15 , d ) $ 20 , e ) $ 25
Rationale: "let q ' s hourly wage be x , then p ' s hourly wage is 1.5 x let t be the number of hours that q needs , then p needs t - 10 hours to do the job . since they both are paid an equal total amount of $ 300 : x * t = 1.5 x * ( t - 10 ) t = 30 hours and q ' s hourly wage is 300 / 30 = $ 10 p ' s hourly wage is 300 / ( t - 10 ) = $ 15 which is $ 5 per hour more . the answer is a ."
Answer: a
Python program:
a = 3 / 2
b = a - 1
c = 10 / b
d = 300 / c
e = 3 / 2
f = e - 1
g = 10 / f
h = g + 10 
i = 300 / h
j = d - i
Problem: the average length of the sides of triangle abc is 12 . what is the perimeter of triangle abc ?
Options: a ) 4
b ) 6
c ) 12
d ) 24
e ) 36
Rationale: ( average ) = ( perimeter ) / 3 ; 12 = ( perimeter ) / 3 ; ( perimeter ) = 36 . answer : e .
Answer: e
Python program:
a = 12 * 3
Problem: a retailer buys 140 pens at the market price of 36 pens from a wholesaler , if he sells these pens giving a discount of 1 % , what is the profit % ?
Options: a ) 105 , b ) 155 , c ) 125 , d ) 185 , e ) 285
Rationale: "let the market price of each pen be $ 1 then , cost price of 140 pens = $ 36 selling price of 140 pens = 99 % of $ 140 = $ 138.60 profit % = ( ( 102.60 * 100 ) / 36 ) % = 285 % answer e"
Answer: e
Python program:
a = 1 / 100
b = 1 - a
c = 36 / 140
d = b - c
e = 36 / 140
f = d / e
g = 100 * f
Problem: if 3 log ( 4 * 5 ^ 2 ) = x , find x
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "3 ( log 2 ^ 2 * 5 ^ 2 ) = x 3 log ( 5 * 2 ) ^ 2 = x 3 * 2 log ( 5 * 2 ) = x 6 log 10 = x log 10 base 10 = 1 so 6 * 1 = x x = 6 answer : b"
Answer: b
Python program:
a = 5 ** 2
b = 4 * a
c = b ** 3
Problem: two trains of equal lengths take 10 sec and 18 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 11 , b ) 9 , c ) 13 , d ) 14 , e ) 12.8
Rationale: "speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 18 = 6.7 m / sec . relative speed = 12 + 6.7 = 18.7 m / sec . required time = ( 120 + 120 ) / 18.7 = 12.8 sec . answer : option e"
Answer: e
Python program:
a = 120 * 2
b = speed + ( 
c = a / b
Problem: if one - third of one fourth of a number is 15 , then 3 - tenth of that number is :
Options: a ) 35 , b ) 25 , c ) 45 , d ) 54 , e ) 52
Rationale: let the number be x . then , 1 / 3 of 1 / 4 of x = 15 x = 15 * 12 = 180 so , required number = ( 3 / 10 * 180 ) = 54 . answer : d
Answer: d
Python program:
a = 15 * 3
b = a + 12 
c = b - 3
Problem: r is the set of positive even integers less than 201 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
Options: a ) none , b ) two , c ) four , d ) five , e ) seven
Rationale: "r is the set of positive even integers less than 201 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ? r = 2,4 , 6,8 , 10,12 . . . s = 4,16 , 36,64 . . . numbers : 4 , 16 , 36 , 64 , 100 , 144 , and 196 are even integers ( less than 201 ) that are in both sets . solution : seven answer : e"
Answer: e
Python program:
a = 4 - 1
Problem: the unit digit in the product ( 722 * 774 * 889 * 223 ) is :
Options: a ) 2 , b ) 7 , c ) 6 , d ) 8 , e ) 1
Rationale: "explanation : unit digit in the given product = unit digit in ( 2 * 4 * 9 * 3 ) = 6 answer : c"
Answer: c
Python program:
a = 722 * 774
b = a * 889
c = b * 223
d = 722 * 774
e = d * 889
f = e * 223
g = 4 + 4 
h = f - g
i = c - h
Problem: a and b invests rs . 3000 and rs . 7000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 9 : 6 , b ) 9 : 8 , c ) 9 : 14 , d ) 9 : 9 , e ) 9 : 5
Rationale: "( 3 * 6 + 6 * 6 ) : ( 7 * 12 ) 54 : 84 = > 9 : 14 . answer : c"
Answer: c
Python program:
a = 3000 * 6
b = 3000 * 2
c = b * 6
d = a + c 
e = 6 + 6 
f = 7000 * e
g = d / f
Problem: cubes with each side one inch long are glued together to form a larger cube . the larger cube ' s face is painted with red color and the entire assembly is taken apart . 23 small cubes are found with no paints on them . how many of unit cubes have at least one face that is painted red ?
