euclaise/mathqa_programs huggingface dataset:
Problem: louie takes out a 3 - month loan of $ 2000 . the lender charges him 10 % interest per month compounded monthly . the terms of the loan state that louie must repay the loan in 3 equal monthly payments . to the nearest dollar , how much does louie have to pay each month ?
Options: a ) a ) 333 , b ) b ) 383 , c ) c ) 402 , d ) d ) 433 , e ) e ) 804
Rationale: here ' s the calculation for that case , assume monthly payment is x . after 1 st month : ( 2000 ) ( 1.1 ) - x = 2200 - x after 2 nd month : ( 2200 - x ) ( 1.1 ) - x = 2420 - 2.21 x after 3 rd month : ( 2420 - 2.21 x ) ( 1.1 ) - x = 2662 - 3.31 x now , the amount after the last payment in 3 rd month must bring the total to 0 . hence : 2662 - 3.31 x = 0 x = 2662 / 3.31 = 804 answer e
Answer: e
Python program:
a = 1 / 10
b = 1 + a 
c = 2000 * b
d = 1 / 10
e = 1 + d 
f = c * e
g = f / 3
Problem: 50 ^ 51 ^ 52 / 11
Options: a ) 6 , b ) 4 , c ) 7 , d ) 3 , e ) 5
Rationale: "we know that 6 ^ 1 = 6 or 6 ^ 2 = 36 so for all power of 6 unit digit is 6 now que is 50 ^ 51 ^ 52 now if we divide 50 / 11 then rem is 6 means 6 ^ 51 = 6 at unit place same for 6 ^ 52 salso give 6 at unit place now finally 50 ^ 51 ^ 52 gives 6 at unit place now 6 / 11 = 6 answer : a"
Answer: a
Python program:
a = 50 ** 51
b = 50 ** 11
c = a / b
Problem: some of 50 % - intensity red paint is replaced with 25 % solution of red paint such that the new paint intensity is 45 % . what fraction of the original paint was replaced ?
Options: a ) 1 / 30 , b ) 1 / 5 , c ) 2 / 3 , d ) 3 / 4 , e ) 4 / 5
Rationale: "45 % is 20 % - points above 25 % and 5 % - points below 50 % . thus the ratio of 25 % - solution to 50 % - solution is 1 : 4 . 1 / 5 of the original paint was replaced . the answer is b ."
Answer: b
Python program:
a = 45 / 100
b = 50 / 100
c = a - b
d = 25 / 100
e = 50 / 100
f = d - e
g = c / f
Problem: if a certain toy store ' s revenue in november was 3 / 5 of its revenue in december and its revenue in january was 1 / 3 of its revenue in november , then the store ' s revenue in december was how many times the average ( arithmetic mean ) of its revenues in november and january ?
Options: a ) 5 / 2 , b ) 7 / 2 , c ) 10 / 3 , d ) 15 / 4 , e ) 25 / 3
Rationale: "n = 3 d / 5 j = n / 3 = d / 5 the average of november and january is ( n + j ) / 2 = 4 d / 5 / 2 = 2 d / 5 d is 5 / 2 times the average of november and january . the answer is a ."
Answer: a
Python program:
a = 3 / 5
b = 3 / 5
c = 1 / 3
d = b * c
e = a + d 
f = e / 2
g = 1 / f
Problem: the cross - section of a cannel is a trapezium in shape . if the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross - section is 640 sq m , the depth of cannel is ?
Options: a ) 76 , b ) 28 , c ) 27 , d ) 80 , e ) 25
Rationale: "1 / 2 * d ( 10 + 6 ) = 640 d = 80 answer : d"
Answer: d
Python program:
a = 10 + 6 
b = a / 2
c = 640 / b
d = c / 6
e = d / 2
Problem: the jogging track in a sports complex is 528 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?
Options: a ) 5.29 min , b ) 3.84 min , c ) 5.08 min , d ) 9.28 min , e ) 5.988 min
Rationale: "clearly , the two will meet when they are 528 m apart . to be ( 4.5 + 3.75 ) = 8.25 km apart , they take 1 hour . to be 528 m apart , they take ( 100 / 825 * 528 / 1000 ) hrs = ( 528 / 8250 * 60 ) min = 3.84 min . answer : b"
Answer: b
Python program:
a = 528 / 1000
b = 4 + 5 
c = a / b
d = c * const_60
Problem: a certain elevator has a safe weight limit of 2,500 pounds . what is the greatest possible number of people who can safely ride on the elevator at one time with the average ( arithmetic mean ) weight of half the riders being 200 pounds and the average weight of the others being 230 pounds ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "lets assume there are 2 x people . half of them have average weight of 200 and other half has 230 . maximum weight is = 2500 so 200 * x + 230 * x = 2500 = > 430 x = 2500 = > x is approximately equal to 6 . so total people is 2 * 6 = 12 we are not taking 12 as answer because say 11 th person has minimum of 180 weight then 200 * 6 + 230 * 6 = 2580 ( which is more than 2500 ) answer e ."
