euclaise/mathqa_programs huggingface dataset:
Problem: mary and harry enter into a partnership by investing $ 700 and $ 300 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if mary received $ 800 more than harry did , what was the profit made by their business in that year ?
Options: a ) 45645433 , b ) 46457457 , c ) 4675 , d ) 3000 , e ) 3432
Rationale: say the profit was $ x . mary ' s share = x / 6 ( half of the third ) + ( x - x / 3 ) * 0.7 harry share = x / 6 ( half of the third ) + ( x - x / 3 ) * 0.3 thus ( x - x / 3 ) * 0.7 - ( x - x / 3 ) * 0.3 = 800 - - > x = 3000 . answer is d
Answer: d
Python program:
a = 800 * 3
b = a / 2
c = 700 - 300
d = 700 + 300 
e = c / d
f = b / e
Problem: a thief goes away with a santro car at a speed of 45 kmph . the theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start ?
Options: a ) a ) 2 , b ) b ) 4 , c ) c ) 7 , d ) d ) 5 , e ) e ) 8
Rationale: explanation : | - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - | 50 45 d = 20 rs = 50 – 45 = 5 t = 20 / 5 = 4 hours answer : option b
Answer: b
Python program:
a = 1 / 2
b = a * 45
c = 50 - 45
d = b / c
e = 1 / 2
f = d - e
Problem: what is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad ?
Options: a ) 814 , b ) 800 , c ) 100 , d ) 200 , e ) 456
Rationale: "length of largest tile = h . c . f . of 1517 cm and 902 cm = 41 cm . area of each tile = ( 41 x 41 ) cm 2 . required number of tiles = ( 1517 x 902 ) / 41 x 41 = 814 . answer : a"
Answer: a
Python program:
a = 15 * 100
b = 17 * 100
c = rectangle_area / (
Problem: the average of runs of a cricket player of 10 innings was 40 . 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 ) 10 , d ) 84 , e ) 17
Rationale: "average after 11 innings = 44 required number of runs = ( 44 * 11 ) - ( 40 * 10 ) = 484 - 400 = 84 . answer : d"
Answer: d
Python program:
a = 10 + 1 
b = 4 + 40 
c = a * b
d = 10 * 40
e = c - d
Problem: find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 18 as remainder
Options: a ) 1235 , b ) 1346 , c ) 1378 , d ) 1634.4 , e ) 1489
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 18 5 x = 1347 x = 269.4 number = 269.4 + 1365 = 1634.4 d"
Answer: d
Python program:
a = 1365 - 18
b = 6 - 1
c = a / b
d = c * 6
Problem: the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 588 sq m , then what is the breadth of the rectangular plot ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 14
Rationale: "let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 588 3 b 2 = 588 b 2 = 196 b = 14 m . answer : option e"
Answer: e
Python program:
a = 588 / 3
b = math.sqrt(a)
Problem: a distributor sells a product through an online store , which take a commission of 20 % of the price set by the distributor . the distributor obtains the product from a producer at the price of $ 20 per item . what is the price that the buyer observers online if the distributor wants to maintain a 20 % profit on the cost of the item ?
Options: a ) $ 30 , b ) $ 31 , c ) $ 32 , d ) $ 33 , e ) $ 34
Rationale: "let x be the price that buyers see online . the distributor wants to receive 1.2 ( original price ) which should be 80 % of x . 1.2 ( 20 ) = 0.8 x x = 1.2 ( 20 ) / 0.8 = 1.5 ( 20 ) = $ 30 the answer is a ."
Answer: a
Python program:
a = 20 / 100
b = a * 20
c = b + 20 
d = 100 - 20
e = d / 100
f = c / e
Problem: 21 friends went to a hotel and decided to pay the bill amount equally . but 20 of them could pay rs . 30 each as a result 21 st has to pay rs . 200 extra than his share . find the amount paid by him .
Options: a ) 120 , b ) 250 , c ) 110 , d ) 220 , e ) none
Rationale: "explanation : average amount paid by 20 persons = rs . 30 increase in average due to rs . 200 paid extra by the 21 st men = rs . 200 / 20 = rs . 10 therefore , average expenditure of 21 friends = rs . 30 + rs . 10 = rs . 40 therefore , amount paid by the 21 st men = rs . 40 + rs . 200 = rs . 240 correct option : e"
Answer: e
Python program:
a = 30 * 20
b = a + 200 
c = b / 20
d = 200 + c
Problem: a train 125 m long passes a man , running at 3 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 48 , b ) 50 , c ) 28 , d ) 26 , e ) 29
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 3 ) km / hr . x - 3 = 45 = = > x = 48 km / hr answer : a"
Answer: a
Python program:
a = 3 * const_0_2778
b = a * 3
c = 125 - b
d = c / 3
e = d / const_0_2778
Problem: if 10 lions can kill 10 deers in 10 minutes how long will it take 100 lions to kill 100 deers ?
