euclaise/mathqa_programs huggingface dataset:
Problem: if x , y , and z are positive integers and 3 x = 5 y = 8 z , then the least possible value of x + y + z is
Options: a ) 45 , b ) 79 , c ) 50 , d ) 55 , e ) 60
Rationale: "given 3 x = 5 y = 8 z x + y + z in terms of x = x + ( 3 x / 5 ) + ( 3 x / 8 ) = 79 x / 40 now checking with each of the answers and see which value gives a minimum integer value . a x = 40 / 79 * 45 , not an integer c , d , e can be ruled out similarly . b is minimum value as x = 79 * 40 / 79 = 79 answer is b"
Answer: b
Python program:
a = 3 * 5
b = a * 8
c = b / 3
d = 3 * 5
e = d * 8
f = e / 5
g = c - f
h = 3 * 5
i = h * 8
j = i / 8
k = g + j
Problem: given f ( x ) = 3 x – 5 , for what value of x does 2 * [ f ( x ) ] – 4 = f ( 3 x – 6 )
Options: a ) 3 , b ) 4 , c ) 6 , d ) 7 , e ) 13
Rationale: "answer = a = 3 f ( x ) = 3 x – 5 2 * [ f ( x ) ] – 4 = f ( 3 x – 6 ) 2 ( 3 x - 5 ) - 4 = 3 ( 3 x - 6 ) - 5 6 x - 14 = 9 x - 23 x = 3"
Answer: a
Python program:
a = 2 * 5
b = a + 4 
c = 3 * 3
d = c + 5 
e = b - d
f = 2 * 3
g = 3 * 1
h = f - g
i = e / h
Problem: a can do a job in 8 days and b can do it in 20 days . a and b working together will finish twice the amount of work in - - - - - - - days ?
Options: a ) 21 ½ days , b ) 11 3 / 7 days , c ) 23 ½ days , d ) 12 ½ days , e ) none of these
Rationale: "explanation : 1 / 8 + 1 / 20 = 7 / 40 40 / 7 = 40 / 7 * 2 = 11 3 / 7 days answer : b"
Answer: b
Python program:
a = 1 / 8
b = 1 / 20
c = a + b
Problem: in an electric circuit , two resistors with resistances 8 ohms and 9 ohms are connected in parallel . in this case , if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of two resistors . what is r value ?
Options: a ) 17
b ) 45 / 78
c ) 72 / 17
d ) 17 / 72
e ) 72
Rationale: the wording is a bit confusing , though basically we are told that 1 / r = 1 / 8 + 1 / 9 , from which it follows that r = 72 / 17 . answer : c .
Answer: c
Python program:
a = 8 * 9
b = 8 + 9 
c = a / b
Problem: the average of runs of a cricket player of 10 innings was 35 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 76 , b ) 79 , c ) 85 , d ) 87 , e ) 89
Rationale: "explanation : average = total runs / no . of innings = 35 so , total = average x no . of innings = 35 x 10 = 350 . now increase in avg = 4 runs . so , new avg = 35 + 4 = 39 runs total runs = new avg x new no . of innings = 39 x 11 = 429 runs made in the 11 th inning = 429 - 350 = 79 answer : b"
Answer: b
Python program:
a = 10 + 1 
b = 4 + 35 
c = a * b
d = 10 * 35
e = c - d
Problem: on dividing 161 by a number , the quotient is 10 and the remainder is 1 . find the divisor .
Options: a ) a ) 12 , b ) b ) 14 , c ) c ) 16 , d ) d ) 18 , e ) e ) 22
Rationale: "d = ( d - r ) / q = ( 161 - 1 ) / 10 = 160 / 10 = 16 c )"
Answer: c
Python program:
a = 161 / 10
b = math.floor(a)
Problem: 16 boys or 24 girls can construct the wall in 6 days . the number of days that 8 boys and 6 girls will take to construct ?
Options: a ) 7 days , b ) 14 days , c ) 6 days , d ) 8 days , e ) 9 days
Rationale: "explanation : 16 boys = 24 girls , 1 boy = 24 / 16 girls 1 boy = 6 / 4 girls 8 boys + 6 girls = 8 ã — 6 / 4 + 12 = 12 + 6 = 18 girls 8 days to complete the work answer : option d"
Answer: d
Python program:
a = 1 / 6
b = a / 24
c = 6 * b
d = 1 / 6
e = d / 16
f = 8 * e
g = c + f 
h = 1 / g
Problem: the average of 11 numbers is 10.7 . if the average of first 6 is 10.5 and that of the last 6.00001 is 11.4 the sixth number is ?