Answer: e
Python program:
a = 10 * 200
b = 200 + 230 
c = a / b
d = c * 2
Problem: the ratio of two quantities is 7 to 12 . if each of the quantities is divided by 3 , what is the ratio of these 2 new quantities ?
Options: a ) 3.5 : 6 , b ) 14 : 24 , c ) 7 : 12 , d ) 2.3 : 4 , e ) it can not be determined from the information given
Rationale: "if both sides of a ratio are divided by the same number there is no change in the ratio . 5 : 6 means 7 x : 12 x . . . the ratio starts as 7 / ( 1 ) : 12 / ( 1 ) . so when you diveide by three it becomes 7 / ( 3 ) : 12 / ( 3 ) . . so if the xs are equal the ratio does not change . . answer : c"
Answer: c
Python program:
a = 7 + 3 
b = 12 + 3 
c = a / b
Problem: if 45 % of z is 72 % of y and y is 75 % of x , what percent of x is z ?
Options: a ) 200 , b ) 120 , c ) 100 , d ) 65 , e ) 50
Rationale: "( 45 / 100 ) z = ( 72 / 100 ) y and y = ( 75 / 100 ) x i . e . y = ( 3 / 4 ) x i . e . ( 45 / 100 ) z = ( 72 / 100 ) * ( 3 / 4 ) x i . e . z = ( 72 * 3 ) x / ( 45 * 4 ) i . e . z = ( 1.2 ) x = ( 120 / 100 ) x i . e . z is 120 % of x answer : option b"
Answer: b
Python program:
a = 75 / 100
b = 45 / 100
c = 72 / 100
d = b / c
e = a / d
f = e * 100
Problem: a certain car can travel 40 minutes on a gallon of gasoline at 70 miles per hour . if the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end , then what percent of the tank was used to travel 80 miles at 60 mph ?
Options: a ) 15 % , b ) 30 % , c ) 25 % , d ) 20 % , e ) 40 %
Rationale: let , tank capacity = t gallon used fuel = ( t - 8 ) gallons distance travelled ( @ 70 miles / hr ) = 80 miles distance travelled in 1 gallon = distance travelled in 40 mins ( @ 60 miles / hr ) = ( 70 / 70 ) * 40 = 40 miles fuel used to travel 80 miles = ( 80 / 40 ) = 2 gallon i . e . used fuel = ( t - 8 ) = 2 gallon i . e . t = 10 gallons i . e . used fuel = ( 2 / 10 ) * 100 = 20 % d
Answer: d
Python program:
a = 40 * 70
b = 80 * 60
c = a / b
d = 40 * 70
e = 80 * 60
f = d / e
g = f + 8 
h = c / g
Problem: on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 420 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 600 , b ) 620 , c ) 500 , d ) 520 , e ) 840
Rationale: "let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 420 ) = 2 + 2 ( extra ) = > 2 x - 840 = x = > x = 840 . answer : e"
Answer: e
Python program:
a = 420 * 2
Problem: population of a city in 20004 was 1200000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45 % , then find the population of city at the end of the year 2007
Options: a ) 354354 , b ) 545454 , c ) 465785 , d ) 456573 , e ) 1300650
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 1300650 e"
Answer: e
Python program:
a = 15 / 100
b = 1 + a 
c = 35 / 100
d = 1 - c
e = b * d
f = 35 / 100
g = 1 + f 
h = e * g
i = 1200000 * h
Problem: two trains 111 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 4.85 , b ) 7.85 , c ) 6.85 , d ) 5.85 , e ) 6.15
Rationale: t = ( 111 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 6.85 answer : c
Answer: c
Python program:
a = 111 + 165 
b = 80 + 65 
c = b * const_0_2778
d = a / c
Problem: working alone , mary can pave a driveway in 5 hours and hillary can pave the same driveway in 2 hours . when they work together , mary thrives on teamwork so her rate increases by 33.33 % , but hillary becomes distracted and her rate decreases by 50 % . if they both work together , how many hours will it take to pave the driveway ?
