euclaise/mathqa_programs huggingface dataset:
Problem: in a mayoral election , candidate x received 1 / 5 more votes than candidate y , and candidate y received 1 / 2 fewer votes than z . if z received 20,000 votes how many votes did candidate x received ?
Options: a ) 12000 , b ) 22000 , c ) 24000 , d ) 26000 , e ) 32000
Rationale: "z = 20 - - > y received 1 / 2 fewer votes than z - - > y = z - 1 / 2 * z = 10 ; x received 1 / 5 more votes than y - - > x = y + 1 / 5 * y = 12 . answer : a ."
Answer: a
Python program:
a = 5 / 2
b = 1 - a
c = const_0_25 * 100
d = c * 100
e = d * 10
f = b * e
g = 1 / 5
h = g + 1 
i = f * h
Problem: ages of two persons differ by 22 years . if 6 year ago , the elder one be 3 times as old the younger one , find their present age
Options: a ) 12,28 , b ) 14,30 , c ) 17,39 , d ) 18,34 , e ) 19,34
Rationale: "explanation : let the age of younger person is x , then elder person age is ( x + 22 ) = > 3 ( x - 6 ) = ( x + 22 - 6 ) [ 6 years before ] = > 3 x - 18 = x + 16 = > x = 17 . so other person age is x + 22 = 39 answer : option c"
Answer: c
Python program:
a = 6 * 6
b = a + 22 
c = b - 6
d = 6 - 1
e = c / d
f = e - 1
Problem: a basket of 1430 apples is divided equally among a group of apple lovers . if 45 people join the group , each apple lover would receive 9 apples less . how many w apples did each person get before 45 people joined the feast ?
Options: a ) 20 . , b ) 21 . , c ) 22 . , d ) 23 . , e ) 24 .
Rationale: "before solving it algebraically , let us prime factorize 1430 = 2 * 5 * 11 * 13 . since number of apples per person * total persons w = 1430 , the answer should be a factor of 1430 . only c is . and that ' s your answer . c"
Answer: c
Python program:
a = 10 + 10 
b = a + 2 
c = 1430 / b
d = c + 45 
e = 1430 / d
f = e + 9
Problem: a watch was sold at a loss of 10 % . if it was sold for rs . 280 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) s : 2000 , b ) s : 1067 , c ) s : 1278 , d ) s : 1028 , e ) s : 1027
Rationale: "90 % 104 % - - - - - - - - 14 % - - - - 280 100 % - - - - ? = > rs : 2000 answer : a"
Answer: a
Python program:
a = 280 * 100
b = 100 + 4 
c = 100 - 10
d = b - c
e = a / d
Problem: a man can row his boat with the stream at 18 km / h and against the stream in 8 km / h . the man ' s rate is ?
Options: a ) 5 kmph , b ) 2 kmph , c ) 7 kmph , d ) 8 kmph , e ) 3 kmph
Rationale: "ds = 18 us = 8 s = ? s = ( 18 - 8 ) / 2 = 5 kmph answer : a"
Answer: a
Python program:
a = 18 - 8
b = a / 2
Problem: free notebooks were distributed equally among children of a class . the number of notebooks each child got was one - eighth of the number of children . had the number of children been half , each child would have got 16 notebooks . how many notebooks were distributed in all ?
Options: a ) 432 , b ) 640 , c ) 256 , d ) 512 , e ) none of these
Rationale: "in case i : let the no . of children = x . hence , total no . of notebooks distributed 1 ⁄ 8 x . x or x 2 ⁄ 8 . . . . . . . ( i ) in case ii : no . of children = x ⁄ 2 now , the total no . of notebooks = 16 × x ⁄ 2 . . . . . . . ( ii ) comparing ( i ) & ( ii ) , we get x 2 ⁄ 8 = 8 x or , x = 64 hence , total no . of notebooks = 64 × 64 / 8 = 512 answer d"
Answer: d
Python program:
a = 16 / 2
b = 16 / 2
c = a * b
d = 16 / 2
e = c * d
Problem: one pipe can fill a tank 3 times as fast as another pipe . if together the two pipes can fill tank in 40 min , then the slower pipe alone will be able to fill the tank in ?