Options: a ) 1 minutes , b ) 10 minute , c ) 100 minutes , d ) 10000 minutes , e ) 1000 minutes
Rationale: "we can try the logic of time and work , our work is to kill the deers so 10 ( lions ) * 10 ( min ) / 10 ( deers ) = 100 ( lions ) * x ( min ) / 100 ( deers ) hence answer is x = 10 answer : b"
Answer: b
Python program:
a = 10 / 10
b = a * 10
Problem: a certain school implemented a reading program for its students , with the goal of getting each student to read 3 books per month year - round . if the school has c classes made up of s students in each class , how many books will the entire student body read in one year ?
Options: a ) 20 cs , b ) cs / 2 , c ) 36 cs , d ) ( 2 cs ) / 12 , e ) ( 24 c ) / s
Rationale: "ans : c solution : simple multiplication s students , c classes , 3 books / month = 36 books a year total number of books = 36 cs"
Answer: c
Python program:
a = 3 * 12
Problem: a can give b 100 meters start and c 300 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 110.22 meters , b ) 111.22 meters , c ) 222.22 meters , d ) 333.22 meters , e ) none of these
Rationale: "explanation : a runs 1000 meters while b runs 900 meters and c runs 700 meters . therefore , b runs 900 meters while c runs 700 meters . so , the number of meters that c runs when b runs 1000 meters = ( 1000 x 700 ) / 900 = 777.77 meters thus , b can give c ( 1000 - 777.77 ) = 222.22 meters start answer : c"
Answer: c
Python program:
a = 100 * 10
b = 100 * 10
c = 100 * 10
d = c - 300
e = b * d
f = 100 * 10
g = f - 100
h = e / g
i = a - h
Problem: if x gets 25 % more than y and y gets 20 % more than z , the share of z out of rs . 740 will be :
Options: a ) rs . 300 , b ) rs . 200 , c ) rs . 240 , d ) rs . 350 , e ) none of these
Rationale: "z share = z , y = 1.2 z x = 1.25 × 1.2 z , x + y + z = 740 ( 1.25 × 1.2 + 1.2 + 1 ) z = 74 3.7 z = 740 , z = 200 answer : . b ."
Answer: b
Python program:
a = 25 / 100
b = 1 + a 
c = 20 / 100
d = 1 + c 
e = b * d
f = 20 / 100
g = 1 + f 
h = e + g 
i = h + 1 
j = 740 / i
Problem: a man buys an item at rs . 750 and sells it at the loss of 20 percent . then what is the selling price of that item
Options: a ) rs . 660 , b ) rs . 760 , c ) rs . 600 , d ) rs . 960 , e ) none of these
Rationale: "explanation : here always remember , when ever x % loss , it means s . p . = ( 100 - x ) % of c . p when ever x % profit , it means s . p . = ( 100 + x ) % of c . p so here will be ( 100 - x ) % of c . p . = 80 % of 750 = 80 / 100 * 750 = 600 option c"
Answer: c
Python program:
a = 20 / 100
b = 1 - a
c = 750 * b
Problem: harry started a 4 - mile hike with a full 10 - cup canteen of water and finished the hike in 2 hours with 2 cup of water remaining in the canteen . if the canteen leaked at the rate of 1 cup per hour and harry drank 3 cups of water during the last mile , how many cups did he drink per mile during the first 3 miles of the hike ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 3 / 3 , d ) 3 / 1 , e ) 3 / 2
Rationale: "no of cups leaked during the trip = 2 cups . no of cups harry drank = 6 cups . no of cups harry drank during the first 3 miles = 3 . drink / mile = 3 / 3 answer : c"
Answer: c
Python program:
a = 10 - 2
b = a - 3
c = b - 2
d = c / 3
Problem: salesperson a ' s compensation for any week is $ 260 plus 6 percent of the portion of a ' s total sales above $ 1,000 for that week . salesperson b ' s compensation for any week is 8 percent of b ' s total sales for that week . for what amount of total weekly sales would both salespeople earn the same compensation ?
