euclaise/mathqa_programs huggingface dataset:
Problem: a grocery store bought some mangoes at a rate of 5 for a dollar . they were separated into two stacks , one of which was sold at a rate of 3 for a dollar and the other at a rate of 9 for a dollar . what was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes ?
Options: a ) 1 : 4 , b ) 1 : 5 , c ) 3 : 2 , d ) 1 : 2 , e ) 2 : 5
Rationale: "the cost price of a mango = 1 / 5 dollars . the selling price of a mango from the first stack = 1 / 3 dollars - - > the profit from one mango = 1 / 3 - 1 / 5 = 2 / 15 = 4 / 30 dollars . the selling price of a mango from the second stack = 1 / 9 dollars - - > the loss from one mango = 1 / 5 - 1 / 9 = 4 / 45 dollars . the profit from one mango from the first stack is 4 times the loss from one mango from the second stack . the ratio is 4 / 30 * 45 / 4 = 3 : 2 c"
Answer: c
Python program:
a = 1 / 3
b = 1 / 5
c = a - b
d = 1 / 5
e = 2 * 4
f = 1 / e
g = d - f
h = c / g
Problem: if 5 % more is gained by selling an article for rs . 420 than by selling it for rs . 380 , the cost of the article is ?
Options: a ) 500 , b ) 688 , c ) 200 , d ) 121 , e ) 800
Rationale: let c . p . be rs . x . then , 5 % of x = 420 - 380 = 40 x / 20 = 40 = > x = 800 answer : e
Answer: e
Python program:
a = 420 - 380
b = 5 / 100
c = a / b
Problem: each of the 39 points is placed either inside or on the surface of a perfect sphere . if 72 % or fewer of the points touch the surface , what is the maximum number of segments which , if connected from those points to form chords , could be the diameter of the sphere ?
Options: a ) 7 , b ) 11 , c ) 13 , d ) 14 , e ) 38
Rationale: "maximum number of points on the surface is 72 % * 39 = 28.08 . . . or 28 since it has to be an integer now note that if two points form a diameter , they can not be part of any other diameter . so in the best case we can pair up the points we have 28 points , so at best we can form 14 pairs ( 28 ) . so , answer is ( d )"
Answer: d
Python program:
a = 72 / 100
b = 39 * a
c = b / 2
Problem: the proportion of water to alcohol in solution a is 5 : 4 and the proportion of water to alcohol in solution b is 6 : 5 . if an equal amount of each solution is mixed together , what is the concentration of alcohol in the new solution ?
Options: a ) 40.9 % , b ) 41.9 % , c ) 42.9 % , d ) 43.9 % , e ) 44.9 %
Rationale: "let v be the total volume of the new solution . then a volume of v / 2 was added from each solution a and b . the amount of alcohol added to the new solution was : ( 4 / 9 ) ( v / 2 ) + ( 5 / 11 ) ( v / 2 ) = 2 v / 9 + 5 v / 22 = 89 v / 198 . the concentration of alcohol is 89 / 198 = 44.9 % the answer is e ."
Answer: e
Python program:
a = 4 + 5 
b = 5 + 6 
c = 4 + 5 
d = b + c 
e = a / d
f = e * 100
Problem: in the coordinate plane , one of the vertices of a square is the point ( - 4 , - 4 ) . if the diagonals of that square intersect at point ( 3 , 2 ) , what is the area of that square ?
Options: a ) 180 , b ) 196 , c ) 160 , d ) 164 , e ) 172
Rationale: "one point ( - 4 - 4 ) , intersection ( 3,2 ) so the distance from the first point - 4 - 3 = - 7 is the midpoint of the square - - > whole side 14 , 14 * 14 = 196 b"
Answer: b
Python program:
a = 4 * 3
b = 4 * 3
c = a * b
Problem: a policeman noticed a criminal from a distance of 180 km . the criminal starts running and the policeman chases him . the criminal and the policeman run at the rate of 8 km and 10 km per hour respectively . what is the distance between them after 3 minutes ?