Options: a ) 160 , b ) 787 , c ) 144 , d ) 128 , e ) 121
Rationale: let the slower pipe alone fill the tank in x min . then , faster pipe will fill it in x / 3 min . 1 / x + 3 / x = 1 / 40 4 / x = 1 / 40 = > x = 160 min . answer : a
Answer: a
Python program:
a = 3 + 1 
b = 1 / a
c = 40 / b
Problem: 1500 is increased by 20 % . find the final number .
Options: a ) 1500 , b ) 1800 . , c ) 1900 , d ) 1700 , e ) 1660
Rationale: final number = initial number + 20 % ( original number ) = 1500 + 20 % ( 1500 ) = 1500 + 300 = 1800 . answer b
Answer: b
Python program:
a = 20 / 100
b = 1500 * a
c = 1500 + b
Problem: the perimeter of an equilateral triangle is 60 . if one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 50 , then how long is the base of isosceles triangle ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: "the base of the isosceles triangle is 50 - 20 - 20 = 10 units the answer is b ."
Answer: b
Python program:
a = 60 / 3
b = 50 - a
c = 60 / 3
d = b - c
Problem: a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 1 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ?
Options: a ) 480 , b ) 120 , c ) 289 , d ) 270 , e ) 927
Rationale: "1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 1 = 120 answer : b"
Answer: b
Python program:
a = 24 * 20
Problem: ( 0.5 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.5 ) ( power 2 ) + 0.05 + ( 0.1 ) ( power 2 ) is :
Options: a ) 0.8 , b ) 0.4 , c ) 0.96 , d ) 0.69 , e ) 0.76
Rationale: "given expression = ( 0.5 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.5 ) ( power 2 ) + ( 0.5 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.5 - 0.1 ) = 0.4 answer is b"
Answer: b
Python program:
a = 0 ** 5
b = 0 ** 1
c = a - b
d = 0 ** 5
e = d + 0 
f = 0 ** 1
g = e + f 
h = c / g
Problem: if p is a prime number greater than 3 , find the remainder when p ^ 2 + 17 is divided by 12 .
Options: a ) 6 , b ) 1 , c ) 0 , d ) 8 , e ) 7
Rationale: "take any prime number greater than 3 and check - say p = 5 so , p ^ 2 + 17 = 25 + 17 = > 42 42 / 12 will have remainder as 6 say p = 7 so , p ^ 2 + 17 = 49 + 17 = > 66 66 / 12 will have remainder as 6 so answer will be ( a ) 6"
Answer: a
Python program:
a = 1 + 4 
b = a ** 2
c = 17 + b 
d = 12 * 3
e = c - d
Problem: 9.8 , 9.8 , 9.9 , 9.9 , 10.0 , 10.0 , 10.1 , 10.5 the mean and the standard deviation of the 8 numbers shown above is 10 and 0.212 respectively . what percent of the 8 numbers are within 1 standard deviation of the mean ?
Options: a ) 90.5 % , b ) 87.5 % , c ) 80.5 % , d ) 77.5 % , e ) 70.5 %
Rationale: within 1 standard deviation of the mean - means in the range { mean - 1 * sd ; mean + 1 * sd } = { 10 - 1 * 0.212 ; 10 + 0.3 } = { 9.788 ; 10.212 } . from the 8 listed numbers , 7 are within this range so 6 / 8 = 87.5 % . answer : b .
Answer: b
Python program:
a = 8 - 1
b = a / 8
c = b * 100
Problem: at the opening of a trading day at a certain stock exchange , the price per share of stock m was $ 25 . if the price per share of stock m was $ 28 at the closing of the day , what was the percent increase in the price per share of stock m for that day ?
Options: a ) 1.4 % , b ) 5.9 % , c ) 12 % , d ) 12.5 % , e ) 23.6 %
Rationale: "opening = 25 closing = 28 rise in price = 3 so , percent increase = 3 / 25 * 100 = 12 answer : c"
Answer: c
Python program:
a = 28 / 25
b = a - 1
c = b * 100
Problem: the average of 13 numbers is 60 . average of the first 7 of them is 57 and that of the last 7 is 61 . find the 8 th number ?
