euclaise/mathqa_programs huggingface dataset:
Problem: how many factors of 440 are odd numbers greater than 1 ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: when factorized , 440 has 4 prime factors . of these prime factors 2 are odd and 2 are even . hence total number of odd factors is 2 * 2 ( 4 ) , which includes 2 . the total number of odd factors greater than 1 are 2 . ( option a )
Answer: a
Python program:
a = 10 * 2
b = const_60 / 0
Problem: annika hikes at a constant rate of 10 minutes per kilometer . she has hiked 2.5 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 35 minutes . if annika continues east , then turns around and retraces her path to reach the start of the trail in exactly 35 minutes , for how many kilometers total did she hike east ?
Options: a ) 3.625 , b ) 3.5 , c ) 3 , d ) 4 , e ) 4.5
Rationale: set up two r x t = d cases . 1 . 1 / 10 km / min x t = 2.5 from which t = 25 mins . we know total journey time now is 35 + 25 = 60 the rate is the same ie 1 / 10 km / min . set up second r x t = d case . 1 / 10 km / min x 60 = 6 km now the total journey would be halved as distance would be same in each direction . 6 / 2 = 3 c
Answer: c
Python program:
a = 35 / 10
b = a - 2
c = b / 2
d = c + 2
Problem: the average temperature of the town in the first 4 days of a month was 58 degrees . the average for the second , third , fourth and fifth days was 59 degrees . if the temperatures of the first and fifth days were in the ratio 7 : 8 , then what is the temperature on the fifth day ?
Options: a ) 62 degrees , b ) 32 degrees , c ) 65 degrees , d ) 66 degrees , e ) 67 degrees
Rationale: explanation : sum of temperatures on 1 st , 2 nd , 3 rd and 4 th days = ( 58 * 4 ) = 232 degrees . . . ( 1 ) sum of temperatures on 2 nd , 3 rd , 4 th and 5 th days - ( 59 * 4 ) = 236 degrees . . . . ( 2 ) subtracting ( 1 ) from ( 2 ) , we get : temp , on 5 th day - temp on 1 st day = 4 degrees . let the temperatures on 1 st and 5 th days be 7 x and 8 x degrees respectively . then , 8 x - 7 x = 4 or x = 4 . answer : b temperature on the 5 th day = 8 x = 32 degrees .
Answer: b
Python program:
a = 4 * 59
b = 4 * 58
c = a - b
d = 8 * c
Problem: 49 ã — 49 ã — 49 ã — 49 x 49 = 7 ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 10 , e ) none of these
Rationale: "49 ã — 49 ã — 49 ã — 49 x 49 = 7 ? or , 7 ( 2 ) ã — 7 ( 2 ) ã — 7 ( 2 ) ã — 7 ( 2 ) x 7 ( 2 ) = 7 ? or 7 ( 10 ) = 7 ? or , ? = 10 answer d"
Answer: d
Python program:
a = 49 / 49
b = a - 1
Problem: reena took a loan of $ . 1200 with simple interest for as many years as the rate of interest . if she paid $ 108 as interest at the end of the loan period , what was the rate of interest ?
Options: a ) 3.6 , b ) 6 , c ) 18 , d ) 3 , e ) none of these
Rationale: let rate = r % and time = r years . then , 1200 x r x r / 100 = 108 12 r 2 = 108 r 2 = 9 r = 3 . answer : d
Answer: d
Python program:
a = 108 * 100
b = a / 1200
c = math.sqrt(b)
Problem: today joelle opened an interest - bearing savings account and deposited $ 5,000 . if the annual interest rate is 4 percent compounded interest , and she neither deposits nor withdraws money for exactly 2 years , how much money will she have in the account ?