Options: a ) 100 m , b ) 80 m , c ) 130 m , d ) 150 m , e ) none of these
Rationale: "explanation : solution : relative speed = ( 10 - 8 ) = 2 km / hr . distance covered in 3 minutes = ( 2 * 3 / 60 ) km = 1 / 10 km = 100 m . . ' . distance between the criminal and policeman = ( 180 - 100 ) m = 80 m . answer : b"
Answer: b
Python program:
a = 3 / const_60
b = a * 1000
c = 180 - b
Problem: if 22 men do a work in 55 days , in how many days will 10 men do it ?
Options: a ) 121 , b ) 123 , c ) 119 , d ) 125 , e ) 127
Rationale: "22 * 55 = 10 * x x = 121 days answer : a"
Answer: a
Python program:
a = 22 * 55
b = a / 10
Problem: the sum of digits of a two digit number is 10 , the difference between the digits is 6 . find the number
Options: a ) 85 , b ) 94 , c ) 82 , d ) 72 , e ) none
Rationale: description : = > x + y = 10 , x - y = 6 adding these 2 x = 16 = > x = 8 , y = 2 . thus the number is 82 answer c
Answer: c
Python program:
a = 10 + 6 
b = a / 2
c = b * 10
d = 10 + 6 
e = d / 2
f = 10 - e
g = c + f
Problem: tough and tricky questions : word problems . a salesman ' s income consists of commission and base salary . his weekly income totals over the past 5 weeks have been $ 406 , $ 413 , $ 420 , $ 436 and $ 395 . what must his average ( arithmetic mean ) income over the next two weeks be to decrease his average weekly income to $ 400 over the 7 - week period ?
Options: a ) $ 350 , b ) $ 400 , c ) $ 365 , d ) $ 385 , e ) $ 375
Rationale: official solution : ( c ) first , we need to add up the wages over the past 5 weeks : $ 406 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2070 . to average $ 400 over 7 weeks , the salesman would need to earn : $ 400 × 7 = $ 2800 . subtract $ 2070 from $ 2800 to determine how much he would need to earn , in total , over the next 2 weeks to average $ 400 for the 7 weeks : $ 2800 – $ 2070 = $ 730 . dividing $ 730 by 2 will give us the amount he needs to earn on average over the next 2 weeks : $ 730 / 2 = $ 365 . the correct answer is choice ( c ) .
Answer: c
Python program:
a = 7 * 400
b = 406 + 413 
c = b + 420 
d = c + 436 
e = d + 395 
f = a - e
g = f / 2
Problem: a man walks at a rate of 10 mph . after every ten miles , he rests for 6 minutes . how much time does he take to walk 40 miles ?
Options: a ) 258 , b ) 318 , c ) 322 , d ) 324 , e ) 330
Rationale: "to cover 40 miles the man needs ( time ) = ( distance ) / ( rate ) = 40 / 10 = 4 hours = 240 minutes . he will also rest 3 times ( after 10 , 20 , and 30 miles ) , so total resting time = 3 * 6 = 18 minutes . total time = 240 + 18 = 258 minutes . answer : a ."
Answer: a
Python program:
a = 6 * 4
b = 40 / 10
c = b * const_60
d = a + c
Problem: a bag contains 3 red , 6 yellow and 8 green balls . 3 balls are drawn randomly . what is the probability that the balls drawn contain balls of different colours ?
Options: a ) 2 / 7 , b ) 3 / 5 , c ) 3 / 11 , d ) 18 / 85 , e ) 7 / 16
Rationale: "total number of balls = 3 + 6 + 8 = 17 n ( s ) = 17 c 3 = 680 n ( e ) = 3 c 1 * 6 c 1 * 8 c 1 = 144 probability = 144 / 680 = 18 / 85 answer is d"
Answer: d
Python program:
a = math.comb(4, 0)
b = 3 + 0 
c = math.comb(b, 1)
d = a * c
e = 3 + 6 
f = e + 8 
g = math.comb(f, 3)
h = d / g
Problem: while working alone at their constant rates , computer x can process 240 files in 12 hours , and computer y can process 240 files in 4 hours . if all files processed by these computers are the same size , how many hours would it take the two computers , working at the same time at their respective constant rates , to process a total of 240 files ?
