euclaise/mathqa_programs huggingface dataset:
Problem: a part - time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee ' s total income did not change . by what percent e should the number of hours worked be increased ?
Options: a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 100 %
Rationale: "correct answer : c solution : c . we can set up equations for income before and after the wage reduction . initially , the employee earns w wage and works h hours per week . after the reduction , the employee earns . 8 w wage and works x hours . by setting these equations equal to each other , we can determine the increase in hours worked : wh = . 8 wx ( divide both sides by . 8 w ) 1.25 h = x we know that the new number of hours worked e will be 25 % greater than the original number . the answer is c ."
Answer: c
Python program:
a = 10 * 4
b = 100 - 20
c = b / 100
d = c * 10
e = a / d
f = e - 4
g = f / 4
h = g * 100
Problem: a rectangle has 20 meter length and 15 meter breadth . find ratio between area of rectangle and square whose side is same with rectangle ' s length .
Options: a ) 3 : 2
b ) 3 : 4
c ) 4 : 5
d ) 2 : 3
e ) 2 : 5
Rationale: area of rectangle = 20 * 15 = 300 area of square = 20 ^ 2 = 400 ratio of rectangle ' area and square ' s area = 300 : 400 = 3 : 4 answer : b
Answer: b
Python program:
a = rectangle_area / (
Problem: a number when divided by 221 gives a remainder 43 , what remainder will be obtained by dividing the same number 17 ?
Options: a ) 9 , b ) 11 , c ) 15 , d ) 5 , e ) 20
Rationale: 221 + 43 = 264 / 17 = 9 answer a
Answer: a
Python program:
a = 17 * 2
b = 43 - a
Problem: george went to a fruit market with certain amount of money . with this money he can buy either 50 oranges or 40 mangoes . he retains 8 % of the money for taxi fare and buys 20 mangoes . how many oranges can he buy ?
Options: a ) 21 , b ) 30 , c ) 20 , d ) 16 , e ) 12
Rationale: "let the amount of money be 200 let cost of 1 orange be 4 let cost of 1 mango be 5 he decides to retain 8 % of 200 = 16 for taxi fare , so he is left with 184 he buys 20 mangoes ( @ 5 ) so he spends 100 money left is 84 ( 184 - 100 ) no of oranges he can buy = 84 / 4 = > 21 so , george can buy 21 oranges . a"
Answer: a
Python program:
a = 8 / 100
b = 1 - a
c = 20 / 50
d = b - c
e = d * 50
Problem: a sum of 14,400 amounts to 16,600 in 3 years at the rate of simple interest . what is the rate of interest ?
Options: a ) 2 % , b ) 1 % , c ) 6 % , d ) 5 % , e ) 8 %
Rationale: "d 5 % s . i . = ( 16600 - 14400 ) = 2200 . rate = ( 100 x 2200 ) / ( 14400 x 3 ) % = 5 %"
Answer: d
Python program:
a = 3 / 3
b = 3 * 3
c = const_0_25 + const_0_25 
d = b + c 
e = a / d
f = e * 100
Problem: a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 70 percent of books that were loaned out are returned and there are 66 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 20 , b ) 30 , c ) 35 , d ) 40 , e ) 55
Rationale: total = 75 books . 65 % of books that were loaned out are returned - - > 100 % - 70 % = 30 % of books that were loaned out are not returned . now , there are 66 books , thus 76 - 68 = 7 books are not returned . { loaned out } * 0.30 = 7 - - > { loaned out } = 30 . answer : b .
Answer: b
Python program:
a = 75 - 66
b = 70 / 100
c = 1 - b
d = a / c
Problem: if a tire rotates at 400 revolutions per minute when the car is traveling 168 km / h , what is the circumference of the tire ?