Options: a ) $ 6000 , b ) $ 8000 , c ) $ 10,000 , d ) $ 12,000 , e ) $ 14,000
Rationale: "260 + 0.06 ( x - 1000 ) = 0.08 x 0.02 x = 200 x = $ 10,000 the answer is c ."
Answer: c
Python program:
a = 6 / 100
b = a * 1
c = 260 - b
d = 8 / 100
e = 6 / 100
f = d - e
g = c / f
h = 6 / 100
i = h * 1
j = 260 - i
k = 8 / 100
l = 6 / 100
m = k - l
n = j / m
o = g + n 
p = o / 1
Problem: a , b and c start a business each investing 2,000 . after 6 months a withdrew 1000 , b withdrew 1000 and c invests 1000 more . at the end of the year , a total profit of 6600 was recorded . find the share of b .
Options: a ) 20,000 , b ) 21,200 , c ) 1,800 , d ) 20,500 , e ) none of these
Rationale: "ratio of the capitals of a , b and c = 2000 ã — 6 + 1000 ã — 6 : 2000 ã — 6 + 1000 ã — 6 : 2000 ã — 6 + 3000 ã — 6 = 18000 : 18000 : 30000 = 18 : 18 : 30 b â € ™ s share = ( 6600 ã — 18 â  „ 66 ) = 1800 answer c"
Answer: c
Python program:
a = 12 - 6
b = a * 1000
c = 100 * 100
d = 2 * c
e = d * 6
f = b + e 
g = 100 * 10
h = f / g
Problem: in the third grade of windblown school there are 96 students , one third of them failed the math test and 1 / 6 failed that literature test . at least how many students failed both tests ?
Options: a ) 0 . , b ) 6 . , c ) 8 . , d ) 10 . , e ) 12 .
Rationale: "total = 96 failed in math = 96 / 3 = 32 failed in literature = 108 / 6 = 16 the least failed in both can be 0 while max can be 16 answer a"
Answer: a
Python program:
a = 96 / 3
b = 96 / 6
c = min(a)
Problem: rajat , vikas and abhishek are submitting questions in the ratio 7 : 3 : 2 . if total number of questions submitted by them is 24 . find the number of questions submitted by vikas .
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: explanation : number of questions submitted by vikas = ( 24 * 3 ) / ( 7 + 3 + 2 ) = 6 answer : d
Answer: d
Python program:
a = 24 / 4
Problem: a number divided by 64 leaves remainder 37 what is the remainder when same number divided by 5
Options: a ) 7 , b ) 8 , c ) 6 , d ) 3 , e ) 1
Rationale: add 64 + 37 = 101 now 101 divided by 5 so we get 1 as reaminder answer : e
Answer: e
Python program:
a = 37 - 5
b = 37 - 5
c = a / b
Problem: a man sold 20 articles for $ 60 and gained 20 % . how many articles should he sell for $ 80 to incur a loss 20 % ?
Options: a ) 45 , b ) 36 , c ) 40 , d ) 50 , e ) 48
Rationale: "production cost per article : $ 60 * ( 100 % - 20 % ) / 20 = $ 2.40 required production costs for a loss of 20 % : $ 80 * ( 100 % + 20 % ) = $ 96 number of articles to be sold for $ 96 to incur a 20 % loss : $ 96 / $ 2.40 = 40 thus , solution c is correct ."
Answer: c
Python program:
a = original_price_before_loss / (
Problem: divide rs . 1100 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ?
Options: a ) s . 800 , b ) s . 400 , c ) s . 600 , d ) s . 900 , e ) s . 1100
Rationale: "a + b + c = 1100 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 1100 = > 275 answer : e"
Answer: e
Python program:
a = 1100 / 3
Problem: a meeting has to be conducted with 5 managers . find the number of ways in which the managers be selected from among 9 managers , if 2 managers will not attend the meeting together ?
Options: a ) 35 , b ) 91 , c ) 120 , d ) 126 , e ) 150
Rationale: "we can either choose all 5 people from 7 manager who have no problems or choose 4 from the 7 and 1 from the 2 managers who have a problem sitting together so 7 c 5 + ( 7 c 4 * 2 c 1 ) this is 21 + 70 91 ans : b"
Answer: b
Python program:
a = math.comb(9, 5)
b = 9 - 2
c = math.comb(b, 2)
d = a - c
Problem: a certain car increased its average speed by 5 miles per hour in each successive 5 - minute interval after the first interval . if in the first 5 - minute interval its average speed was 2 miles per hour , how many miles did the car travel in the third 5 - minute interval ?