Options: a ) 2 , b ) 2.4 , c ) 2.7 , d ) 3 , e ) 3.5
Rationale: "both computers together process files at a rate of 240 / 12 + 240 / 4 = 20 + 60 = 80 files per hour . the time required to process 240 files is 240 / 80 = 3 hours the answer is d ."
Answer: d
Python program:
a = 240 / 12
b = 240 / 4
c = a + b 
d = 240 / c
Problem: let s be the set of all positive integers that , when divided by 8 , have a remainder of 5 . what is the 72 th number in this set ?
Options: a ) 573 , b ) 608 , c ) 613 , d ) 616 , e ) 621
Rationale: the set s = { 5 , 13 , 21 , 29 , . . . . . . . . . . . . . . . . . . . . . } 1 st number = 8 * 0 + 5 = 5 2 nd number = 8 * 1 + 5 = 13 3 rd number = 8 * 2 + 5 = 21 72 th number = 8 * ( 72 - 1 ) + 5 = 573 answer = a
Answer: a
Python program:
a = 72 - 1
b = a * 8
c = b + 5
Problem: how many positive integers will divide evenly into 190 ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 12 , e ) 16
Rationale: the question is asking how many factors 190 has . 190 = 2 * 5 * 19 the number of factors is 2 ^ 3 = 8 the answer is c .
Answer: c
Python program:
a = 1 + 1 
b = 1 + 1 
c = a * b
d = 1 + 1 
e = c * d
Problem: solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 50 milliliters of solution x to create a solution that is 25 percent alcohol by volume ?
Options: a ) 150 , b ) 500 / 3 , c ) 400 , d ) 480 , e ) 600
Rationale: "we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 50 then y = 150 answer : a"
Answer: a
Python program:
a = 25 - 10
b = 30 - 25
c = a / b
d = c * 50
Problem: in a certain quiz that consists of 10 questions , each question after the first is worth 4 points more than the preceding question . if the 10 questions on the quiz are worth a total of 400 points , how many points is the third question worth ?
Options: a ) 14 , b ) 18 , c ) 22 , d ) 26 , e ) 30
Rationale: "x x + 4 x + 8 x + 12 x + 16 x + 20 x + 24 x + 28 x + 32 x + 36 10 x + 180 = 400 10 x = 220 x = 22 3 rd question = x + 8 = 22 + 8 = 30 answer e"
Answer: e
Python program:
a = 400 / 10
b = 10 - 4
c = b - 1
d = a + c
Problem: a pharmaceutical company received $ 5 million in royalties on the first $ 40 million in sales of and then $ 9 million in royalties on the next $ 210 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 40 million in sales to the next $ 210 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 66 %
Rationale: "( 9 / 210 ) / ( 5 / 40 ) = 12 / 35 = 34 % it means that 9 / 210 represents only 34 % . therefore a decrease of 66 % . answer e"
Answer: e
Python program:
a = 5 / 40
b = a * 100
Problem: jane makes toy bears . when she works with an assistant , she makes 80 percent more bears per week and works 20 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ?