Options: a ) $ 5200 , b ) $ 5408 , c ) $ 5208 , d ) $ 5608 , e ) $ 5808
Rationale: "interest for 1 st year = 5000 * 4 / 100 = 200 interest for 2 nd year = 5200 * 4 / 100 = 208 total = 5000 + 200 + 208 = 5408 answer : b"
Answer: b
Python program:
a = 3 * 2
b = a * 100
c = b * 10
d = 3 * 2
e = d * 100
f = e * 10
g = f * 4
h = g / 100
i = c + h 
j = 3 * 2
k = j * 100
l = k * 10
m = 3 * 2
n = m * 100
o = n * 10
p = o * 4
q = p / 100
r = l + q 
s = r * 4
t = s / 100
u = i + t
Problem: ana climbs up stairs 20 floors building and back . she takes the exact same route both ways . on the trip up she climbs an average speed of 2 steps per second . on the trip back she climbs down at an average speed of 4 steps per second . what is her approximate average speed for the round trip in miles per hour ?
Options: a ) 1 , b ) 1.25 , c ) 1.33 , d ) 1.5 , e ) 1.75
Rationale: average speed = total distance / total time here number of steps to 20 th floor and back is same as she takes the same route . d = 2 t 1 and d = 4 t 2 therefore , t 1 = d / 2 and t 2 = d / 4 t 1 + t 2 = 3 d / 4 therefore , average speed = 2 d / 3 d / 4 = 2 d * 4 / 3 d answer is 1.3 since , the options are far away we need not solve till the decimal points so correct answer is option c
Answer: c
Python program:
a = 20 / 2
b = 20 / 4
c = a + b 
d = 20 / c
Problem: a cube of edge 6 cm is cut into cubes each of edge 2 cm . the ratio of the total surface area of one of the small cubes to that of the large cube is equal to :
Options: a ) 1 : 9 , b ) 1 : 225 , c ) 1 : 52 , d ) 1 : 522 , e ) none
Rationale: "sol . required ratio = 6 * 2 * 2 / 6 * 6 * 6 = 1 / 9 = 1 : 9 . answer a"
Answer: a
Python program:
a = 4 / 100
Problem: two positive integers differ by 4 , and sum of their reciprocals is 6 . then one of the numbers is
Options: a ) a ) 3 , b ) b ) 1 , c ) c ) 5 , d ) 4 , e ) e ) 28
Rationale: "algebraic approach : let n be the smaller integer = > 1 / n + 1 / ( n + 4 ) = 6 or ( ( n + 4 ) + n ) / n ( n + 4 ) = 6 or ( n ^ 2 + 4 n ) * 6 = 2 n + 4 or n = 2 as n can not be - negative solve for n = > n = 4 . hence , d"
Answer: d
Python program:
a = 6 + 6
Problem: if a mixture is 3 ⁄ 7 alcohol by volume and 4 ⁄ 7 water by volume , what is the ratio of the volume of alcohol to the volume of water in this mixture ?
Options: a ) 3 ⁄ 7 , b ) 4 ⁄ 7 , c ) 3 ⁄ 4 , d ) 4 ⁄ 3 , e ) 7 ⁄ 4
Rationale: "should be a sub - 600 level q . . volume = { 3 / 7 } / { 4 / 7 } = 3 / 4 answer : c"
Answer: c
Python program:
a = 3 / 7
b = 4 / 7
c = a / b
Problem: the ratio of two quantities is 4 : 3 . if each of the quantities is decreased by 8 , their ratio changes to 3 : 1 then the smallest number is ?
Options: a ) 5.2 , b ) 6.9 , c ) 9.6 , d ) 7.8 , e ) 4.7
Rationale: "let the numbers be 4 x and 3 x then 4 x - 8 / 3 x - 8 = 3 / 1 4 x - 8 = 9 x - 24 5 x = 16 x = 3.2 smallest number = 3 * 3.2 = 9.6 answer is c"
Answer: c
Python program:
a = 4 + 8 
b = 3 + 8 
c = a / b
Problem: the instructions state that cheryl needs 4 / 19 square yards of one type of material and 2 / 13 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 4 / 26 square yards left that she did not use . what is the total amount of square yards of material cheryl used ?