Options: a ) 43 , b ) 30 , c ) 35 , d ) 45 , e ) 50
Rationale: "sum of all the 13 numbers = 13 * 60 = 780 sum of the first 7 of them = 7 * 57 = 399 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 427 + 399 - 780 = 46 . answer a"
Answer: a
Python program:
a = 8 * 61
b = 13 * 60
c = 57 * 7
d = b - c
e = a - d
Problem: martin bought 10 concert tickets , some at the full price of $ 2.00 per ticket , and some at a discounted price of $ 1.60 per ticket . if he spent a total of $ 19.20 , how many discounted tickets did he buy ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 2
Rationale: "let x be the number of tickets he bought at $ 2 per ticket . then 2 x + ( 10 - x ) 1.6 = 19.2 0.4 x = 3.2 = > x = 8 discounted tickets = 10 - x = 2 ans : e"
Answer: e
Python program:
a = 10 * 2
b = 1 * 60
c = a - b
Problem: the length of a rectangular field is 7 / 5 its width . if the perimeter of the field is 360 meters , what is the width of the field ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 75
Rationale: "let l be the length and w be the width . l = ( 7 / 5 ) w perimeter : 2 l + 2 w = 360 , 2 ( 7 / 5 ) w + 2 w = 360 solve the above equation to find : w = 75 m and l = 105 m . correct answer e ) 75"
Answer: e
Python program:
a = 7 / 5
b = 7 / 5
c = a + b 
d = c + 2 
e = 360 / d
Problem: the salary of a typist was at first raised by 10 % and then the same was reduced by 5 % . if he presently draws rs . 2090 . what was his original salary ?
Options: a ) 2277 , b ) 2999 , c ) 1000 , d ) 2651 , e ) 2000
Rationale: "x * ( 110 / 100 ) * ( 95 / 100 ) = 2090 x * ( 11 / 10 ) * ( 1 / 100 ) = 22 x = 2000 answer : e"
Answer: e
Python program:
a = 10 / 100
b = 1 + a 
c = 5 / 100
d = 1 - c
e = b * d
f = 2090 / e
Problem: given f ( x ) = 2 x – 3 , for what value of x does 2 * [ f ( x ) ] – 21 = f ( x – 4 ) ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "2 ( 2 x - 3 ) - 21 = 2 ( x - 4 ) - 3 2 x = 16 x = 8 the answer is e ."
Answer: e
Python program:
a = 2 * 3
b = a + 21 
c = 2 * 4
d = c + 3 
e = b - d
f = 2 * 2
g = 2 * 1
h = f - g
i = e / h
Problem: a train passes a platform in 40 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is
Options: a ) 280 meter , b ) 240 meter , c ) 200 meter , d ) 300 meter , e ) none of these
Rationale: "explanation : speed of the train = 54 km / hr = ( 54 × 10 ) / 40 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 40 = > 300 + l = 15 × 40 = 600 = > l = 600 - 300 = 300 meter answer : option d"
Answer: d
Python program:
a = const_0_2778 * 54
b = 40 - 20
c = a * b
Problem: a train running at the speed of 40 km / hr crosses a pole in 27 seconds . what is the length of the train ?
Options: a ) 250 , b ) 300 , c ) 350 , d ) 400 , e ) 450
Rationale: "speed = ( 40 * 5 / 18 ) m / sec = ( 100 / 9 ) m / sec length of the train = ( speed x time ) = ( 100 / 9 * 29 ) m = 300 m . answer : b"
Answer: b
Python program:
a = 40 * 1000
b = a / 3600
c = b * 27
Problem: find the least number of 5 digits , which is exactly divisible by 89 .
Options: a ) 27 , b ) 37 , c ) 932 , d ) 12 , e ) 91
Rationale: answer : a
Answer: a
Python program:
a = 10 * 1000
b = a - 1
c = b / 89
d = c + 1 
e = math.floor(d)
f = e * 89
g = f / 4
h = g / 100
i = h + 2
Problem: a rope of which a calf is tied is increased from 16 m to 23 m , how much additional grassy ground shall it graze ?