Options: a ) 9 , b ) 9.2 , c ) 10 , d ) 13.7 , e ) 12
Rationale: explanation : 1 to 11 = 11 * 10.7 = 117.7 1 to 6 = 6 * 10.5 = 63 6 to 11 = 6 * 11.4 = 68.4 63 + 68.4 = 131.4 – 117.7 = 13.7 6 th number = 13.7 d )
Answer: d
Python program:
a = 11 * 4
b = 10 * 5
c = a + b 
d = 11 * 10
e = c - d
Problem: the denominator of a fraction is 8 greater than the numerator . if the numerator and the denominator are increased by 5 , the resulting fraction is equal to 6 â  „ 7 . what is the value of the original fraction ?
Options: a ) 25 / 33 , b ) 31 / 39 , c ) 37 / 45 , d ) 43 / 51 , e ) 53 / 61
Rationale: "let the numerator be x . then the denominator is x + 8 . x + 5 / x + 13 = 6 / 7 . 7 x + 35 = 6 x + 78 . x = 43 . the original fraction is 43 / 51 . the answer is d ."
Answer: d
Python program:
a = 5 + 8 
b = 6 * a
c = b - 7
d = 7 - 6
e = c / d
f = 5 + 8 
g = 6 * f
h = g - 7
i = 7 - 6
j = h / i
k = j + 8 
l = e / k
Problem: evaluate 50 ! / 47 !
Options: a ) 102500 , b ) 112584 , c ) 117600 , d ) 118450 , e ) 128450
Rationale: "evaluate 50 ! / 47 ! = 50 * 49 * 48 * ( 47 ! ) / 47 ! = 50 * 49 * 48 = 117600 answer : c"
Answer: c
Python program:
a = 47 / 50
b = 50 / a
Problem: a 425 meter long train crosses a platform in 55 seconds while it crosses a signal pole in 40 seconds . what is the length of the platform ?
Options: a ) 155.68 , b ) 160 , c ) 159.38 , d ) 180 , e ) 175
Rationale: "speed = [ 425 / 40 m / sec = 42.5 / 4 m / sec . let the length of the platform be x meters . then , x + 425 / 55 = 42.5 / 4 4 ( x + 425 ) = 2337.5 è x = 159.38 m . answer : c"
Answer: c
Python program:
a = 425 / 40
b = a * 55
c = b - 425
Problem: a train running at the speed of 60 km / hr crosses a pole in 8 seconds . find the length of the train .
Options: a ) 133.33 , b ) 882 , c ) 772 , d ) 252 , e ) 121
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 8 = 133.33 meter . answer : a"
Answer: a
Python program:
a = 60 * 1000
b = a / 3600
c = b * 8
Problem: annika hikes at a constant rate of 12 minutes per kilometer . she has hiked 2.75 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 40 minutes . if annika continues east , then turns around and retraces her path to reach the start of the trail in exactly 40 minutes , for how many kilometers total did she hike east ?
Options: a ) 3.625 , b ) 3.5 , c ) 3 , d ) 3.04 , e ) 4
Rationale: "set up two r x t = d cases . 1 . 1 / 12 km / min x t = 2.75 from which t = 33 mins . we know total journey time now is 40 + 33 = 73 . the rate is the same ie 1 / 12 km / min . set up second r x t = d case . 1 / 12 km / min x 73 = 6.08 km now the total journey would be halved as distance would be same in each direction . 6.08 / 2 = 3.04 d ."
Answer: d
Python program:
a = 40 / 12
b = a - 2
c = b / 2
d = c + 2
Problem: tom and jerry enter into a partnership by investing $ 700 and $ 300 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if tom received $ 800 more than jerry did , what was the profit made by their business in that year ?
Options: a ) 3000 , b ) 4000 , c ) 5000 , d ) 6900 , e ) 6677
Rationale: say the profit was $ x . tom share = x / 6 ( half of the third ) + ( x - x / 3 ) * 0.7 jerry share = x / 6 ( half of the third ) + ( x - x / 3 ) * 0.3 thus ( x - x / 3 ) * 0.7 - ( x - x / 3 ) * 0.3 = 800 - - > x = 3000 . answer is a
Answer: a
Python program:
a = 1 / 3
b = 1 - a
c = 700 + 300 
d = b / c
e = 700 * d
f = 1 / 3
g = f / 2
h = e + g 
i = 1 / 3
j = 1 - i
k = 700 + 300 
l = j / k
m = 300 * l
n = 1 / 3
o = n / 2
p = m + o 
q = h - p
r = 800 / q
Problem: simplify : 0.72 * 0.43 + 0.12 * 0.34
Options: a ) 0.3504 , b ) 0.4209 , c ) 0.4889 , d ) 0.6412 , e ) 0.4612
Rationale: given exp . = 0.72 * 0.43 + ( 0.12 * 0.34 ) = 0.3096 + 0.0408 = 0.3504 answer is a
Answer: a
Python program:
a = 0 * 72
b = 0 * 12
c = a + b
Problem: a jeep takes 8 hours to cover a distance of 280 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 ) 28 kmph , b ) 52 kmph , c ) 20 kmph , d ) 23 kmph , e ) 65 kmph
Rationale: "time = 8 distance = 280 3 / 2 of 8 hours = 8 * 3 / 2 = 12 hours required speed = 280 / 12 = 23 kmph d )"
Answer: d
Python program:
a = 3 / 2
b = a * 8
c = 280 / b
Problem: the simple interest on rs . 34 for 8 months at the rate of 6 paise per rupeeper month is
Options: a ) 16.32 , b ) 16.9 , c ) 12.25 , d ) 13.21 , e ) none
Rationale: "sol . s . i . = rs . [ 34 * 6 / 100 * 8 ] = rs . 16.32 answer a"
Answer: a
Python program:
a = 34 * 8
b = a * 6
c = b / 100
Problem: a swimmer can swim in still water at 4 km / h . if the speed of the water current is 2 km / h , how many hours will the swimmer take to swim against the current for 3 km ?