Options: a ) 7 meters , b ) 9 meters , c ) 8 meters , d ) 5 meters , e ) 3 meters
Rationale: "400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 168,000 m : c is the circumference c = 3 meters correct answer a"
Answer: a
Python program:
a = 2 * 3
b = a * 10
c = b * 400
d = 168 / c
e = d * 1000
Problem: in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 7 people all together . how many people can sit in a bus ?
Options: a ) 52 , b ) 49 , c ) 95 , d ) 88 , e ) 66
Rationale: "right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 7 total people can seat = 81 + 7 = 88 answer : d"
Answer: d
Python program:
a = 15 - 3
b = 15 + a 
c = b * 3
d = c + 7
Problem: a worker ' s take - home pay last year was the same each month , and she saved the same fraction of her take - home pay each month . the total amount of money that she had saved at the end of the year was 2 times the amount of that portion of her monthly take - home pay that she did not save . if all the money that she saved last year was from her take - home pay , what fraction of her take - home pay did she save each month ?
Options: a ) 1 / 7 , b ) 1 / 6 , c ) 1 / 5 , d ) 1 / 4 , e ) 1 / 3
Rationale: "let x be the fraction of her take - home pay that the worker saved . let p be the monthly pay . 12 xp = 2 ( 1 - x ) p 12 xp = 2 p - 2 xp 14 xp = 2 p x = 1 / 7 the answer is a ."
Answer: a
Python program:
a = 12 / 2
b = a + 1 
c = 1/(b)
Problem: if a certain number of labours can dig earth 100 m deep , 25 m long , and 30 m broad in 12 days , then find the number of days the same number of labours will require to dig earth 75 m deep , 20 m long and 50 m broad .
Options: a ) 12 , b ) 18 , c ) 6 , d ) 1 , e ) 2
Rationale: explanation : more number of days means more length , more depth and more width . hence , its a direct proportion . ( 100 * 25 * 30 ) : ( 75 * 20 * 50 ) : : 12 : x 75000 : 75000 : : 12 : x x = 12 answer : a
Answer: a
Python program:
a = 75 * 20
b = a * 50
c = 100 * 25
d = c * 30
e = b / d
f = e * 12
Problem: a shopkeeper sold an article offering a discount of 5 % and earned a profit of 27.3 % . what would have been the percentage of profit earned if no discount had been offered ?
Options: a ) 28.5 , b ) 27.675 , c ) 30 , d ) 34 % , e ) none of these
Rationale: "giving no discount to customer implies selling the product on printed price . suppose the cost price of the article is 100 . then printed price = 100 ã — ( 100 + 27.3 ) / ( 100 â ˆ ’ 5 ) = 100 ã — 127.3 / 95 = 134 hence , required % profit = 134 â € “ 100 = 34 % answer d"
Answer: d
Python program:
a = 100 + 27 
b = a * 100
c = 100 - 5
d = b / c
e = d - 100
Problem: in town x , 64 percent of the population are employed , and 45 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 45 % , c ) 32 % , d ) 40 % , e ) 28 %
Rationale: "answer b male - employed - 64 % female - employed - 19 % total employed 64 % means total unemployed = 36 % therefore d and e are not correct because female unemployed has to be less than 36 % female - unemployed = 32 % male unemployed = 4 % 48 % + 4 % = 52 % 16 % + 32 % = 48 % plug in a and b in place of 32 % and the sum is not 100 % 19 / 64 = 28 e"
Answer: e
Python program:
a = 64 - 45
b = a / 64
c = b * 100
Problem: x and y invested in a business . they earned some profit which they divided in the ratio of 2 : 3 . if x invested rs . 40,000 , the amount invested by y is
Options: a ) 33488 , b ) 63809 , c ) 60000 , d ) 37887 , e ) 77824
Rationale: "explanation : suppose y invested rs . y . then 40000 / y = 2 / 3 or y = 60000 . answer : c ) 60000"
Answer: c
Python program:
a = 1 + 4 
b = a * 1000
c = b * 2
d = c / 3
Problem: 135 kg of an alloy a is mixed with 145 kg of alloy b . if alloy a has lead and tin in the ratio 3 : 5 and alloy b has tin and copper in the ratio 2 : 3 , then the amount of tin in the new alloy is ?