Options: a ) 1217 , b ) 1219 , c ) 1210 , d ) 1212 , e ) 858
Rationale: "π ( 232 – 162 ) = 858 answer : e"
Answer: e
Python program:
a = 23 ** 2
b = 10 ** 2
c = a - b
d = 16 * 2
e = d + 2 
f = 4 + 3 
g = e / f
h = c * g
Problem: there is a rectangular prism made of 1 in cubes that has been covered in tin foil . there are exactly 128 cubes that are not touching any tin foil on any of their sides . if the width of the figure created by these 128 cubes is twice the length and twice the height , what is the measure m in inches of the width of the foil covered prism ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 10
Rationale: "if the width is w , then length and height would be w / 2 . so , w * w / 2 * w / 2 = 128 = > w ^ 3 = ( 2 ^ 3 ) * 64 = ( 2 ^ 3 ) * ( 4 ^ 3 ) = > w = 2 * 4 m = 8 in . along the width of the cuboid , 8 cubes do n ' t touch the tin foil . so the actual width will be non - touching cubes + touching cubes = 8 + 2 = 10 ans e ."
Answer: e
Python program:
a = 1 * 2
b = 1 * a
c = 128 / b
d = 1/(3)
e = c ** d
f = 1 * 2
g = e * f
h = 1 * 2
i = g + h
Problem: the sum of all consecutive odd integers from − 23 to 31 , inclusive , is
Options: a ) 96 , b ) 112 , c ) 158 , d ) 192 , e ) 235
Rationale: the sum of the odd numbers from - 23 to + 23 is 0 . let ' s add the remaining numbers . 25 + 27 + 29 + 31 = 112 the answer is b .
Answer: b
Python program:
a = 23 + 2 
b = 23 + 2 
c = b + 2 
d = a + c 
e = 23 + 2 
f = e + 2 
g = f + 2 
h = d + g 
i = h + 31
Problem: david obtained 76 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology what are his average marks ?
Options: a ) 75 , b ) 37 , c ) 26 , d ) 97 , e ) 27
Rationale: "average = ( 76 + 65 + 82 + 67 + 85 ) / 5 = 375 / 5 = 75 . answer : a"
Answer: a
Python program:
a = 76 + 65 
b = a + 82 
c = b + 67 
d = c + 85 
e = 2 + 3 
f = d / e
Problem: in a kilometer race , a beats b by 80 meters or 8 seconds . what time does a take to complete the race ?
Options: a ) 77 sec , b ) 92 sec , c ) 67 sec , d ) 16 sec , e ) 76 sec
Rationale: time taken by b run 1000 meters = ( 1000 * 8 ) / 80 = 100 sec . time taken by a = 100 - 8 = 92 sec . answer : b
Answer: b
Python program:
a = 1 * 1000
b = 80 / 8
c = a / b
d = c - 8
Problem: the least number which when divided by 5 , 6 , 7 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder , is
Options: a ) 1677 , b ) 1683 , c ) 2523 , d ) 3363 , e ) none of these
Rationale: explanation : l . c . m of 5 , 6 , 7 , 8 = 840 therefore required number is of the form 840 k + 3 . least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 therefore required number = ( 840 x 2 + 3 ) = 1683 . answer : b
Answer: b
Python program:
a = math.lcm(5, 6)
b = math.lcm(a, 7)
c = math.lcm(b, 8)
d = c * 2
Problem: a policeman noticed a criminal from a distance of 240 km . the criminal starts running and the policeman chases him . the criminal and the policeman run at the rate of 8 km and 9 km per hour respectively . what is the distance between them after 3 minutes ?