Options: a ) 4 / 19 , b ) 1 / 9 , c ) 2 / 3 , d ) 1 1 / 9 , e ) 2 1 / 9
Rationale: "total bought = 4 / 19 + 2 / 13 left part 4 / 26 - - - > 2 / 13 so used part 4 / 19 + 2 / 13 - 2 / 13 = 4 / 19 answer : a"
Answer: a
Python program:
a = 4 / 19
b = 2 / 13
c = a + b 
d = 4 / 26
e = c - d
Problem: running at the same constant rate , 6 identical machines can produce a total of 270 bottles per minute . at this rate , how many bottles could 16 such machines produce in 4 minutes ?
Options: a ) 2880 , b ) 1800 , c ) 2700 , d ) 10800 , e ) none of these
Rationale: "solution let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) â ˆ ´ 6 ã — 1 ã — x = 16 ã — 4 ã — 270 â ‡ ” x = 16 x 4 x 270 / 6 = 2880 . answer a"
Answer: a
Python program:
a = 270 / 6
b = a * 4
c = b * 16
Problem: all the milk in container a which was filled to its brim was poured into two containers b and c . the quantity of milk in container b was 62.5 % less than the capacity of container a . if 154 liters was now transferred from c to b , then both the containers would have equal quantities of milk . what was the initial quantity of milk in container a ?
Options: a ) 1232 , b ) 1723 , c ) 1129 , d ) 2613 , e ) 1372
Rationale: "a b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 154 liters was transferred from container c to container b , then both the containers would have equal quantities of milk . 5 k - 154 = 3 k + 154 = > 2 k = 308 = > k = 154 the initial quantity of milk in a = 8 k = 8 * 154 = 1232 liters ."
Answer: a
Python program:
a = 1/(2)
b = 62 / 5
c = 1 - b
d = a - c
e = 154 / d
Problem: of the 170 people at a party , 70 were women , and 30 women tried the appetizer . if 60 people did not try the appetizer , what is the total number of men who tried the appetizer ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: total people at party = 170 women = 70 so men 170 - 70 = 100 no . of pple who tried appetizer = 170 - 60 ( given info ) = 110 no of women who tried appetizer = 30 so remaining ppl ( men ) who tried the appetizer = 110 - 30 = 80 correct option e
Answer: e
Python program:
a = 170 - 60
b = a - 30
Problem: if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 130 , how much more remains to be paid ?
Options: a ) $ 880 , b ) $ 990 , c ) $ 1,000 , d ) $ 1,170 , e ) $ 1,210
Rationale: 10 / 100 p = 130 > > p = 130 * 100 / 10 = 1300 1300 - 130 = 1170 answer : d
Answer: d
Python program:
a = 100 / 10
b = 130 * a
c = b - 130
Problem: a man swims downstream 36 km and upstream 18 km taking 6 hours each time , what is the speed of the man in still water ?
Options: a ) 4.5 , b ) 5.5 , c ) 6.5 , d ) 4.8 , e ) 2
Rationale: "36 - - - 6 ds = 6 ? - - - - 1 18 - - - - 6 us = 3 ? - - - - 1 m = ? m = ( 6 + 3 ) / 2 = 4.5 answer : a"
Answer: a
Python program:
a = 18 / 6
b = 36 / 6
c = a + b 
d = c / 2
Problem: a rectangular block 12 cm by 36 cm by 60 cm is cut into an exact number of equal cubes . find the least possible number of cubes ?