Options: a ) 64
b ) 72
c ) 86
d ) 98
e ) 102
Rationale: use the options . the options which after getting added to 23 shows a cube of a number could be right . here 64 + 23 = 87 72 + 23 = 95 86 + 23 = 109 98 + 23 = 121 102 + 23 = 125 - - - ( 5 * 5 * 5 ) so we have 102 as the answer ! e
Answer: e
Python program:
a = 1 + 3 
b = 1 + a 
c = b ** 3
d = c - 23
Problem: what is the % change in the area of a rectangle when its length increases by 25 % and its width decreases by 25 % ?
Options: a ) 0 % , b ) 20 % increase , c ) 20 % decrease , d ) 6 % decrease , e ) insufficient data
Rationale: "( 125 / 10 ) * ( 75 / 10 ) = 9375 / 100 ~ 94 of original area 0.94 is a 6 % decrease from 100 / 100 - > d"
Answer: d
Python program:
a = 100 + 25 
b = 100 - 25
c = a * b
d = c / 100
e = 100 - d
Problem: bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 70 white marbles . how many red marbles could be in bag a ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 14
Rationale: "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 k w = 70 = 6 k + 4 k = > k = 7 total red ' s in bag a will be 2 k = 14 e"
Answer: e
Python program:
a = 3 * 2
b = a + 4 
c = 70 / b
Problem: sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum . sandy attempts 30 sums and obtains 60 marks . how many sums did sandy get correct ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
Rationale: "let x be the correct sums and ( 30 - x ) be the incorrect sums . 3 x - 2 ( 30 - x ) = 60 5 x = 120 x = 24 the answer is d ."
Answer: d
Python program:
a = 2 * 30
b = a + 60 
c = 2 + 3 
d = b / c
Problem: a car dealership has 40 cars on the lot , 20 % of which are silver . if the dealership receives a new shipment of 80 cars , 35 % of which are not silver , what percentage of total number of cars are silver ?
Options: a ) 30 % , b ) 35 % , c ) 40 % , d ) 45 % , e ) 50 %
Rationale: "the number of silver cars is 0.2 * 40 + 0.35 * 80 = 36 the percentage of cars which are silver is 36 / 120 = 30 % the answer is a ."
Answer: a
Python program:
a = 20 / 100
b = 40 * a
c = 35 / 100
d = 80 * c
e = b + d 
f = 40 + 80 
g = e / f
h = g * 100
Problem: at a certain company , each employee has a salary grade s that is at least 1 and at most 5 . each employee receives an hourly wage p , in dollars , determined by the formula p = 9.50 + 0.25 ( s – 1 ) . an employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 2 ?
Options: a ) $ 0.50 , b ) $ 0.75 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75
Rationale: "salary grade of 5 is p ( 5 ) = 9.50 + 0.25 ( 5 – 1 ) = 9.50 + 0.25 * 4 ; salary grade of 2 is p ( 2 ) = 9.50 + 0.25 ( 2 – 1 ) = 9.50 + 0.25 ; p ( 5 ) - p ( 2 ) = 9.50 + 0.25 * 4 - 9.50 - 0.25 = 0.75 . answer : b ."
Answer: b
Python program:
a = 5 - 1
b = 0 * 25
c = b + 0
Problem: what is the product of all the possible values of x if x ^ 2 - 2 x - 8 ?
Options: a ) – 29 , b ) – 12 , c ) - 8 , d ) 29 , e ) 168
Rationale: "explanation : = > y = x ^ 2 - 2 x - 8 = > y = ( x + 2 ) ( x - 4 ) = > x = - 2 , y = 4 product x = ( - 2 ) ( 4 ) = - 8 answer option - 8 answer : c"
Answer: c
Python program:
a = 8 / 1
Problem: in a class of 30 students , 5 students did not borrow any books from the library , 10 students each borrowed 1 book , 8 students each borrowed 2 books , and the rest of the students each borrowed at least 4 books . if the average ( arithmetic mean ) number of books borrowed per student was 2 , what is the maximum number of books that any single student could have borrowed ?