Options: a ) 100 m , b ) 120 m , c ) 190 m , d ) 150 m , e ) none of these
Rationale: "explanation : solution : relative speed = ( 9 - 8 ) = 1 km / hr . distance covered in 3 minutes = ( 1 * 3 / 60 ) km = 1 / 20 km = 50 m . . ' . distance between the criminal and policeman = ( 240 - 50 ) m = 190 m . answer : c"
Answer: c
Python program:
a = 3 / const_60
b = a * 1000
c = 240 - b
Problem: what least number must be added to 1120 , so that the sum is completely divisible by 23 ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "49 * 23 = 1127 1127 - 1120 = 7 answer : e"
Answer: e
Python program:
a = 4 * 10
b = a + 2 
c = b * 23
d = c - 1120
Problem: 24 men can complete a work in 16 days . 32 women can complete the same work in 24 days . 16 men and 16 women started working and worked for 12 days . how many more men are to be added to complete the remaining work in 2 days ?
Options: a ) 16 , b ) 24 , c ) 36 , d ) 48 , e ) 49
Rationale: explanation : 1 man ’ s 1 day work = 1 / 384 1 woman ’ s 1 day work = 1 / 768 work done in 12 days = 12 ( 16 / 384 + 16 / 768 ) = 12 * 3 / 48 = 3 / 4 remaining work = 1 / 4 ( 16 men + 16 women ) ’ s 2 day work = 2 ( 16 / 384 + 16 / 768 ) = 1 / 8 remaining work = 1 / 4 - 1 / 8 = 1 / 8 1 / 384 work is done in 1 day by 1 man 1 / 8 work will be done in 2 days by 384 x 1 / 8 x 1 / 2 = 24 men answer : option b
Answer: b
Python program:
a = 24 * 2
b = a - 24
Problem: at an elementary school , 60 % of the faculty members are women and 60 % of the faculty members are married . if 3 / 4 of the men are single , what fraction of the women are married ?
Options: a ) 5 ⁄ 7 , b ) 7 ⁄ 10 , c ) 1 ⁄ 3 , d ) 7 ⁄ 30 , e ) 5 ⁄ 6
Rationale: "2 x 2 table works perfect : - - - - - - - - - - - - - - - - - - - - m - - - - - - w - - - - - - - - total marrried - - - - - - - - - 10 - - - - - 50 - - - - - - - - - 60 not married - - - - - 30 - - - - - 10 - - - - - - - - - 40 total - - - - - - - - - - - - - 40 - - - - - 60 - - - - - - - - 100 need married woman / total woman , so 50 / 60 = 5 / 6 e"
Answer: e
Python program:
a = 3 / 4
b = 1 - a
Problem: the manager of a produce market purchased a quantity of tomatoes for $ 0.80 per pound . due to improper handling , 10 percent of the tomatoes , by weight , were ruined and discarded . at what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 8 percent of the cost of the tomatoes .
Options: a ) $ 0.94 , b ) $ 0.96 , c ) $ 0.98 , d ) $ 1.00 , e ) $ 1.20
Rationale: "assume the manager bought 100 tomatoes . cost price = 80 given : 10 % are damaged - - > available tomatoes to sell = 90 90 * x - 80 = 0.08 * 80 90 x - 80 = 6.4 90 x = 86.64 x = 86.64 / 90 = 87 / 90 ( approx ) = 29 / 30 = 0.966 x is slightly under 0.9666 = 0.96 answer : b"
Answer: b
Python program:
a = 8 / 100
b = 1 + a 
c = 100 - 10
d = c / 100
e = 0 / 80
f = b * e
Problem: a group of men decided to do a work in 50 days , but 10 of them became absent . if the rest of the group did the work in 60 days , find the original number of men ?
Options: a ) 60 , b ) 50 , c ) 40 , d ) 100 , e ) 25
Rationale: "original number of men = 10 * 60 / ( 60 - 50 ) = 60 answer is a"
Answer: a
Python program:
a = 10 * 60
b = 60 - 50
c = a / b
Problem: 30 % of a number is more than 60 % of 50 by 30 . find the number ?