Options: a ) 6 , b ) 10 , c ) 15 , d ) 40 , e ) 22
Rationale: "volume of the block = 12 * 36 * 60 = 25920 cm ^ 3 side of the largest cube = h . c . f of 12 , 36,60 = 12 cm volume of the cube = 12 * 12 * 12 = 1728 cm ^ 3 number of cubes = 25920 / 1728 = 15 answer is c"
Answer: c
Python program:
a = rectangle_area / (
b = a - 10
c = 3 * 2
d = 1000 * c
e = b + d 
f = 3 * 1000
g = 60 * 10
h = f + g 
i = e / h
Problem: a man swims downstream 65 km and upstream 35 km taking 5 hours each time ; what is the speed of the current ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "65 - - - 5 ds = 13 ? - - - - 1 35 - - - - 5 us = 7 ? - - - - 1 s = ? s = ( 13 - 7 ) / 2 = 3 answer : b"
Answer: b
Python program:
a = 35 / 5
b = 65 / 5
c = a + b 
d = c / 2
Problem: a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 3500 . the difference between the profit shares of a and c is ?
Options: a ) 621 , b ) 1400 , c ) 236 , d ) 600 , e ) 211
Rationale: "explanation : ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 3500 = > 5 parts out of 15 parts is rs . 3500 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 3500 ) = rs . 1400 answer : b"
Answer: b
Python program:
a = 12000 / 10000
b = 8000 / 10000
c = a - b
d = c * 3500
Problem: how many pieces of 75 cm can be cut from a rope 60 meters long ?
Options: a ) 80 , b ) 40 , c ) 60 , d ) none , e ) can not be determined
Rationale: "explanation : total pieces of 75 cm that can be cut from a rope of 60 meters long is = ( 60 meters ) / ( 75 cm ) = ( 60 meters ) / ( 0.75 meters ) = 80 answer : a"
Answer: a
Python program:
a = 60 / 75
Problem: a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 8 % . what was its profit on the items sold in february ?
Options: a ) 27.5 % , b ) 30 % , c ) 35 % , d ) 37.5 % , e ) 38 %
Rationale: "assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.92 * 150 x = 138 x hence total profit = 38 % option e"
Answer: e
Python program:
a = 100 - 8
b = a / 100
c = 100 + 20 
d = 100 + 25 
e = d / 100
f = c * e
g = b * f
h = g - 100
Problem: ( ? ) + 3699 + 1985 - 2047 = 31111
Options: a ) 27488 , b ) 27424 , c ) 27474 , d ) 27784 , e ) 27468
Rationale: c 27474 x + 3699 + 1985 - 2047 = 31111 x + 3699 + 1985 = 31111 + 2047 x + 5684 = 33158 x = 33158 - 5684 = 27474 .
Answer: c
Python program:
a = 3699 + 1985 
b = a - 2047
c = 31111 - b
Problem: pens , pencils and markers in a jenna ' s desk are in the ratio of 2 : 2 : 5 . if there are 10 pens , the number of markers in jenna ' s desk is :
Options: a ) 30 , b ) 22 , c ) 20 , d ) 25 , e ) 100
Rationale: explanation : let pens = 2 x , pencils = 2 x & markers = 5 x . now , 2 x = 10 hence x = 5 . number of markers = 5 x which is 25 . answer : d
Answer: d
Python program:
a = 10 * 5
b = a / 2
Problem: carl is facing very difficult financial times and can only pay the interest on a $ 20,000 loan he has taken . the bank charges him a quarterly compound rate of 5 % . what is the approximate interest he pays annually ?
Options: a ) $ 1200 , b ) $ 2000 , c ) $ 2150 , d ) $ 4000 , e ) $ 12000
Rationale: "usually , you are given the annual rate of interest and it is mentioned that it is annual rate . the bank charges him a quarterly compounded annual rate of 20 % . here you find per quarter rate as ( 20 / 4 ) % = 5 % i have actually never seen a question with quarter rate given but since this question did not mentionannual rate of interestand since the options did not make sense with 5 % annual rate of interest , it is apparent that the intent was a 5 % quarterly rate . so the bank charges 5 % every quarter and compounds it in the next quarter . had it been a simple quarterly rate , we would have just found 4 * 5 % of 20,000 = $ 4000 as our answer . but since , the interest is compounded , it will be a bit more than $ 2000 . option ( d ) looks correct ."