Options: a ) 5 , b ) 8 , c ) 16 , d ) 18 , e ) 20
Rationale: "the average number of books per student was 2 means that total of 2 * 30 = 60 books were borrowed ; 5 + 12 + 8 = 25 students borrowed total of 5 * 0 + 12 * 1 + 8 * 2 = 28 books ; so 60 - 28 = 32 books are left to distribute among 30 - 25 = 5 students , these 5 arethe rest who borrowed at least 4 books ; tomaximizethe number of books one student from above 5 could have borrowed we shouldminimizethe number of books other 4 students from 5 could have borrowed . minimum these 4 students could have borrowed is 4 books per student , so total number of books they could have borrowed is 4 * 4 = 16 books . so the 5 th student could have borrowed is 32 - 16 = 16 books . answer : c ."
Answer: c
Python program:
a = 30 * 2
b = 8 * 2
c = 10 + b 
d = 5 * 4
e = c + d 
f = a - e
g = f + 4
Problem: in a office work is distribute between p persons . if 1 / 4 members are absent then work increased for each person is ?
Options: a ) 33.33 % , b ) 24.33 % , c ) 15.33 % , d ) 16.33 % , e ) 17.33 %
Rationale: "let total % of work is 100 % total person = p 1 / 4 person are absent of total person . so absent person is 1 / 4 p ie p / 4 . left person is , p - p / 4 = 3 p / 4 . p person do the work 100 % 1 person do the work 100 * p % 3 p / 4 person do the work ( 100 * p * 4 ) / 3 p % = 133.33 % work increased for each person is = ( 133.33 - 100 ) % = 33.33 % answer : a"
Answer: a
Python program:
a = 100 * 4
b = 4 - 1
c = a / b
d = c - 100
Problem: john has $ 1,200 at the beginning of his trip , after spending money , he still has exactly $ 800 less than he spent on the trip . how much money does john still have ?
Options: a ) $ 200 , b ) $ 400 , c ) $ 600 , d ) $ 800 , e ) $ 1,200
Rationale: "suppose total money spent = x not spend ( money he still has ) = x - 800 x + x - 800 = 1200 x = 1000 money not spend = 1000 - 800 = 200 answer : a"
Answer: a
Python program:
a = 100 * 10
b = a + 800 
c = 100 * 10
d = c + 800 
e = 800 + d 
f = e / 2
g = b - f
Problem: if a , b and c together can finish a piece of work in 2 days . a alone in 12 days and b in 18 days , then c alone can do it in ?
Options: a ) 5 days , b ) 4 days , c ) 3 days , d ) 2 days , e ) 7 days
Rationale: "c = 1 / 2 - 1 / 12 – 1 / 18 = 1 / 3 = > 3 days answer : c"
Answer: c
Python program:
a = 1 / 12
b = const_0_25 - a
c = 1 / 18
d = b - c
e = 1 / d
Problem: a tank with a volume of 30 cubic feet has one inlet pipe and 2 outlet pipes . the inlet pipe fills water into the tank at the rate of 3 cubic inches / min and the 2 outlet pipes empty it out at the rates of 9 cubic inches / min and 6 cubic inches / min respectively . if all 3 pipes are opened when the tank is full , how many minutes does it take to empty the tank ? ( 1 foot = 12 inches )
Options: a ) 2110 , b ) 3210 , c ) 4320 , d ) 5430 , e ) 6540
Rationale: "the tank is emptied at this rate : 9 + 6 - 3 = 12 cubic inches / min the tank has a volume of 30 * 12 * 12 * 12 = 51840 cubic inches . the time it takes to empty the tank is 51840 / 12 = 4320 minutes . the answer is c ."
Answer: c
Python program:
a = 9 ** 3
b = 30 * a
c = 9 + 6 
d = c - 3
e = b / d
Problem: a cistern is normally filled in 12 hours but takes two hours longer to fill because of a leak in its bottom . if the cistern is full , the leak will empty it in ?
Options: a ) 33 , b ) 84 , c ) 40 , d ) 99 , e ) 11
Rationale: "1 / 12 - 1 / x = 1 / 14 x = 84 answer : b"
Answer: b
Python program:
a = 1 / 12
b = 12 + 2 
c = 1 / b
d = a - c
e = 1/(d)
Problem: when positive integer n is divided by positive integer j , the remainder is 28 . if n / j = 154.04 , what is value of j ?