Options: a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: "we can use fractional equivalents here to solve the problem 80 % = 4 / 5 ; this means that in 1 st case if she prepares 5 bears , in 2 nd case she prepares 9 bears 10 % = 1 / 10 ; this means that in 1 st case if she needs 10 hours , in 2 nd case she needs 9 hours now we come to productivity based on above fractional values the productivity in 1 st case is 0.5 bears / hour and in the 2 nd case it is 1 bear / hour hence the productivity is double with the assistant i . e . the increase in productivity is 180 % d"
Answer: d
Python program:
a = 100 - 80
b = a - 20
c = 20 / b
d = c * 100
Problem: the diameter of a garden roller is 1.4 m and it is 3 m long . how much area will it cover in 5 revolutions ? ( use ï € = 22 â  „ 7 )
Options: a ) 60 m 2 , b ) 64 m 2 , c ) 68 m 2 , d ) 66 m 2 , e ) none of these
Rationale: "required area covered in 5 revolutions = 5 ã — 2 ï € rh = 5 ã — 2 ã — 22 â  „ 7 ã — 0.7 ã — 3 = 66 m 2 answer d"
Answer: d
Python program:
a = 22 / 7
b = 3 * a
c = 1 / 4
d = b * c
e = d * 3
f = 5 * e
Problem: what will be the fraction of 8 %
Options: a ) 1 / 20 , b ) 1 / 50 , c ) 1 / 75 , d ) 2 / 25 , e ) none of these
Rationale: "explanation : 8 * 1 / 100 = 2 / 25 . option d"
Answer: d
Python program:
a = 8 / 2
b = circle_area / (
Problem: shipment - - - no . of defective chips / shipment - - - total chips in shipment s 1 - - - - - - - - - - - - - - - - - - - - - - 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 5000 s 2 - - - - - - - - - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 12000 s 3 - - - - - - - - - - - - - - - - - - - - - - 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 15000 s 4 - - - - - - - - - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 16000 a computer chip manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments s 1 , s 2 , s 3 , and s 4 combined , as shown in the table above . what ’ s the expected number of defective chips in a shipment of 60000 chips ?
Options: a ) 14 , b ) 20 , c ) 22 , d ) 24 , e ) 15
Rationale: for a total of 51000 chips ( adding s 1 , s 2 , s 3 , s 4 ) total number of defective chips is 17 ( ( adding defective chips of s 1 , s 2 , s 3 , s 4 ) so ratio is 12 / 48000 or 1 every 4000 chips . keeping this ratio constant for 60000 chips number of defective chips will be ( 1 / 4000 ) * 60000 = 15 e
Answer: e
Python program:
a = 5000 + 12000 
b = a + 15000 
c = b + 16000 
d = 2 + 4 
e = d + 2 
f = e + 4 
g = c / f
h = 60000 / g
Problem: 3 / 4 of 1 / 2 of 2 / 5 of 5020 = ?
Options: a ) 392 , b ) 229 , c ) 753 , d ) 493 , e ) 540
Rationale: "c 753 ? = 5020 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 753"
Answer: c
Python program:
a = 3 / 4
b = 1 / 2
c = a * b
d = 2 / 5
e = c * d
f = e * 5020
Problem: a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 360 m long platform ?
Options: a ) 19 , b ) 27 , c ) 29 , d ) 48 , e ) 28
Rationale: "let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 360 ) / 36 * 5 / 18 = 48 min . answer : d"
Answer: d
Python program:
a = const_0_2778 * 36
b = a * 12
c = 360 + b 
d = const_0_2778 * 36
e = c / d
Problem: an auto assembly plant performs 6 functions with each frame that arrives : add axles , add wheels to the axles , install the windshield to the frame , install the instrument panel , install the steering wheel , and install the interior seating . once those 6 tasks are performed , each car goes to a separate building for finishing touches . if these tasks can be arranged along a linear assembly line in any order , except that the axles must be installed before the wheels can be added , how many t ways can the assembly line be arranged ?
Options: a ) 120 , b ) 240 , c ) 360 , d ) 480 , e ) 720
Rationale: c ) 360 short way : there are 6 c ! ways to do the six tasks . half will have wheels before axles and half will have axles before wheels . so we want t = 6 c ! / 2 - > 720 / 2 = 360
Answer: c
Python program:
a = math.factorial(4)
b = math.factorial(6)
c = math.factorial(4)
d = b / c
e = math.factorial(2)
f = d / e
g = a * f
Problem: three numbers are in the ratio 1 : 4 : 6 and their h . c . f is 9 . the numbers are :
Options: a ) 1 , 4,6 , b ) 12 , 24,36 , c ) 10 , 20 , 30 , d ) 12 , 24 , 36 , e ) 9 , 36,54 .