Answer: d
Python program:
a = 100 * 100
b = 5 / 100
c = 1 + b 
d = c ** 4
e = a * d
f = 100 * 100
g = e - f
Problem: how many digits are in ( 8 × 10 ^ 10 ) ( 10 × 10 ^ 5 ) ?
Options: a ) 17 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: the question simplfies to ( 8 × 10 ^ 10 ) ( 10 ^ 6 ) = > 8 * 10 ^ 16 = > will contain 16 zeros + 1 digit 8 = > 17 ans a
Answer: a
Python program:
a = 3 + 4 
b = 10 + a
Problem: a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 3 : 4 . the ratio of economy cars to sport utility vehicles is 4 : 3 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 9 : 8 , b ) 8 : 9 , c ) 3 : 2 , d ) 2 : 3 , e ) 16 : 9
Rationale: "the ratio of economy to luxury cars is 3 : 4 - - > e : l = 3 : 4 = 12 : 16 . the ratio of economy cars to sport utility vehicles is 4 : 3 - - > e : s = 4 : 3 = 12 : 9 . thus , l : s = 16 : 9 . answer : e ."
Answer: e
Python program:
a = 4 * 3
b = 3 * 3
c = a / b
d = 3 * 4
e = 4 * 4
f = d / e
g = c / f
Problem: a sum of rs . 1530 has been divided among a , b and c such that a gets of what b gets and b gets of what c gets . b ’ s share is :
Options: a ) rs . 120 , b ) rs . 160 , c ) rs . 270 , d ) rs . 300 , e ) none
Rationale: "explanation let c ’ s share = rs . x then , b ’ s share = rs . x / 4 , a ’ s share = rs . ( 2 / 3 x x / 4 ) = rs . x / 6 = x / 6 + x / 4 + x = 1530 = > 17 x / 12 = 1530 = > 1530 x 12 / 17 = rs . 1080 hence , b ’ s share = rs . ( 1080 / 4 ) = rs . 270 . answer c"
Answer: c
Python program:
a = 1530 / 10
b = a * 2
c = b - 12
d = c - 12
Problem: two pipes can fill the cistern in 10 hr and 12 hr respectively , while the third empty it in 40 hr . if all pipes are opened simultaneously , then the cistern will be filled in
Options: a ) 6.32 hr , b ) 8 hr , c ) 8.5 hr , d ) 10 hr , e ) none of these
Rationale: "solution : work done by all the tanks working together in 1 hour . 1 / 10 + 1 / 12 − 1 / 40 = 3 / 19 hence , tank will be filled in 19 / 3 = 6.32 hour option ( a )"
Answer: a
Python program:
a = 1 / 10
b = 1 / 12
c = a + b 
d = 1 / 40
e = c - d
f = 1/(e)
Problem: if 5 men undertook a piece of construction work and finished half the job in 15 days . if two men drop out , then the job will be completed in
Options: a ) 5 days , b ) 15 days , c ) 10 days , d ) 25 days , e ) 20 days
Rationale: that is , half the work done = 5 * 15 * 1 / 2 then , 5 * 15 * 1 / 2 = 3 * ? * 1 / 2 i . e . 5 * 15 = 3 * ? = 5 * 15 / 3 = 25 day d
Answer: d
Python program:
a = 15 * 5
b = 5 - 2
c = a / b
Problem: two trains are moving in the same direction at 144 kmph and 72 kmph . the faster train crosses a man in the slower train in 19 seconds . find the length of the faster train ?
Options: a ) 320 , b ) 340 , c ) 360 , d ) 380 , e ) 400
Rationale: "relative speed = ( 144 - 72 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in 19 sec = 19 * 20 = 380 m . the length of the faster train = 380 m . answer : d"
Answer: d
Python program:
a = 144 - 72
b = a / const_3_6
c = b * 19
Problem: a no . when divided by 225 gives a remainder 43 , what remainder will beobtained by dividingthe same no . 17 ?