Options: a ) 2 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: "initial working rates : mary = 1 / 5 per hour hillary = 1 / 2 per hour rate when working together : mary = 1 / 5 + ( 1 / 3 * 1 / 5 ) = 1 / 4 per hour hillary = 1 / 2 - ( 1 / 2 * 1 / 2 ) = 1 / 4 per hour together they work 1 / 4 + 1 / 4 = 1 / 2 per hour so they will need 2 hours to complete the driveway . the correct answer is a ."
Answer: a
Python program:
a = 1 / 5
b = 33 / 33
c = b + 1 
d = a * c
e = 1 / 2
f = 50 / 100
g = e * f
h = d + g 
i = 1/(h)
Problem: the two lines y = x and x = - 2 intersect on the coordinate plane . if z represents the area of the figure formed by the intersecting lines and the x - axis , what is the side length of a cube whose surface area is equal to 6 z ?
Options: a ) 16 , b ) 8 √ 2 , c ) 8 , d ) √ 2 , e ) ( √ 2 ) / 3
Rationale: "800 score official solution : the first step to solving this problem is to actually graph the two lines . the lines intersect at the point ( - 2 , - 2 ) and form a right triangle whose base length and height are both equal to 4 . as you know , the area of a triangle is equal to one half the product of its base length and height : a = ( 1 / 2 ) bh = ( 1 / 2 ) ( 2 × 2 ) = 2 ; so z = 2 . the next step requires us to find the length of a side of a cube that has a face area equal to 2 . as you know the 6 faces of a cube are squares . so , we can reduce the problem to finding the length of the side of a square that has an area of 2 . since the area of a square is equal to s ² , where s is the length of one of its side , we can write and solve the equation s ² = 2 . clearly s = √ 2 , oranswer choice ( d ) ."
Answer: d
Python program:
a = 2 * 2
b = a / 2
c = math.sqrt(b)
Problem: sum of two numbers is 15 . two times of the first exceeds by 5 from the three times of the other . then the numbers will be ?
Options: a ) 5 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "explanation : x + y = 15 2 x – 3 y = 5 x = 10 y = 5 a )"
Answer: a
Python program:
a = 5 / 2
b = 15 - a
c = b / 2
d = 15 - c
Problem: some of 50 % - intensity red paint is replaced with 20 % solution of red paint such that the new paint intensity is 30 % . what fraction of the original paint was replaced ?
Options: a ) 1 / 30 , b ) 1 / 5 , c ) 2 / 3 , d ) 3 / 4 , e ) 4 / 5
Rationale: 30 % is 10 % - points above 20 % and 20 % - points below 50 % . thus the ratio of 25 % - solution to 50 % - solution is 2 : 1 . 2 / 3 of the original paint was replaced . the answer is c .
Answer: c
Python program:
a = 30 / 100
b = 50 / 100
c = a - b
d = 20 / 100
e = 50 / 100
f = d - e
g = c / f
Problem: two women started running simultaneously around a circular track of length 1800 m from the same point at speeds of 10 km / hr and 20 km / hr . when will they meet for the first time any where on the track if they are moving in opposite directions ?
Options: a ) 72 , b ) 74 , c ) 76 , d ) 78 , e ) 80
Rationale: time taken to meet for the first time anywhere on the track = length of the track / relative speed = 1800 / ( 30 + 60 ) 5 / 18 = 1800 * 18 / 90 * 5 = 72 seconds . answer : a
Answer: a
Python program:
a = 10 * const_0_2778
b = 20 * const_0_2778
c = a + b 
d = 1800 / c
e = d / 3
Problem: the average runs scored by a batsman in 20 matches is 40 . in the next 10 matches the batsman scored an average of 20 runs . find his average in all the 30 matches ?
Options: a ) 31 , b ) 46 , c ) 88 , d ) 33.33 , e ) 12
Rationale: "total score of the batsman in 20 matches = 800 . total score of the batsman in the next 10 matches = 200 . total score of the batsman in the 30 matches = 1000 . average score of the batsman = 1000 / 30 = 33.33 answer : d"
Answer: d
Python program:
a = 40 * 20
b = 20 * 10
c = a + b 
d = 20 + 10 
e = c / d
Problem: a goods train runs at the speed of 72 kmph and crosses a 240 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 270 m , c ) 643 m , d ) 280 m , e ) 270 m
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 + 240 / 26 = 20 x + 240 = 520 x = 280 . answer : d"
Answer: d
Python program:
a = const_0_2778 * 72
b = 240 / a
c = 26 - b
d = const_0_2778 * 72
e = c * d
Problem: if 9 a - b = 10 b + 70 = - 12 b - 2 a , what is the value of 2 a + 22 b ?