Rationale: "let the required numbers be x , 4 x and 6 x . then , their h . c . f = x . so , x = 9 . the numbers are 9 , 36,54 . answer : e"
Answer: e
Python program:
a = 1 * 6
b = a * 100
c = 4 * 6
d = b + c
Problem: the average marks of a class of 30 students is 30 and that of another class of 50 students is 60 . find the average marks of all the students ?
Options: a ) 52.5 , b ) 52.9 , c ) 52.1 , d ) 48.75 , e ) 42.5
Rationale: "sum of the marks for the class of 30 students = 30 * 30 = 900 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 80 students = 900 + 3000 = 3900 average marks of all the students = 3900 / 80 = 48.75 answer : d"
Answer: d
Python program:
a = 30 * 30
b = 50 * 60
c = a + b 
d = 30 + 50 
e = c / d
Problem: an urn contains 5 red , 6 blue and 8 green balls . 3 balls are randomly selected from the urn , find the probability that the drawn ball are 2 blue and 1 red ?
Options: a ) 25 / 323 , b ) 21 / 969 , c ) 28 / 989 , d ) 74 / 879 , e ) 23 / 589
Rationale: "sample space = no . of ways 3 balls were drawn from urn = 19 c 3 = 969 no . ways 2 blue balls and 1 red were drawn from bag = 6 c 2 * 5 c 1 = 75 probability = 75 / 969 = 25 / 323 ans - a"
Answer: a
Python program:
a = math.comb(6, 2)
b = math.comb(5, 1)
c = a * b
d = 5 + 6 
e = d + 8 
f = math.comb(e, 3)
g = c / f
Problem: john purchased 1300 large bottles at $ 1.89 per bottle and 750 small bottles at $ 1.38 per bottle . what was the approximate average price paid per bottle ?
Options: a ) $ 1.63 , b ) $ 1.64 , c ) $ 1.68 , d ) $ 1.70 , e ) $ 1.76
Rationale: "( 1300 * 1.89 + 750 * 1.38 ) / ( 1300 + 750 ) = ~ 1.70 option ( d )"
Answer: d
Python program:
a = 1300 * 1
b = 750 * 1
c = a + b 
d = 1300 + 750 
e = c / d
Problem: two consultants can type up a report in 12.5 hours and edit it in 7.5 hours . if mary needs 30 hours to type the report and jim needs 12 hours to edit it alone , how many hours q will it take if jim types the report and mary edits it immediately after he is done ?
Options: a ) 41.4 , b ) 34.1 , c ) 13.4 , d ) 12.4 , e ) 10.8
Rationale: break down the problem into two pieces : typing and editing . mary needs 30 hours to type the report - - > mary ' s typing rate = 1 / 30 ( rate reciprocal of time ) ( point 1 in theory below ) ; mary and jim can type up a report in 12.5 and - - > 1 / 30 + 1 / x = 1 / 12.5 = 2 / 25 ( where x is the time needed for jim to type the report alone ) ( point 23 in theory below ) - - > x = 150 / 7 ; jim needs 12 hours to edit the report - - > jim ' s editing rate = 1 / 12 ; mary and jim can edit a report in 7.5 and - - > 1 / y + 1 / 12 = 1 / 7.5 = 2 / 15 ( where y is the time needed for mary to edit the report alone ) - - > y = 20 ; how many q hours will it take if jim types the report and mary edits it immediately after he is done - - > x + y = 150 / 7 + 20 = ~ 41.4 answer : a .
Answer: a
Python program:
a = 1 / 12
b = 1 / 30
c = a - b
d = 1/(c)
e = 1 / 7
f = 1 / 12
g = e - f
h = 1/(g)
i = d + h
Problem: two men a and b start from place x walking at 4 ½ kmph and 5 ¾ kmph respectively . how many km apart they are at the end of 3 ½ hours if they are walking in the same direction ?