Options: a ) 400 , b ) 350 , c ) 700 , d ) 750 , e ) 800
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 154.04 here 154 is the quotient . given that remainder = 28 so , 154.04 = 154 + 28 / j so , j = 700 answer : c"
Answer: c
Python program:
a = 4 * 10
b = a + 2 
c = 100 + b 
d = 154 - 4
e = 28 / d
Problem: 45 litres of diesel is required to travel 600 km using a 800 cc engine . if the volume of diesel required to cover a distance varies directly as the capacity of the engine , then how many litres of diesel is required to travel 800 km using 1200 cc engine ?
Options: a ) 80 litres , b ) 90 litres , c ) 120 litres , d ) 170 litres , e ) none of these
Rationale: "explanatory answer to cover a distance of 800 kms using a 800 cc engine , the amount of diesel required = 800 / 600 * 45 = 60 litres . however , the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity . i . e . , for instance , if the capacity of engine doubles , the diesel requirement will double too . therefore , with a 1200 cc engine , quantity of diesel required = 1200 / 800 * 60 = 90 litres . answer b"
Answer: b
Python program:
a = 800 * 600
b = 45 / a
c = 800 * b
d = 1200 * c
Problem: christine and siri have 21 rs between them . christine has 20 rs more than siri . how much does christine have .
Options: a ) 16.5 , b ) 17.5 , c ) 18.5 , d ) 19.5 , e ) 20.5
Rationale: let siri has x rs , then christine has 20 + x rs given x + ( 20 + x ) = 21 = > 2 x = 1 or x = 0.5 so christine and siri has 20.5 and 0.5 rs respectively . answer : e
Answer: e
Python program:
a = 21 - 20
b = a / 2
c = b + 20
Problem: in 10 years , a will be twice as old as b was 10 years ago . if a is now 4 years older than b the present age of b is
Options: a ) 37 , b ) 38 , c ) 39 , d ) 34 , e ) 41
Rationale: let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 4 = > 2 b - b - 4 = 30 b = 34 so the present age of b is 34 years answer : d
Answer: d
Python program:
a = 2 * 10
b = a + 10 
c = b + 4
Problem: the cost of 10 kg of mangos is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is $ 23 . find the total cost of 4 kg of mangos , 3 kg of rice and 5 kg of flour ?
Options: a ) 347.4 , b ) 984.4 , c ) 877.4 , d ) 637.4 , e ) 667.4
Rationale: let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 23 = 2 r a = 12 / 5 r and r = 69 a = 165.6 required total cost = 4 * 165.6 + 3 * 69 + 5 * 23 = 662.4 + 207 + 115 = $ 984.40 b
Answer: b
Python program:
a = 24 / 10
b = 23 * 6
c = b / 2
d = a * c
e = 4 * d
f = 23 * 6
g = f / 2
h = 3 * g
i = e + h 
j = 5 * 23
k = i + j
Problem: if x is equal to the sum of the integers from 50 to 60 , inclusive , and y is the number of even integers from 50 to 60 , inclusive , what is the value of x + y ?
Options: a ) 171 , b ) 281 , c ) 391 , d ) 491 , e ) 611
Rationale: "sum s = n / 2 { 2 a + ( n - 1 ) d } = 11 / 2 { 2 * 50 + ( 11 - 1 ) * 1 } = 11 * 55 = 605 = x number of even number = ( 60 - 50 ) / 2 + 1 = 6 = y x + y = 605 + 6 = 611 e"
Answer: e
Python program:
a = 50 + 60 
b = a / 2
c = 60 - 50
d = c + 1 
e = b * d
f = 60 - 50
g = f / 2
h = g + 1 
i = e + h
Problem: a number x is 7 times another number y . the percentage that y is less than x is
Options: a ) 12.5 % , b ) 85.7 % , c ) 80 % , d ) 11 % , e ) 1 %
Rationale: "say y = 1 and x = 7 . then y = 1 is less than x = 7 by ( 7 - 1 ) / 7 * 100 = 6 / 7 * 100 = 85.7 % . answer : b ."
Answer: b
Python program:
a = 7 - 1
b = a / 7
c = b * 100
Problem: an alloy weighing 48 ounces is 25 % gold . how many ounces of pure gold must be added to create an alloy that is 40 % gold ?
Options: a ) 15 , b ) 20 , c ) 12 , d ) 14 , e ) 7
Rationale: an alloy of 48 oz which is 25 % gold means there is 12 oz of gold . to get to an alloy that is 40 % gold , let ' s use this expression : ( 12 + x ) / ( 48 + x ) = 0.40 with x representing the amount of pure gold that must be added to get to 40 % . the expression we are using represents the new total weight of pure gold over the new total weight of the alloy and this fraction should represent 40 % or 0.4 . you will see that 12 is the correct answer , as 24 / 60 = 0.4 choose c
Answer: c
Python program:
a = 40 - 25
b = 48 * a
c = b / 12
d = c - 48
Problem: a certain sum is invested at simple interest at 15 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 420 . find the sum ?