Options: a ) 100.6 kg , b ) 142 kg , c ) 135 kg , d ) 110.8 kg , e ) 114 kg
Rationale: "quantity of tin in 135 kg of a = 135 * 5 / 8 = 84 kg quantity of tin in 145 kg of b = 145 * 2 / 5 = 58 kg quantity of tin in the new alloy = 84 + 58 = 142 kg answer is b"
Answer: b
Python program:
a = 3 + 5 
b = 135 / a
c = b * 5
d = 2 + 3 
e = 145 / d
f = e * 2
g = c + f
Problem: a sum of money lent out at s . i . amounts to a total of $ 520 after 2 years and to $ 820 after a further period of 5 years . what was the initial sum of money that was invested ?
Options: a ) $ 340 , b ) $ 360 , c ) $ 380 , d ) $ 400 , e ) $ 420
Rationale: "s . i for 5 years = $ 820 - $ 520 = $ 300 the s . i . is $ 60 / year s . i . for 2 years = $ 120 principal = $ 520 - $ 120 = $ 400 the answer is d ."
Answer: d
Python program:
a = 820 - 520
b = 2 / 5
c = a * b
d = 520 - c
Problem: a person borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 61 ⁄ 4 % p . a for 2 years . find his gain in the transaction per year .
Options: a ) 167.5 , b ) 150 , c ) 225 , d ) 112.5 , e ) 212.5
Rationale: "explanation : the person borrows rs . 5000 for 2 years at 4 % p . a . simple interest simple interest that he needs to pay = prt / 100 = 5000 × 4 × 2 / 100 = 400 he also lends it at 6 1 ⁄ 4 % p . a for 2 years simple interest that he gets = prt / 100 = 5000 × 254 × 21 / 00 = 625 his overall gain in 2 years = rs . 625 - rs . 400 = rs . 225 his overall gain in 1 year = 2252 = rs . 112.5 answer : option d"
Answer: d
Python program:
a = 5000 * 61
b = a * 2
c = b / 100
d = 5000 * 4
e = d * 2
f = e / 100
g = c - f
h = g / 2
Problem: a small water pump would take 4 hours to fill an empty tank . a larger pump would take 1 / 2 hour to fill the same tank . how many hours would it take both pumps , working at their respective constant rates , to fill the empty tank if they began pumping at the same time ?
Options: a ) 1 / 6 , b ) 4 / 9 , c ) 1 / 4 , d ) 5 / 9 , e ) 1 / 3
Rationale: "rate of the small pump is 1 / 4 tank / hour rate of the larger pump is 1 / ( 1 / 2 ) or 2 tank / hour ; combined rate of the two pumps is 1 / 4 + 2 = 9 / 4 tank / hour , together they will fill the empty tank in 1 / ( 9 / 4 ) ) = 4 / 9 hours ( time = job / rate ) . answer : b"
Answer: b
Python program:
a = 1/(4)
b = a + 2 
c = 1/(b)
Problem: a man cycling along the road noticed that every 3 minutes a bus overtakes him and every 9 minutes he meets an oncoming bus . if all buses and the cyclist move at a constant speed , what is the time interval between consecutive buses ?
Options: a ) 5 minutes , b ) 6 minutes , c ) 8 minutes , d ) 9 / 2 minutes , e ) 10 minutes
Rationale: "let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 9 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 9 , d = 9 b - 9 c ; every 3 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 3 , d = 3 b + 3 c ; d = 9 b - 9 c = 3 b + 3 c , - - > b = 2 c , - - > d = 9 b - 9 b / 2 = 9 b / 2 . interval = \ frac { d } { b } = \ frac { 9 / 2 b } { b } = 9 / 2 answer : d ( 9 / 2 minutes ) ."