Options: a ) 4 3 / 6 , b ) 4 3 / 9 , c ) 4 3 / 8 , d ) 4 3 / 4 , e ) 4 3 / 1
Rationale: "rs = 5 3 / 4 - 4 1 / 2 = 1 1 / 4 t = 3 1 / 2 h . d = 5 / 4 * 7 / 2 = 35 / 8 = 4 3 / 8 km answer : c"
Answer: c
Python program:
a = 1 / 2
b = 3 + a 
c = 3 / 4
d = 5 + c 
e = 1 / 2
f = 4 + e 
g = d - f
h = b * g
i = h + 2
Problem: if 2 ^ 4 , 3 ^ 3 , and 12 ^ 3 are factors of the product of 1,452 and w , where w is a positive integer , what is the smallest possible value of w ?
Options: a ) 198 , b ) 288 , c ) 432 , d ) 396 , e ) 484
Rationale: i will go with c ( pending elements to match is 2 ^ 2 * 3 ^ 2 * 12 ^ 1 = 432
Answer: c
Python program:
a = 2 ** 2
b = a * 3
c = 12 / 2
d = b * c
e = d * 2
Problem: for all positive integers m and v , the expression m θ v represents the remainder when m is divided by v . what is the value of ( ( 94 θ 33 ) θ 17 ) - ( 96 θ ( 33 θ 17 ) ) ?
Options: a ) - 10 , b ) - 2 , c ) 8 , d ) 13 , e ) 17
Rationale: "( ( 94 θ 33 ) θ 17 ) the remainder of 98 divided by 33 is 28 ; the remainder of 28 divided by 17 is 11 ; ( 96 θ ( 33 θ 17 ) ) the remainder of 33 divided by 17 is 16 ; the remainder of 96 divided by 16 is 0 . 11 - 0 = 11 . answer : d ."
Answer: d
Python program:
a = reminder - (
Problem: a sports equipment store sold ping pong rackets for a total of $ 735 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ?
Options: a ) 50 , b ) 100 , c ) 490 , d ) 500 , e ) 75
Rationale: "average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 735 x = 75 pairs were sold . answer : e"
Answer: e
Python program:
a = 735 / 9
Problem: john distributes his pencil among his 4 friends rose , mary , ranjan , and rohit in the ratio 1 / 3 : 1 / 3 : 1 / 4 : 1 / 5 . what is the minimum no . of pencils that the person should have ?
Options: a ) 45 , b ) 67 , c ) 70 , d ) 77 , e ) 98
Rationale: "rakesh : rahul : ranjan : rohit = 1 / 3 : 1 / 3 : 1 / 4 : 1 / 5 step 1 : at first we need to do is lcm of 3 , 3,4 and 5 is 60 . step 2 : then pencil are distributed in ratio among friends , rakesh = ( 1 / 3 x 60 ) = 20 . rahul = ( 1 / 3 x 60 ) = 20 . ranjan = ( 1 / 4 x 60 ) = 15 . rohit = ( 1 / 5 x 60 ) = 12 . step 3 : total number of pencils are ( 20 x + 20 x + 15 x + 12 x ) = 67 x . for minimum number of pencils x = 1 . the person should have atleast 67 pencils . b )"
Answer: b
Python program:
a = math.lcm(3, 1)
b = math.lcm(a, 1)
c = math.lcm(b, 3)
d = c / 3
e = math.lcm(3, 1)
f = math.lcm(e, 1)
g = math.lcm(f, 3)
h = g / 1
i = d + h 
j = math.lcm(3, 1)
k = math.lcm(j, 1)
l = math.lcm(k, 3)
m = l / 1
n = i + m 
o = math.lcm(3, 1)
p = math.lcm(o, 1)
q = math.lcm(p, 3)
r = q / 3
s = n + r
Problem: divide rs . 3250 among a , b and c so that a receives 1 / 5 as much as b and c together and b receives 2 / 3 as a and c together . b ' s share is ?