Options: a ) s . 5000 , b ) s . 7000 , c ) s . 14000 , d ) s . 17000 , e ) s . 27000
Rationale: "let the sum be rs . x . ( x * 15 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 420 = > 30 x / 100 - 24 x / 100 = 420 = > 6 x / 100 = 420 = > x = 7000 . answer : b"
Answer: b
Python program:
a = 15 - 12
b = a * 2
c = b / 100
d = 420 / c
Problem: if the average ( arithmetic mean ) of 7 consecutive integers is 20 , then the product of the greatest and least integer is
Options: a ) 343 , b ) 393 , c ) 363 , d ) 391 , e ) 409
Rationale: n = smallest number n + 6 = largest number ( n + n + 6 ) / 2 = 20 = > ( 2 n + 6 ) / 2 = 20 = > n + 3 = 20 = > n = 17 so product of n and n + 6 = ( 17 ) ( 23 ) = 391 answer - d
Answer: d
Python program:
a = 7 * 20
b = 3 * 7
c = a - b
d = c / 7
e = 7 - 1
f = 7 * 20
g = 3 * 7
h = f - g
i = h / 7
j = e + i 
k = d * j
Problem: a train , 120 meters long travels at a speed of 45 km / hr crosses a bridge in 30 seconds . the length of the bridge is
Options: a ) 270 m , b ) 255 m , c ) 235 m , d ) 220 m , e ) 240 m
Rationale: "explanation : assume the length of the bridge = x meter total distance covered = 120 + x meter total time taken = 30 s speed = total distance covered / total time taken = ( 120 + x ) / 30 m / s = > 45 ã — ( 10 / 36 ) = ( 120 + x ) / 30 = > 45 ã — 10 ã — 30 / 36 = 120 + x = > 45 ã — 10 ã — 10 / 12 = 120 + x = > 15 ã — 10 ã — 10 / 4 = 120 + x = > 15 ã — 25 = 120 + x = 375 = > x = 375 - 120 = 255 answer : option b"
Answer: b
Python program:
a = 45 * const_0_2778
b = a * 30
c = b - 120
Problem: find the compound ratio of ( 2 : 3 ) , ( 6 : 11 ) and ( 11 : 6 ) is
Options: a ) 3 : 2 , b ) 2 : 1 , c ) 1 : 2 , d ) 4 : 5 , e ) 2 : 3
Rationale: "required ratio = 2 / 3 * 6 / 11 * 11 / 6 = 2 / 1 = 2 : 3 answer is e"
Answer: e
Python program:
a = 2 / 3
b = 2 / 3
c = 6 / 3
d = b * c
e = a * d
Problem: the number 90 can be written as the sum of the squares of 4 different positive integers . what is the sum of these 4 integers ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 13
Rationale: "4 ^ 2 + 3 ^ 2 + 8 ^ 2 + 1 ^ 2 = 90 - - > 1 + 3 + 8 + 4 = 16 . b"
Answer: b
Python program:
a = 4 + 3 
b = 3 + 2 
c = a + b 
d = c + 4
Problem: a train with 120 wagons crosses john who is going in the same direction , in 36 seconds . it travels for half an hour from the time it starts overtaking the john ( he is riding on the horse ) before it starts overtaking the mike ( who is also riding on his horse ) coming from the opposite direction in 24 seconds . in how much time ( in secs ) after the train has crossed the mike do the john meets to mike ?
Options: a ) 3576 s , b ) 3589 s , c ) 3596 s , d ) 3598 s , e ) 3576 s
Rationale: "let the length of the train be l metres and speeds of the train arun and sriram be r , a and s respectively , then - - - - - - - - - - ( i ) and - - - - - - - - - ( ii ) from eq . ( i ) and ( ii ) 3 ( r - a ) = 2 ( r + k ) r = 3 a + 2 k in 30 minutes ( i . e 1800 seconds ) , the train covers 1800 r ( distance ) but the arun also covers 1800 a ( distance ) in the same time . therefore distance between arun and sriram , when the train has just crossed sriram = 1800 ( r - a ) - 24 ( a + k ) time required = = ( 3600 - 24 ) = 3576 s e"
Answer: e
Python program:
a = 36 + 24 
b = 36 - 24
c = a / b
d = c - 1
e = 10 * 3
f = e * const_60
g = d * f
h = g / 2
i = h - 24