Answer: d
Python program:
a = 9 + 3 
b = 3 - 9
c = a / b
d = 3 / c
e = 3 - d
f = e / 1
Problem: a pump can fill a tank with water in 2 hours . because of a leak , it took 2 2 / 3 hours to fill the tank . the leak can drain all the water of the tank in
Options: a ) 6 hours , b ) 8 hours , c ) 9 hours , d ) 10 hours , e ) 12 hours
Rationale: "explanation : solution 1 the pump can fill the tank in 2 hour . but , because of the leak , it took 2 2 / 3 hours to fill the tank . i . e . , the additional water filled by the pump in 2 / 3 hour is emptied by the leak in 2 2 / 3 = 8 / 3 hours . therefore , the water filled by pump in 2 bour can be emptied by the leak in 8 / 3 x 3 = 8 hours . i . e . , the leak can drain all the water of the tank in 8 hours . answer is b"
Answer: b
Python program:
a = 2 / 2
b = 2 * 3
c = b + 2 
d = c / 3
e = 1/(d)
f = a - e
g = 1/(f)
Problem: a goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 240 m , c ) 260 m , d ) 270 m , e ) none of the above
Rationale: "speed = ( 72 x ( 5 / 18 ) ) m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , ( ( x + 250 ) / 26 ) = 20 x + 250 = 520 x = 270 . d"
Answer: d
Python program:
a = const_0_2778 * 72
b = 250 / a
c = 26 - b
d = const_0_2778 * 72
e = c * d
Problem: if teena is driving at 55 miles per hour and is currently 7.5 miles behind joe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 22.5 miles ahead of joe ?
Options: a ) 15 , b ) 60 , c ) 75 , d ) 90 , e ) 120
Rationale: "this type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30 - 40 seconds for a difficult one . teena covers 55 miles in 60 mins . joe covers 40 miles in 60 mins so teena gains 15 miles every 60 mins teena need to cover 7.5 + 22.5 miles . teena can cover 7.5 miles in 30 mins teena will cover 22.5 miles in 90 mins so answer 30 + 90 = 120 mins . ( answer e )"
Answer: e
Python program:
a = 55 - 40
b = a + 7 
c = 55 - 40
d = b / c
e = d * const_60
Problem: what is the average of first 21 multiples of 5 ?
Options: a ) a ) 70 , b ) b ) 77 , c ) c ) 55 , d ) d ) 81 , e ) e ) 82
Rationale: required average = 7 ( 1 + 2 + . . . . + 21 ) / 21 ( 5 / 21 ) x ( ( 21 x 22 ) / 2 ) ( because sum of first 21 natural numbers ) = 55 c
Answer: c
Python program:
a = 21 + 1 
b = 21 * a
c = b / 2
d = c / 21
e = d * 5
Problem: the sale price sarees listed for rs . 560 after successive discount is 20 % and 30 % is ?
Options: a ) 321 , b ) 314 , c ) 316 , d ) 265 , e ) 162
Rationale: "explanation : 560 * ( 80 / 100 ) * ( 70 / 100 ) = 314 answer : b"
Answer: b
Python program:
a = 560 * 20
b = a / 100
c = 560 - b
d = 560 * 20
e = d / 100
f = 560 - e
g = f * 30
h = g / 100
i = c - h
Problem: 45 girls and 60 boys are present at a party . there are 17 girl - boy are in relationship among them . if a girl and a boy is selected at random , what is the probability that they will be a couple ?
Options: a ) 1 / 200 , b ) 1 / 100 , c ) 90 / 2900 , d ) 17 / 2700 , e ) 1 / 20
Rationale: "in how many ways we can select a girl and a boy from 45 lady and 60 gentlemen ? in 45 * 60 = 2,700 ways . we have a total of 17 couples so , the probability of selecting a couple is 17 / 2,700 = 17 / 2700 . ans - d"
Answer: d
Python program:
a = math.comb(45, 1)
b = math.comb(60, 1)
c = a * b
d = math.comb(17, 1)
e = c - d
f = math.comb(45, 1)
g = math.comb(60, 1)
h = f * g
i = e / h
Problem: a can complete a work in 12 days and b can do the same work in 8 days . if a after doing 2 days , leaves the work , find in how many days b will do the remaining work ?