Options: a ) 120 , b ) 200 , c ) 180 , d ) 300 , e ) 140
Rationale: "( 30 / 100 ) * x – ( 60 / 100 ) * 50 = 30 2 / 7 x = 60 x = 200 answer : b"
Answer: b
Python program:
a = 50 * 60
b = a / 100
c = b + 30 
d = c * 100
e = d / 30
Problem: operation # is defined as adding a randomly selected two digit multiple of 8 to a randomly selected two digit prime number and reducing the result by half . if operation # is repeated 10 times , what is the probability that it will yield at least two integers ?
Options: a ) 0 % , b ) 10 % , c ) 20 % , d ) 30 % , e ) 40 %
Rationale: any multiple of 8 is even . any two - digit prime number is odd . ( even + odd ) / 2 is not an integer . thus # does not yield an integer at all . therefore p = 0 . answer : a .
Answer: a
Python program:
a = 10 + 3 
b = 8 + a 
c = b / 2
Problem: right triangle abc is the base of the prism in the figure above . if ab = ac = â ˆ š 10 and the height of the prism is 4 , what is the volume of the prism ?
Options: a ) 40 , b ) 85 , c ) 20 , d ) 60 , e ) 45
Rationale: "volume of prism = area of base * height = 1 / 2 * ( square root of 10 ) * ( square root of 10 ) * 4 = 20 answer : c"
Answer: c
Python program:
a = math.sqrt(10)
b = math.sqrt(10)
c = volume_rectangular_prism / (
Problem: a woman swims downstream 54 km and upstream 6 km taking 6 hours each time , what is the speed of the woman in still water ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "54 - - - 6 ds = 9 ? - - - - 1 6 - - - - 6 us = 1 ? - - - - 1 m = ? m = ( 9 + 1 ) / 2 = 5 answer : d"
Answer: d
Python program:
a = 54 / 6
b = 6 / 6
c = a + b 
d = c / 2
Problem: what is the least number which when divided by 7 , 9 , 12 and 18 leaves remainder 4 in each care ?
Options: a ) 230 , b ) 240 , c ) 236 , d ) 256 , e ) 266
Rationale: "explanation : lcm of 7 , 9 , 12 and 18 is 252 required number = 252 + 4 = 256 answer : option d"
Answer: d
Python program:
a = math.lcm(7, 9)
b = math.lcm(12, 18)
c = math.lcm(a, b)
d = c + 4
Problem: how many points ( x , y ) lie on the line segment between ( 15 , 12 2 / 3 ) and ( 7 , 17 2 / 3 ) such that x and y are both integers ?
Options: a ) 1 , b ) 5 , c ) 7 , d ) 8 , e ) 9
Rationale: slope = ( 17 2 / 3 - 12 2 / 3 ) / ( 7 - 15 ) = - 5 / 8 y = mx + b = > 12 2 / 3 = - 15 * 5 / 8 + b = > b = 1 y = - 75 x / 8 + 22 only integer values work , and the only multiples of 8 between 7 and 15 for x value is 8 , thus 1 point . a
Answer: a
Python program:
a = 7 / 7
Problem: a statue is being carved by a sculptor . the original piece of marble weighed 250 kg . in the first week 30 per cent is cut away . in the second week 20 per cent of the remainder is cut away . in the third week the statue is completed when 25 percent of the remainder is cut away . what is the weight of the final statue ?
Options: a ) 105 kg , b ) 145 kg , c ) 165 kg , d ) 115 kg , e ) 100 kg
Rationale: "a 105 kg = 250 ã — 0.7 ã — 0.8 ã — 0.75 ."
Answer: a
Python program:
a = 25 / 100
b = 1 - a
c = 20 / 100
d = 1 - c
e = 30 / 100
f = 1 - e
g = 250 * f
h = d * g
i = b * h
Problem: a bowl was filled with 10 ounces of water , and 0.008 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.004 % , b ) 0.04 % , c ) 0.40 % , d ) 4 % , e ) 40 %
Rationale: "total amount of water evaporated each day during a 50 - day period = . 008 * 50 = . 008 * 100 / 2 = . 8 / 2 = . 4 percent of the original amount of water evaporated during this period = ( . 4 / 10 ) * 100 % = 4 % answer d"
Answer: d
Python program:
a = 50 * 0
b = a / 10
c = b * 100
Problem: a goods train runs at the speed of 72 km / hr and crosses a 260 m long platform in 26 sec . what is the length of the goods train ?