Options: a ) 1.0 , b ) 1.5 , c ) 2.0 , d ) 2.5 , e ) 3.0
Rationale: "in the third time interval the average speed of the car was 2 + 5 + 5 = 12 miles per hour ; in 5 minutes ( 1 / 12 hour ) at that speed car would travel 12 * 1 / 12 = 1 miles . answer : a ."
Answer: a
Python program:
a = 2 + 5 
b = a + 5 
c = 5 / const_60
d = b * c
Problem: two trains of equal length , running with the speeds of 60 and 40 kmph , take 60 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 10 sec , b ) 16 sec , c ) 12 sec , d ) 67 sec , e ) 13 sec
Rationale: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 50 d = 60 * 100 / 18 = 1000 / 3 rs = 60 + 40 = 100 * 5 / 18 t = 1000 / 3 * 18 / 500 = 12 sec answer : c"
Answer: c
Python program:
a = 60 - 40
b = const_0_2778 * a
c = b * 60
d = 60 + 40 
e = const_0_2778 * d
f = 1/(e)
g = c * f
Problem: what will be the vulgar fraction of 0.60
Options: a ) 3 / 7 , b ) 3 / 5 , c ) 3 / 2 , d ) 3 / 7 , e ) 3 / 8
Rationale: "explanation : 0.6 = 60 / 100 = 3 / 5 option b"
Answer: b
Python program:
a = 0 / 60
b = circle_area / (
Problem: how many 3 digit positive integers w exist that when divided by 7 leave a remainder of 5 ?
Options: a ) 128 , b ) 142 , c ) 143 , d ) 141 , e ) 129
Rationale: "minimum three digit number is 100 and maximum three digit number is 999 . the first three digit number that leaves remainder 5 when divided by 7 is 103 . 14 * 7 = 98 + 5 = 103 the second three digit number that leaves remainder 5 when divided by 7 is 110 . 15 * 7 = 105 + 5 = 110 the third three digit number that leaves remainder 5 when divided by 7 is 117 and so on the last three digit number that leaves remainder 5 when divided by 7 is 999 142 * 7 = 994 + 5 = 999 therefore , we identify the sequence 103 , 110,117 . . . . . 999 use the formula of last term last term = first term + ( n - 1 ) * common difference you will get the answer 129 that is definitely e ."
Answer: e
Python program:
a = 100 * 10
b = a - 1
c = 10 + 4 
d = c * 7
e = d + 5 
f = b - e
g = f / 7
Problem: find the missing figures : 0.2 % of ? = 0.02
Options: a ) 50 , b ) 100 , c ) 10 , d ) 1000 , e ) 110
Rationale: "let 0.2 % of x = 0.02 . then , 0.2 * x / 100 = 0.02 x = [ ( 0.02 * 100 ) / 0.2 ] = 100 . answer is b ."
Answer: b
Python program:
a = 0 / 2
b = 0 / 2
Problem: find the value of 18396 x 9999 = m ?
Options: a ) 194852714 , b ) 183941604 , c ) 183851704 , d ) 183951714 , e ) 183768244
Rationale: "18396 x 9999 = 18396 x ( 10000 - 1 ) = 18396 x 10000 - 18396 x 1 = 183960000 - 18396 = 183941604 b"
Answer: b
Python program:
a = 9999 - 4
b = a * 18396
Problem: the sum of the squares of three numbers is 100 , while the sum of their products taken two at a time is 48 . their sum is :
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) none of these
Rationale: "x ^ + y ^ 2 + z ^ 2 = 100 xy + yz + zx = 48 as we know . . ( x + y + z ) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 ( xy + yz + zx ) so ( x + y + z ) ^ 2 = 100 + ( 2 * 48 ) ( x + y + z ) ^ 2 = 196 so x + y + z = 14 answer : e"
Answer: e
Python program:
a = 100 - 48
b = a / 2
c = math.sqrt(b)
d = c * 100
e = 100 - 48
f = e / 2
g = 100 - f
h = math.sqrt(g)
i = d + h
Problem: if , 1 * 3 * 5 = 16 3 * 5 * 7 = 38 then find , 13 * 15 * 17 = ?