Options: a ) 2 days , b ) 4 1 / 2 days , c ) 6 1 / 2 days , d ) 7 3 / 4 days , e ) 10 days
Rationale: the required answer = ( 12 - 2 ) * 8 / 12 = 80 / 12 = 6 1 / 2 days answer is c
Answer: c
Python program:
a = 12 * 2
b = 12 / 2
c = a + b
Problem: a train 800 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 2 min , then the length of the tunnel is ?
Options: a ) 2898 , b ) 1800 , c ) 500 , d ) 297 , e ) 435
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 2 min = 120 sec . let the length of the train be x meters . then , ( 800 + x ) / 120 = 65 / 3 x = 1800 m . answer : b"
Answer: b
Python program:
a = 78 - 2
b = a * const_0_2778
c = 800 / b
Problem: given that e and f are events such that p ( e ) = 25 , p ( f ) = 75 and p ( e n f ) = 75 , find p ( e | f ) and p ( f | e )
Options: a ) 5 , b ) 46 , c ) 52 , d ) 12 , e ) 3
Rationale: here , e and f are events p ( e | f ) = p ( enf ) / p ( f ) = 75 / 25 = 3 p ( f | e ) = p ( enf ) / p ( e ) = 75 / 75 = 1 . e )
Answer: e
Python program:
a = 75 / 25
Problem: a train 2500 m long can cross an electric pole in 100 sec and then find the speed of the train ?
Options: a ) 90 , b ) 60 , c ) 120 , d ) 180 , e ) 360
Rationale: "length = speed * time speed = l / t s = 2500 / 100 s = 25 m / sec speed = 25 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 90 kmph answer : a"
Answer: a
Python program:
a = 2500 / 1000
b = 100 / 3600
c = a / b
Problem: if integer k is equal to the sum of all even multiples of 35 between 280 and 630 , what is the greatest prime factor of k ?
Options: a ) 5 , b ) 7 , c ) 11 , d ) 13 , e ) 11 * 455
Rationale: "if we break down what the stem is asking what is the sum of all mult of 30 between 300 and 600 . using arithmetic progression to find n : 630 = 280 + ( n - 1 ) 35 350 + 35 = 35 n 385 = 35 n = > n = 11 the sum would be : 11 * mean mean = [ 630 + 280 ] / 2 = 455 11 * 455 = e"
Answer: e
Python program:
a = 630 / 35
b = math.floor(a)
c = b * 35
d = 280 / 35
e = math.floor(d)
f = e * 35
g = c - f
h = g / 35
i = h + 1 
j = i / 2
Problem: if 360 is divided into 4 parts proportional to 5 , 7 , 4 , 8 then the smallest part is :
Options: a ) 50 , b ) 60 , c ) 40 , d ) 18 , e ) 22
Rationale: given ratio = 5 : 7 : 4 : 8 , sum of ratio = 24 : . the smallest part = ( 360 * 4 / 24 ) = 60 answer : b
Answer: b
Python program:
a = 5 + 7 
b = a + 4 
c = b + 8 
d = 4 / c
e = d * 360
Problem: 1370 , 1320 , 1070 , - 180 , - 6430 , x
Options: a ) - 37680 , b ) 6530 , c ) 6630 , d ) 6730 , e ) 6830
Rationale: "1370 - 50 * ( 5 ^ 0 ) = 1320 1320 - 50 * ( 5 ^ 1 ) = 1070 1070 - 50 * ( 5 ^ 2 ) = - 180 - 180 - 50 * ( 5 ^ 3 ) = - 6430 - 6430 - 50 * ( 5 ^ 4 ) = - 37680 answer : a ."