Options: a ) 2 , b ) 7 , c ) 9 , d ) 11 , e ) 13
Rationale: "225 + 43 = 268 / 17 = 13 ( remainder ) e"
Answer: e
Python program:
a = 225 + 43 
b = a / 17
Problem: a child want to buy 3 new toys . if there are 10 toys that satisfy the child ' s criteria , in how many different ways can the child select the 3 new toys if the order of selection does n ' t matter .
Options: a ) 20 , b ) 120 , c ) 210 , d ) 15 , e ) 45
Rationale: "the number of ways of choosing 3 toys out of 10 are counted by = 10 c 3 ways = 120 answer : option b"
Answer: b
Python program:
a = math.comb(10, 3)
Problem: in what ratio mental a at rs . 68 per kg be mixed with another metal at rs . 96 per kg so that cost of alloy ( mixture ) is rs . 76 per kg ?
Options: a ) 5 : 8 , b ) 4 : 7 , c ) 3 : 7 , d ) 9 : 5 , e ) 5 : 2
Rationale: "( 96 - 76 ) / ( 76 - 68 ) = 20 / 8 = 5 / 2 answer : e"
Answer: e
Python program:
a = 96 - 76
b = 96 - 68
c = a / b
d = 96 - 76
e = 96 - 68
f = d / e
g = 1 - f
h = c / g
Problem: what is the ratio between perimeters of two squares one having 3 times the diagonal then the other ?
Options: a ) 3 : 2
b ) 3 : 0
c ) 4 : 1
d ) 3 : 1
e ) 2 : 2
Rationale: d = 3 d d = d a √ 2 = 3 d a √ 2 = d a = 3 d / √ 2 a = d / √ 2 = > 3 : 1 answer : d
Answer: d
Python program:
a = 3 / 3
b = 3 / a
Problem: the shopkeeper increased the price of a product by 25 % so that customer finds it difficult to purchase the required amount . but somehow the customer managed to purchase only 72 % of the required amount . what is the net difference in the expenditure on that product ?
Options: a ) 12.5 % , b ) 10 % , c ) 15 % , d ) 17 % , e ) 19 %
Rationale: "quantity x rate = price 1 x 1 = 1 0.72 x 1.25 = 0.9 decrease in price = ( 0.1 / 1 ) × 100 = 10 % b )"
Answer: b
Python program:
a = 100 * 100
b = 100 + 25 
c = b * 72
d = a - c
e = d * 100
f = 100 * 100
g = e / f
Problem: two trains 140 m and 150 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.9 sec , b ) 13.8 sec , c ) 53.8 sec , d ) 10.44 sec , e ) 10.4 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 140 + 150 = 290 m . required time = 290 * 9 / 250 = 10.44 sec . answer : d :"
Answer: d
Python program:
a = 140 + 150 
b = 60 + 40 
c = b * const_0_2778
d = a / c
Problem: a , b and c start a business each investing 20000 . after 5 months a withdrew 10000 , b withdrew 15000 and c invests 5000 more . at the end of the year , a total profit of 58000 was recorded . find the share of b .