Options: a ) - 4 , b ) - 70 , c ) 0 , d ) 2 , e ) 4
Rationale: "this implies 9 a - b = 10 b + 70 , 9 a - b = - 12 b - 2 a , 10 b + 70 = - 12 b - 2 a manipulating the second equation gives us 10 b + 70 = - 12 b - 2 a = = > 2 a + 22 b = - 70 answer is b"
Answer: b
Python program:
a = 70 / 2
b = a * 2
c = negate * (
Problem: how much time will a train of length 300 m moving at a speed of 72 kmph take to cross another train of length 500 m , moving at 36 kmph in the same direction ?
Options: a ) 50 , b ) 80 , c ) 88 , d ) 76 , e ) 12
Rationale: "the distance to be covered = sum of their lengths = 300 + 500 = 800 m . relative speed = 72 - 36 = 36 kmph = 36 * 5 / 18 = 10 mps . time required = d / s = 800 / 10 = 80 sec . answer : b"
Answer: b
Python program:
a = 300 + 500 
b = 72 - 36
c = b * const_0_2778
d = a / c
Problem: a tank contains 8,000 gallons of a solution that is 4 percent sodium chloride by volume . if 3,000 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 3.40 % , b ) 4.40 % , c ) 5.40 % , d ) 6.40 % , e ) 7.40 %
Rationale: "we start with 8,000 gallons of a solution that is 4 % sodium chloride by volume . this means that there are 0.04 x 8,000 = 320 gallons of sodium chloride . when 3,000 gallons of water evaporate we are left with 5,000 gallons of solution . from here we can determine what percent of the 5,000 gallon solution is sodium chloride . ( sodium chloride / total solution ) x 100 = ? ( 320 / 5,000 ) x 100 = ? 0.064 x 100 = ? = 6.4 % answer is d ."
Answer: d
Python program:
a = 100 * 100
b = 4 / 100
c = a * b
d = 100 * 100
e = 2 + 3 
f = 2 + 3 
g = f * 2
h = g * 100
i = e * h
j = 2 + 3 
k = j * 100
l = i + k 
m = d - l
n = c / m
o = n * 100
Problem: x , y and z , each working alone can complete a job in 2 , 4 and 6 days respectively . if all three of them work together to complete a job and earn $ 2000 , what will be z ' s share of the earnings ?
Options: a ) $ 1080.90 , b ) $ 1000.90 , c ) $ 1070.90 , d ) $ 1050.90 , e ) $ 1090.90
Rationale: the dollars earned will be in the same ratio as amount of work done 1 day work of z is 1 / 6 ( or 2 / 12 ) 1 day work of the combined workforce is ( 1 / 2 + 1 / 4 + 1 / 6 ) = 11 / 12 z ' s contribution is 2 / 9 of the combined effort translating effort to $ = 6 / 11 * 2000 = $ 1090.90 hence : e
Answer: e
Python program:
a = 1/(2)
b = 1/(4)
c = a + b 
d = 1/(6)
e = c + d 
f = 2000 / e
g = 1/(2)
h = f * g
Problem: the least number , which when divided by 12 , 15 , 20 and 54 leaves in each case a remainder of 8 is :
Options: a ) 504 , b ) 536 , c ) 544 , d ) 548 , e ) 568
Rationale: "required number = ( l . c . m . of 12 , 15 , 20 , 54 ) + 8 = 540 + 8 = 548 . answer : option d"
Answer: d
Python program:
a = 54 * 10
Problem: nicky and cristina are running a race . since cristina is faster than nicky , she gives him a 30 meter head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ?
Options: a ) 15 seconds , b ) 18 seconds , c ) 25 seconds , d ) 30 seconds , e ) 45 seconds
Rationale: "used pluging in method say t is the time for cristina to catch up with nicky , the equation will be as under : for nicky = n = 3 * t + 30 for cristina = c = 5 * t @ t = 15 , n = 75 c = 75 right answer ans : a"
Answer: a
Python program:
a = 5 - 3
b = 30 / a
Problem: how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 8 m x 6.6 m x 22.5 cm ?