Answer: a
Python program:
a = negate - (
Problem: a scale 10 ft . 5 inches long is divided into 5 equal parts . find the length of each part .
Options: a ) 25 inches , b ) 77 inches , c ) 66 inches , d ) 97 inches , e ) 66 inches
Rationale: "explanation : total length of scale in inches = ( 10 * 12 ) + 5 = 125 inches length of each of the 5 parts = 125 / 5 = 25 inches answer : a"
Answer: a
Python program:
a = 10 * 12
b = a + 5 
c = b / 5
Problem: a train 150 m long passes a man , running at 6 kmph in the direction opposite to that of the train , in 6 seconds . the speed of the train is
Options: a ) 54 kmph , b ) 60 kmph , c ) 66 kmph , d ) 72 kmph , e ) 84 kmph
Rationale: "speed of train relative to man : 150 / 6 * 18 / 5 km / hr = 90 km / hr let speed of train = x therefore x + 6 = 90 x = 90 - 6 x = 84 km / hr answer : e"
Answer: e
Python program:
a = 6 * const_0_2778
b = a * 6
c = 150 - b
d = c / 6
e = d / const_0_2778
Problem: a thief runs away from a with a speed of 20 km / hr . a police from a station 60 km away started chasing him after 1 hr . with a speed of 40 km / hr . time taken by the police to catch the thief is :
Options: a ) 4 hrs , b ) 4.5 hrs , c ) 5.4 hrs , d ) 6 hrs . , e ) none of these
Rationale: explanation : solution : distance traveled by the thief in 1 hr . = 20 km . total distance of them after 1 hr = ( 60 + 20 ) km = 80 km . their relative speed = ( 40 - 20 ) = 20 km / hr . time taken to catch the thief = 80 / 20 = 4 hrs . answer : a
Answer: a
Python program:
a = 20 * 1
b = 60 + a 
c = 60 - 40
d = b / c
Problem: what is the square root of 16 , divided by 2 ?
Options: a ) 9 , b ) 2 , c ) 122 , d ) 6 , e ) 1
Rationale: "square root is a number times itself square root of 16 = 4 , 4 / 2 = 2 ( b ) 2"
Answer: b
Python program:
a = math.sqrt(16)
b = a / 2
Problem: the value of ( 4.7 × 13.26 + 4.7 × 9.43 + 4.7 × 77.31 ) is :
Options: a ) 0.47 , b ) 47 , c ) 470 , d ) 4700 , e ) none of these
Rationale: solution given expression = 4.7 × ( 13.26 + 9.43 + 77.31 ) = 4.7 × 100 = 470 . answer c
Answer: c
Python program:
a = 13 + 26 
b = a + 77 
c = 4 * 7
Problem: an ant walks an average of 500 meters in 60 minutes . a beetle walks 15 % less distance at the same time on the average . assuming the beetle walks at her regular rate , what is its speed in km / h ?
Options: a ) 1.0 , b ) 0.5 , c ) 0.75 , d ) 0.425 , e ) 0.3
Rationale: "the ant walks an average of 500 meters in 60 minutes 500 meters in 1 hours the beetle walks 15 % less distance = 500 - 75 = 425 meters in 60 minutes 0.425 km in 1 hours speed = 0.425 * 1 = 0.425 km / h i guess option d should be 0.425"
Answer: d
Python program:
a = 500 / 1000
b = 60 / const_60
c = a / b
d = 15 / 100
e = 1 - d
f = c * e
Problem: a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 10 gallons of water and 20 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ?