Options: a ) 20,000 , b ) 21,200 , c ) 28,200 , d ) 13,500 , e ) none of these
Rationale: ratio of the capitals of a , b and c = 20000 ã — 5 + 10000 ã — 7 : 20000 ã — 5 + 5000 ã — 7 : 20000 ã — 5 + 25000 ã — 7 = 170000 : 135000 : 275000 = 170 : 135 : 275 . b â € ™ s share = ( 58000 ã — 135 â  „ 580 ) = 13500 answer d
Answer: d
Python program:
a = 20000 * 5
b = 20000 - 15000
c = 12 - 5
d = b * c
e = a + d 
f = 20000 * 5
g = 20000 - 10000
h = 12 - 5
i = g * h
j = f + i 
k = 20000 * 5
l = 20000 - 15000
m = 12 - 5
n = l * m
o = k + n 
p = j + o 
q = 20000 * 5
r = 20000 + 5000 
s = 12 - 5
t = r * s
u = q + t 
v = p + u 
w = e / v
x = 58000 * w
y = const_60 + 5 
z = x / y
Problem: a glass was filled with 10 ounces of water , and 0.06 ounce of the water evaporated each day during a 20 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.002 % , b ) 0.02 % , c ) 0.2 % , d ) 12 % , e ) 20 %
Rationale: "we are given that 0.06 ounces of water evaporated each day . furthermore , we know that this process happened over a 20 - day period . to calculate the total amount of water that evaporated during this time frame we need to multiply 0.06 by 20 . this gives us : 0.06 x 20 = 1.2 ounces finally , we are asked for “ what percent ” of the original amount of water evaporated during this period . to determine this percentage , we have to make sure we translate the expression correctly . we can translate it to : ( amount evaporated / original amount ) x 100 % ( 1.2 / 10 ) x 100 % ( 12 / 100 ) x 100 % = 12 % answer d"
Answer: d
Python program:
a = 0 * 6
b = a / 10
c = b * 100
Problem: in a class of 25 students , 3 students did not borrow any books from the library , 11 students each borrowed 1 book , 6 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "the total number of books the students borrowed is 25 * 2 = 50 . the students who borrowed zero , one , or two books borrowed 11 * 1 + 6 * 2 = 23 books . the 5 students who borrowed at least three books borrowed 50 - 23 = 27 books . if 4 of these students borrowed exactly 3 books , then the maximum that one student could have borrowed is 27 - 12 = 15 books . the answer is d ."
Answer: d
Python program:
a = 25 * 2
b = 11 * 1
c = b + 6 
d = c + 3 
e = 25 - d
f = e - 1
g = f * 3
h = 11 * 1
i = 6 * 3
j = h + i 
k = g + j 
l = a - k
Problem: if two painters can complete two rooms in two hours , how many painters would it take to do 18 rooms in 6 hours ?
Options: a ) 8 , b ) 6 , c ) 5 , d ) 4 , e ) 1
Rationale: "explanation : two painters can complete two rooms in two hours . so 18 rooms can be painted in 6 hrs by 6 painters answer : b ) 6 painters"
Answer: b
Python program:
a = 6 * 3
b = a * 3
c = 3 * 3
d = b / c
Problem: how much space , in cubic units , is left vacant when maximum number of 7 x 7 x 7 cubes are fitted in a rectangular box measuring 14 x 21 x 17 ?
Options: a ) 878 , b ) 879 , c ) 880 , d ) 881 , e ) 882
Rationale: "no of cubes that can be accommodated in box = ( 14 * 21 * 17 ) / ( 7 * 7 * 7 ) 12 * 16 in numerator can be perfectly divided by 7 * 7 in denominator . side with length 17 ca n ' t be perfectly divided by 7 and hence is the limiting factor . closet multiple of 7 less that 17 is 14 . so vacant area in cube = = 14 * 21 * ( 17 - 14 ) = 14 * 21 * 3 = 882 ans - e"
Answer: e
Python program:
a = 7 * 2
b = 14 - a
c = 21 * 17
d = b * c
Problem: according to a recent survey report issued by the commerce ministry , government of india , 30 % of the total fdi goes to gujarat and 20 % of this goes to rural areas . if the fdi in gujarat , which goes to urban areas , is $ 72 m , then find the size of fdi in rural andhra pradesh , which attracts 50 % of the fdi that comes to andhra pradesh , which accounts for 20 % of the total fdi ?
Options: a ) 30 m , b ) 40 m , c ) 35 m , d ) 38 m , e ) 50 m
Rationale: 30 % of total fdi given to gujarat is $ 90 m . so , 100 % is $ 300 m . 20 % of 300 m = 60 m . 50 % of 60 m = 30 m . answer : a
Answer: a
Python program:
a = 30 / 100
b = 100 - 20
c = b / 100
d = a * c
e = 72 / d
f = 50 / 100
g = 20 / 100
h = f * g
i = e * h