Options: a ) 6400 , b ) 6410 , c ) 6440 , d ) 6500 , e ) 7040
Rationale: number of bricks = volume of wall / volume of bricks = 800 x 660 x 22.5 / 25 x 11.25 x 6 = = 7040 answer : e
Answer: e
Python program:
a = 8 * 100
b = 6 * 6
c = a * b
d = c * 22
e = 25 * 11
f = e * 6
g = d / f
Problem: the total number of students in grades 1 and 2 is 30 more than the total number of students in grades 2 and 5 . how much lesser is the number of students in grade 5 as compared to grade 1 ?
Options: a ) 20 , b ) 30 , c ) 10 , d ) 40 , e ) 15
Rationale: ( grade 1 + grade 2 ) - ( grade 2 + grade 5 ) = 30 grade 1 - grade 5 = 30 answer : b
Answer: b
Python program:
a = 30 + 5 
b = a + 2 
c = b + 2 
d = c + 2 
e = d + 3 
f = e + 4 
g = f + 12 
h = g / 2
Problem: a football player scores 5 goals in his fifth match thus increasing his average goals score by 0.2 . the total number of goals in his 5 matches would be
Options: a ) 14 , b ) 16 , c ) 18 , d ) 10 , e ) 21
Rationale: "while this question can be solved with a rather straight - forward algebra approach ( as the other posters have noted ) , it can also be solved by testing the answers . one of those numbers must be the total number of goals . . . from a tactical standpoint , it ' s best to test either answer b or answer d , so if the answer is not correct , then you would have a gauge for whether you should gohigherorlowerwith your next test . here , i ' ll start with answer e = 21 goals if . . . . total goals = 21 goals 5 th game = 5 goals 1 st 4 games = 16 goals avg . for 1 st 4 games = 16 / 4 = 4 goal / game avg . for all 5 games = 21 / 5 = 4.2 goals / game this is an exact match for what we ' re told in the prompt , so answer e must be the answer ."
Answer: e
Python program:
a = 4 * 5
b = 4 * 5
c = b * 0
d = a - c
e = d + 5
Problem: a jar full of whisky contains 40 % alcohol . a part of this whisky is replaced by another containg 19 % alcohol and now the percentage of alcohol was found to be 22 % . what quantity of whisky is replaced ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 2 / 5 , d ) 3 / 5 , e ) 4 / 5
Rationale: "let us assume the total original amount of whiskey = 10 ml - - - > 4 ml alcohol and 6 ml non - alcohol . let x ml be the amount removed - - - > total alcohol left = 4 - 0.4 x new quantity of whiskey added = x ml out of which 0.19 is the alcohol . thus , the final quantity of alcohol = 4 - 0.4 x + 0.19 x - - - - > ( 4 - 0.21 x ) / 10 = 0.26 - - - > x = 20 / 3 ml . per the question , you need to find the x ml removed as a ratio of the initial volume - - - > ( 20 / 3 ) / 10 = 3 / 5 . hence , d is the correct answer ."
Answer: d
Python program:
a = 40 - 22
b = 40 - 19
c = a / b
Problem: a jeep takes 4 hours to cover a distance of 620 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 148 kmph , b ) 152 kmph , c ) 106 kmph , d ) 103 kmph , e ) 165 kmph
Rationale: "time = 4 distance = 620 3 / 2 of 4 hours = 4 * 3 / 2 = 6 hours required speed = 620 / 6 = 103 kmph d )"
Answer: d
Python program:
a = 3 / 2
b = a * 4
c = 620 / b
Problem: the mean of 50 observations was 36 . it was found later that an observation 60 was wrongly taken as 23 . the corrected new mean is ?
Options: a ) 36.7 , b ) 36.1 , c ) 36.5 , d ) 36.9 , e ) 36.3
Rationale: "correct sum = ( 36 * 50 + 60 - 23 ) = 1837 . correct mean = 1837 / 50 = 36.7 answer : a"
Answer: a
Python program:
a = 36 * 50
b = 50 - 2
c = b - 23
d = a + c 
e = d / 50
Problem: in a party every person shakes hands with every other person . if there were a total of 105 handshakes in the party then what is the number of persons present in the party ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "explanation : let the number of persons be n â ˆ ´ total handshakes = nc 2 = 105 n ( n - 1 ) / 2 = 105 â ˆ ´ n = 15 answer : a"
Answer: a
Python program:
a = 105 * 2
b = a * 4
c = b + 1 
d = math.sqrt(c)
e = d + 1 
f = e / 2
Problem: at a certain organisation , the number of male members went up by 12 % in the year 2001 from year 2000 , and the number of females members went down by 4 % in the same time period . if the total membership at the organisation went up by 1.2 % from the year 2000 to 2001 , what was the ratio of male members to female members in the year 2000 ?