Options: a ) 37.5 , b ) 75 , c ) 100 , d ) 150 , e ) 175
Rationale: "original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 20 gallons salt is added and 10 gallons of water is added . so salt now becomes - > ( 0.2 x + 20 ) and water - - > ( 0.6 x + 10 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 20 ) = ( 0.6 x + 10 ) / 2 , solving , x = 150 . answer : d"
Answer: d
Python program:
a = 20 * 2
b = a - 10
c = 20 / 100
d = 1 - c
e = 20 / 100
f = 1 - e
g = 1 / 4
h = f * g
i = d - h
j = 20 / 100
k = 2 * j
l = i - k
m = b / l
Problem: roses can be purchased individually for $ 2.30 , one dozen for $ 36 , or two dozen for $ 50 . what is the greatest number of roses that can be purchased for $ 680 ?
Options: a ) 156 , b ) 162 , c ) 325 , d ) 324 , e ) 326
Rationale: "buy as many $ 50 deals as possible . we can by 650 / 50 = 13 two dozen roses , thus total of 13 * 24 = 312 roses . we are left with 680 - 650 = $ 30 . we can buy 30 / 2.3 = ~ 13 roses for that amount . total = 312 + 13 = 325 . answer : c ."
Answer: c
Python program:
a = 680 / 50
b = math.floor(a)
c = 12 * 2
d = b * c
e = 680 / 50
f = math.floor(e)
g = f * 50
h = 680 - g
i = h / 2
j = math.floor(i)
k = d + j
Problem: in the land of oz only one or two - letter words are used . the local language has 65 different letters . the parliament decided to forbid the use of the seventh letter . how many words have the people of oz lost because of the prohibition ?
Options: a ) 65 , b ) 66 , c ) 67 , d ) 131 , e ) 130
Rationale: the answer to the question is indeed e . the problem with above solutions is that they do not consider words like aa , bb , . . . the number of 1 letter words ( x ) that can be made from 65 letters is 65 ; the number of 2 letter words ( xx ) that can be made from 65 letters is 65 * 65 , since each x can take 65 values . total : 65 + 65 * 65 . similarly : the number of 1 letter words ( x ) that can be made from 64 letters is 64 ; the number of 2 letter words ( xx ) that can be made from 64 letters is 64 * 64 , since each x can take 64 values . total : 64 + 64 * 64 . the difference is ( 65 + 65 * 65 ) - ( 64 + 64 * 64 ) = 130 . answer : e .
Answer: e
Python program:
a = 1 + 65 
b = a + 65
Problem: baker ram is storing cake boxes in cartons that measure 25 inches by 42 inches by 60 inches . if the measurement of each cake box is 8 inches by 7 inches by 5 inches , then what is the maximum number of cake boxes that can be placed in each carton ?
Options: a ) 330 , b ) 300 , c ) 252 , d ) 225 , e ) 210
Rationale: baker ram is storing cake boxes in cartons the dimensions of the carton are 25 x 42 x 60 and those of each cake box are 8 x 7 x 5 . to maximize number of boxes try and fit maximum into the base of the box . if you take the base as 25 x 42 and fit 5 x 6 boxes of 5 x 7 , then the total number of boxes is 5 x 6 x integer ( 60 / 8 ) = 5 x 6 x 7 = 210 . alternatively you could try taking the base as 60 x 42 and fit 12 x 6 boxes of 5 x 7 , then the total number of boxes is 12 x 6 x integer ( 25 / 8 ) = 12 x 6 x 3 = 216 . but since that is not an answer option , i go with ( e ) 210 .
Answer: e
Python program:
a = 4 + 2 
b = a * 7
c = b * 5
Problem: a 40 - liter solution of alcohol and water is 5 percent alcohol . if 4.5 liters of alcohol and 5.5 liters of water are added to this solution , what percent of the solution produced is alcohol ?
Options: a ) 7 % , b ) 10 % , c ) 13 % , d ) 16 % , e ) 19 %
Rationale: the percent of alcohol in the solution is ( 0.05 ( 40 ) + 4.5 ) / 50 = 6.5 / 50 = 13 % the answer is c .
Answer: c
Python program:
a = 5 / 100
b = 40 * a
c = b + 4 
d = 4 + 5 
e = 40 + d 
f = c / e
g = f * 100