Options: a ) 6500 , b ) 3250 , c ) 1100 , d ) 1300 , e ) 1200
Rationale: "a + b + c = 3250 a = 1 / 5 ( b + c ) ; b = 2 / 3 ( a + c ) b / ( a + c ) = 2 / 3 b = 1 / 5 * 6500 = > 1300 answer : d"
Answer: d
Python program:
a = 3250 / 3
Problem: the mean of 50 observations is 200 . but later he found that there is decrements of 15 from each observations . what is the the updated mean is ?
Options: a ) 150 , b ) 185 , c ) 190 , d ) 210 , e ) 220
Rationale: "185 answer is b"
Answer: b
Python program:
a = 200 - 15
Problem: if the perimeter of a rectangular garden is 600 m , its length when its breadth is 150 m is ?
Options: a ) 150 m , b ) 899 m , c ) 200 m , d ) 166 m , e ) 187 m
Rationale: "2 ( l + 150 ) = 600 = > l = 150 m answer : a"
Answer: a
Python program:
a = 600 / 2
b = a - 150
Problem: a train 110 m long is running with a speed of 60 km / hr . in what time will it pass a trolley that is running with a speed of 12 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 4.31 , b ) 6.75 , c ) 7.92 , d ) 5.5 , e ) 6.5
Rationale: speed of train relative to trolley = 60 + 12 = 72 km / hr . = 72 * 5 / 18 = 20 m / sec . time taken to pass the trolley = 110 * 1 / 20 = 5.5 sec . answer : d
Answer: d
Python program:
a = 60 + 12 
b = a * const_0_2778
c = 110 / b
Problem: in a certain parallelogram the degree measure of one angle exceeds that of the other by 10 what is the degree measure of the smaller angle ?
Options: a ) 75 , b ) 80 , c ) 85 , d ) 90 , e ) 95
Rationale: "in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 ° ) . given : x + ( x + 10 ) = 180 - - > x = 85 . answer : c ."
Answer: c
Python program:
a = 3600 / 10
b = 10 * 2
c = a - b
d = c / 4
Problem: the average of 10 numbers was calculated as 18 . it is discovered later on that while calculating the average , one number , namely 66 , was incorrectly read as 26 . what is the correct average ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "10 * 18 - 26 + 66 = 220 220 / 10 = 22 the answer is c ."
Answer: c
Python program:
a = 10 * 18
b = 66 - 26
c = a + b 
d = c / 10
Problem: each child has 5 crayons and 14 apples . if there are 10 children , how many crayons are there in total ?
Options: a ) 22 , b ) 65 , c ) 12 , d ) 36 , e ) 50
Rationale: 5 * 10 = 50 . answer is e .
Answer: e
Python program:
a = 10 * 5
Problem: how many integers between 1 and 1050 are divisible by 10 , 25 , and 35 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 3
Rationale: prime factorization of given numbers 10 = 2 * 5 25 = 5 ^ 2 35 = 5 * 7 lcm of the given numbers = 2 * 5 ^ 2 * 7 = 50 * 7 = 350 therefore , number of integers = 1050 / 350 = 3 answer : option e
Answer: e
Python program:
a = math.lcm(10, 25)
b = math.lcm(a, 35)
c = 1050 / b
Problem: 78 , 64 , 48 , 30 10 , ( . . . )
Options: a ) - 12 number , b ) - 14 , c ) 2 , d ) 8 , e ) 6
Rationale: "explanation : 78 - 14 = 64 64 - 16 = 48 48 - 18 = 30 30 - 20 = 10 10 - 22 = - 12 answer : option a"
Answer: a
Python program:
a = negate - (
Problem: a cycle is bought for rs . 900 and sold for rs . 1440 , find the gain percent ?
Options: a ) 39 % , b ) 20 % , c ) 23 % , d ) 74 % , e ) 60 %
Rationale: "900 - - - - 540 100 - - - - ? = > 60 % answer : e"
Answer: e
Python program:
a = 1440 - 900
b = a / 900
c = b * 100