Options: a ) 1 : 2 , b ) 1 : 3 , c ) 2 : 3 , d ) 3 : 2 , e ) 2 : 1
Rationale: "men increase by 12 % = = > 1.12 m = males in 2001 women decrease by 4 % = = > 0.96 f = women in 2001 total employees increase by 1.2 % = = > 1.012 * ( m + f ) = total number of employees in 2001 obviously ( males in 2001 ) + ( females in 2001 ) = total number of employees in 2001 1.12 m + 0.96 f = 1.012 * ( m + f ) 1.12 m + 0.96 f = 1.012 m + 1.012 f 1.12 m - 1.012 m = 1.012 f - 0.96 f 0.108 m = 0.052 f m / f = ( 0.052 ) / ( 0.108 ) = 52 / 108 = 1 / 2 answer = ( a )"
Answer: a
Python program:
a = 1 / 2
b = 1 + a 
c = b * 1000
d = 4 / 100
e = 1 - d
f = e * 1000
g = c - f
h = 12 / 100
i = 1 + h 
j = i * 1000
k = 1 / 2
l = 1 + k 
m = l * 1000
n = j - m
o = g / n
Problem: what least value should be replaced by * in 842 * 124 so the number become divisible by 9
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "explanation : trick : number is divisible by 9 , if sum of all digits is divisible by 9 , so ( 8 + 4 + 2 + * + 1 + 2 + 4 ) = 21 + * should be divisible by 9 , 21 + 6 will be divisible by 9 , so that least number is 6 . answer : option d"
Answer: d
Python program:
a = 124 - 124
b = 124 - a
Problem: there are 7 players in a bowling team with an average weight of 76 kg . if two new players join the team , one weighs 110 kg and the second weighs 60 kg , what will be the new average weight ?
Options: a ) 78 kg . , b ) 70 kg . , c ) 75 kg . , d ) 70 kg . , e ) 72 kg .
Rationale: "the new average will be = ( 76 * 7 + 110 + 60 ) / 9 = 78 kgs a is the answer"
Answer: a
Python program:
a = 7 * 76
b = 110 + 60 
c = a + b 
d = 7 + 2 
e = c / d
Problem: ratio between rahul and deepak is 4 : 3 , after 2 years rahul age will be 26 years . what is deepak present age .
Options: a ) 14 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "explanation : present age is 4 x and 3 x , = > 4 x + 2 = 26 = > x = 6 so deepak age is = 3 ( 6 ) = 18 option b"
Answer: b
Python program:
a = 26 - 2
b = a * 3
c = b / 4
Problem: the sum of all consecutive odd integers from − 25 to 35 , inclusive , is
Options: a ) 130 , b ) 135 , c ) 155 , d ) 195 , e ) 235
Rationale: "the sum of the odd numbers from - 25 to + 25 is 0 . let ' s add the remaining numbers . 27 + 29 + 31 + 33 + 35 = 5 ( 31 ) = 155 the answer is c ."
Answer: c
Python program:
a = 25 + 2 
b = 25 + 2 
c = b + 2 
d = a + c 
e = 25 + 2 
f = e + 2 
g = f + 2 
h = d + g 
i = h + 35
Problem: a train crosses a platform of 130 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ?
Options: a ) 150 , b ) 887 , c ) 167 , d ) 197 , e ) 230
Rationale: "length of the train be ‘ x ’ x + 130 / 15 = x + 250 / 20 20 x + 2600 = 15 x + 3750 5 x = 1150 x = 230 m answer : e"
Answer: e
Python program:
a = 15 / 3
b = 15 / a
c = 250 * b
d = 15 / 3
e = 20 / d
f = 130 * e
g = c - f
Problem: one computer can upload 100 megabytes worth of data in 4 seconds . two computers , including this one , working together , can upload 1300 megabytes worth of data in 20 seconds . how long would it take for the second computer , working on its own , to upload 100 megabytes of data ?
Options: a ) 6 , b ) 2.5 , c ) 9 , d ) 11 , e ) 13
Rationale: "since the first computer can upload 100 megabytes worth of data in 4 seconds then in 4 * 5 = 20 seconds it can upload 5 * 100 = 500 megabytes worth of data , hence the second computer in 20 seconds uploads 1300 - 500 = 800 megabytes worth of data . the second computer can upload 100 megabytes of data in 2.5 seconds . answer : b ."
Answer: b
Python program:
a = 1300 / 20
b = 100 / 4
c = a - b