Options: a ) 278 , b ) 166 , c ) 151 , d ) 260 , e ) 109
Rationale: speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 260 ) / 26 = 20 x = 260 m . answer : d
Answer: d
Python program:
a = 72 / 3600
b = a * 1000
c = b * 26
d = c - 260
Problem: when positive integer n is divided by positive integer j , the remainder is 12 . if n / j = 134.08 , what is value of j ?
Options: a ) 22 , b ) 56 , c ) 78 , d ) 112 , e ) 150
Rationale: "1 ) we know that decimal part of decimal quotient = { remainder / divisor } so 0.08 , the decimal part of the decimal quotient , must equal the remainder , 12 , divided by the divisor j . 0.08 = 12 / j 0.08 * j = 12 j = 12 / 0.08 = 1200 / 8 = 300 / 2 = 150 so j = 150 , answer = e ."
Answer: e
Python program:
a = 4 * 10
b = a + 2 
c = 100 + b 
d = 134 - 8
e = 12 / d
Problem: q is a set of 8 distinct prime numbers . if the sum of the integers in q is even and the number x is a member of q , then what is the least value that x can be ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 7
Rationale: 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 = 77 ( discard as sum is odd ) 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 = 98 ( sum is even ) least number = 3 b
Answer: b
Python program:
a = 8 / 4
b = a + 1
Problem: in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 58 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320.40 $ , b ) 383.40 $ , c ) 420.40 $ , d ) 450.40 $ , e ) 473.40 $
Rationale: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 58 ) = 473.40 hence answer will be ( e )"
Answer: e
Python program:
a = 0 * 65
b = a * 12
Problem: in the xy - plane , a triangle has vertices ( 0,0 ) , ( 4,0 ) and ( 4,7 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ?
Options: a ) 4 / 7 , b ) 2 / 3 , c ) 3 / 5 , d ) 3 / 7 , e ) 1 / 2
Rationale: "the area of the right triangle is ( 1 / 2 ) * 4 * 7 = 14 . only the points ( a , b ) below the line y = x satisfy a - b > 0 . the part of the triangle which is below the line y = x has an area of ( 1 / 2 ) ( 4 ) ( 4 ) = 8 . p ( a - b > 0 ) = 8 / 14 = 4 / 7 the answer is a ."
Answer: a
Python program:
a = 0 + 0 
b = 4 / a
Problem: ( 565945 x 121 ) = ?
Options: a ) 68463812 , b ) 68463813 , c ) 68479345 , d ) 68463814 , e ) 68463814
Rationale: 565945 * 121 = 68479345 ans c
Answer: c
Python program:
a = 4 + 1 
b = a ** 4
c = 565945 * b
Problem: mixture a is 20 percent alcohol , and mixture b is 50 percent alcohol . if the two are poured together to create a 15 gallon mixture that contains 30 percent alcohol , approximately how many gallons of mixture a are in the mixture ?
Options: a ) 3 gallons , b ) 4 gallons , c ) 5 gallons , d ) 10 gallons , e ) 12 gallons
Rationale: let a = number of gallons on mixture a in 15 gallon mixture b = number of gallons on mixture b in 15 gallon mixture ( 20 / 100 ) a + ( 50 / 100 ) b = ( 30 / 100 ) ( a + b ) - - 1 a + b = 15 - - 2 on solving equations 1 and 2 , we get a = 10 b = 5 answer d 10 gallons
Answer: d
Python program:
a = 20 * 50
b = a / 50
c = b / 2
Problem: sum of two numbers prime to each other is 14 and their l . c . m . is 45 . what are the numbers ?
Options: a ) 6 and 5 , b ) 8 and 5 , c ) 9 and 5 , d ) 8 and 5 , e ) 3 and 5
Rationale: "as two numbers are prime , satisfies all but option c will make the product of numbers i . e 45 answer : c"
Answer: c
Python program:
a = 45 + 14