Options: a ) 89 , b ) 49 , c ) 68 , d ) 268 , e ) 55
Rationale: d 268 ( 17 * 15 ) + 13 = 268
Answer: d
Python program:
a = 15 * 17
b = 13 + a
Problem: if 20 men can build a wall 66 metres long in 6 days , what length of a similar can be built by 86 men in 8 days ?
Options: a ) 53 m , b ) 46 m , c ) 94 m , d ) 49 m , e ) 64 m
Rationale: "let the required length be x metres more men , more length built ( direct proportion ) less days , less length built ( direct proportion ) men 20 : 35 days 6 : 3 : : 56 : x therefore ( 20 x 6 x x ) = ( 35 x 3 x 56 )  x = ( 35 x 3 x 56 ) / 120 = 49 hence , the required length is 49 m . answer is d"
Answer: d
Python program:
a = 86 * 8
b = 20 * 6
c = a / b
d = 66 * c
Problem: the calendar of the year 2024 can be used again in the year ?
Options: a ) 2288 , b ) 2052 , c ) 2778 , d ) 2719 , e ) 1711
Rationale: "explanation : given year 2024 when divided by 4 , leaves a remainder 0 . note : when remainder is 0 , 28 is added to the given year to get the result . so , 2024 + 28 = 2052 answer : b ) 2052"
Answer: b
Python program:
a = 4 * 4
b = a - 2
c = b * 2
d = c + 2024
Problem: the pinedale bus line travels at an average speed of 60 km / h , and has stops every 5 minutes along its route . yahya wants to go from his house to the pinedale mall , which is 6 stops away . how far away , in kilometers , is pinedale mall away from yahya ' s house ?
Options: a ) 20 km , b ) 30 km , c ) 40 km , d ) 50 km , e ) 60 km
Rationale: number of stops in an hour : 60 / 5 = 12 distance between stops : 60 / 12 = 5 km distance between yahya ' s house and pinedale mall : 5 x 6 = 30 km imo , correct answer is ` ` b . ' '
Answer: b
Python program:
a = 5 * 6
b = a / const_60
c = 60 * b
Problem: a sixth grade teacher asked her students to draw rectangles with positive integer length and a perimeter of 42 . the difference between the largest and smallest possible ares of the rectangles that the students could have come up with is ?
Options: a ) 50 sq units
b ) 60 sq units
c ) 70 sq units
d ) 80 sq units
e ) 90 sq units
Rationale: sum of length and breadth will be 21 units . 42 / 2 = 21 area will be max when lxb = 11 x 10 = 110 sq units area will be min when lxb = 20 x 1 = 20 sq units . . the difference between the largest and smallest possible ares of the rectangles that the students could have come up with = 110 - 20 = 90 sq units answer : e
Answer: e
Python program:
a = 42 / 2
b = a - 10
c = b * 10
d = 42 / 2
e = d - 1
f = e * 1
g = c - f
Problem: 3 partners a , b , c starts a business . twice a ' s capital is equal to thrice b ' s capital and b ' s capital is 4 times c ' s capital . out of a total profit of rs . 16500 at the end of the year , b ' s share is
Options: a ) rs . 4000 , b ) rs . 6000 , c ) rs . 7500 , d ) rs . 6600 , e ) none
Rationale: solution let c = x . then , b = 4 x and 2 a = 3 x 4 x = 12 x or a = 6 x . ∴ a : b : c = 6 x : 4 x : x = 6 : 4 : 1 . so b ' s capital = rs ( 16500 x 4 / 11 ) = rs . 6000 . answer b
Answer: b
Python program:
a = 3 + 4 
b = a + 4 
c = 4 / b
d = c * 16500
Problem: a retailer sells 6 shirts . the first 2 he sells for $ 40 and $ 50 . if the retailer wishes to sell the 6 shirts for an overall average price of over $ 50 , what must be the minimum average price of the remaining 4 shirts ?
Options: a ) $ 37.00 , b ) $ 40.00 , c ) $ 45.50 , d ) $ 48.00 , e ) $ 52.50
Rationale: "first 2 shirts are sold for $ 40 and $ 50 = $ 90 . to get average price of $ 50 , total sale should be 6 * $ 50 = $ 300 so remaining 4 shirts to be sold for $ 300 - $ 90 = $ 210 answer should be 210 / 4 = $ 52.50 that is e"
Answer: e
Python program:
a = 6 * 50
b = 40 + 50 
c = a - b
d = 6 - 2
e = c / d
Problem: the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8800 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) s . 3300 , b ) s . 4570 , c ) s . 4500 , d ) s . 4550 , e ) s . 2500
Rationale: "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8800 = 35200 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 3200 salary of may is rs . 6500 salary of january = rs . 3300 answer : a"
Answer: a
Python program:
a = 8000 * 4
b = 8800 * 4
c = b - 6500
d = a - c
Problem: with both inlets open , a water tank will be filled with water in 20 minutes . the first inlet alone would fill the tank in 2 hours . if in every minutes the second inlet admits 50 cubic meters of water than the first , what is the capacity of the tank ?
Options: a ) 9,000 , b ) 1,500 , c ) 1,750 , d ) 1,200 , e ) 1,300
Rationale: "the work done by inlet a and b together in 1 min = 1 / 20 the work done by inlet a ( first inlet ) in 1 min = 1 / 120 the work done by inlet b ( second inlet ) in 1 min = ( 1 / 20 ) - ( 1 / 120 ) = 1 / 24 difference of work done by b and a = b - a = 50 cubic meter i . e . ( 1 / 24 ) - ( 1 / 120 ) = 50 cubic meter i . e . 1500 cubic meter answer : option b"
Answer: b
Python program:
a = const_60 / 20
b = 1/(2)
c = a - b
d = c / const_60
e = const_60 * 2
f = 1/(e)
g = d - f
h = 50 / g
i = h / 1000
Problem: the ratio between the radii of two spheres is 1 : 3 . find the ratio between their volumes ?
Options: a ) 1 : 28
b ) 1 : 27
c ) 1 : 29
d ) 1 : 39
e ) 1 : 22
Rationale: explanation : r 1 : r 2 = 1 : 3 r 13 : r 23 = 1 : 27 answer : option b
Answer: b
Python program:
a = 3 ** 3
b = 1 / a
Problem: every year taylor goes to the same carnival , and he attempts to shoot a basketball into a small hoop , hoping that he will win a 10 - foot tall teddy bear . if the probability that taylor does not make a basket is 1 / 3 , what is the probability that taylor makes exactly one basket in 3 tries ?
Options: a ) 1 / 9 , b ) 2 / 9 , c ) 2 / 5 , d ) 3 / 5 , e ) 3 / 7
Rationale: probability of basket = 2 / 3 probability of no basket = 1 / 3 required probability = 3 * 2 / 3 * 1 / 3 * 1 / 3 = 2 / 9 b is the answer .
Answer: b
Python program:
a = 1 / 3
b = 1 / 3
c = 1 - b
d = a * c
Problem: the average of 13 result is 20 . average of the first 8 of them is 20 and that of the last 8 is 40 . find the 8 th result ?
Options: a ) 35 , b ) 37 , c ) 46 , d ) 90 , e ) 100
Rationale: "sum of all the 13 results = 13 * 20 = 260 sum of the first 7 of them = 8 * 20 = 160 sum of the last 7 of them = 8 * 40 = 320 so , the 8 th number = 260 + 160 - 320 = 100 . e"
Answer: e
Python program:
a = 8 * 20
b = 8 * 40
c = a + b 
d = 13 * 20
e = c - d
Problem: 16 boys or 24 girls can construct the wall in 6 days . the number of days that 4 boys and 12 girls will take to construct ?
Options: a ) 7 days , b ) 14 days , c ) 6 days , d ) 8 days , e ) 9 days
Rationale: explanation : 16 boys = 24 girls , 1 boy = 24 / 16 girls 1 boy = 6 / 4 girls 4 boys + 12 girls = 4 ã — 6 / 4 + 12 = 6 + 12 = 18 girls 8 days to complete the work answer : option d
Answer: d
Python program:
a = 1 / 6
b = a / 24
c = 12 * b
d = 1 / 6
e = d / 16
f = 4 * e
g = c + f 
h = 1 / g
Problem: the price of rice falls by 20 % . how much rice can be bought now with the money that was sufficient to buy 40 kg of rice previously ?
Options: a ) 5 kg , b ) 15 kg , c ) 25 kg , d ) 50 kg , e ) none
Rationale: "solution : let rs . 100 be spend on rice initially for 40 kg . as the price falls by 20 % , new price for 40 kg rice , = ( 100 - 20 % of 100 ) = 80 new price of rice = 80 / 40 = rs . 2 per kg . rice can bought now at = 100 / 2 = 50 kg . answer : option d"
Answer: d
Python program:
a = 100 - 20
b = a / 40
c = 100 / b