Options: a ) 1.5 , b ) 1.75 , c ) 2.0 , d ) 2.25 , e ) 2.5
Rationale: "the swimmer can swim against the current at a speed of 4 - 2 = 2 km / h . the time it will take is 3 / 2 = 1.5 hours . the answer is a ."
Answer: a
Python program:
a = 4 - 2
b = 3 / a
Problem: what sum of money put at c . i amounts in 2 years to rs . 8880 and in 3 years to rs . 9261 ?
Options: a ) 8164 , b ) 8877 , c ) 2877 , d ) 2678 , e ) 1011
Rationale: "8880 - - - - 381 100 - - - - ? = > 4.29 % x * 104.29 / 100 * 104.29 / 100 = 8880 x * 1.0876 = 8880 x = 8880 / 1.0876 = > 8164.38 answer : a"
Answer: a
Python program:
a = 9261 / 8880
b = a - 1
c = b + 1 
d = c ** 2
e = 8880 / d
Problem: how many seconds will a 400 metre long train take to cross a man running with a speed of 6 km / hr in the direction of the moving train if the speed of the train is 30 km / hr ?
Options: a ) 25 , b ) 30 , c ) 45 , d ) 64 , e ) 60
Rationale: "explanation : speed of train relatively to man = ( 30 - 6 ) km / hr = 24 km / hr = ( 24 x 5 / 18 ) m / sec = 6.66 m / sec time taken to pass the man = ( 400 / 6.66 ) sec = 60 sec . answer : e"
Answer: e
Python program:
a = 30 - 6
b = const_0_2778 * a
c = 400 / b
Problem: what is the maximum number of pieces of birthday cake of size 4 ” by 4 ” that can be cut from a cake 16 ” by 16 ” ?
Options: a ) 5 , b ) 4 , c ) 16 , d ) 20 , e ) 25
Rationale: "the prompt is essentially asking for the maximum number of 4 x 4 squares that can be cut from a larger 16 by 16 square . since each ' row ' and each ' column ' of the larger square can be sub - divided into 4 ' pieces ' each , we have ( 4 ) ( 4 ) = 16 total smaller squares ( at maximum ) . c"
Answer: c
Python program:
a = 16 * 16
b = 4 * 4
c = a / b
Problem: a student needs 30 % of the marks on a test to pass the test . if the student gets 80 marks and fails the test by 10 marks , find the maximum marks set for the test .
Options: a ) 240 , b ) 300 , c ) 360 , d ) 420 , e ) 480
Rationale: "30 % = 90 marks 1 % = 3 marks 100 % = 300 marks the answer is b ."
Answer: b
Python program:
a = 80 + 10 
b = 30 / 100
c = a / b
Problem: a work crew of 6 men takes 9 days to complete one - half of a job . if 12 men are then added to the crew and the men continue to work at the same rate , how many days will it take the enlarged crew to do the rest of the job ?
Options: a ) 2 , b ) 3 , c ) 3 1 / 3 , d ) 4 , e ) 4 4 / 5
Rationale: "suppose 1 man can do work in x days . . so 6 men will do in . . 6 / x = 1 / 9 * 1 / 2 as half job is done x = 108 now 12 more are added then 18 / 108 = 1 / 2 * 1 / d for remaining half job d = 3 number of days b"
Answer: b
Python program:
a = 6 * 9
b = 6 + 12 
c = a / b
d = 9 + c
Problem: in a class , 6 students can speak gujarati , 15 can speak hindi and 6 can speak marathi . if two students can speak two languages and one student can speak all the 3 languages , then how many students are there in the class
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: n ( aubuc ) = 6 + 15 + 6 - 2 - 2 - 2 + 1 = 22 answer : b
Answer: b
Python program:
a = 15 + 6 
b = a + 1
Problem: jack and jill are marathon runners . jack can finish a marathon ( 41 km ) in 4.5 hours and jill can run a marathon in 4.1 hours . what is the ratio of their average running speed ? ( jack : jill )
Options: a ) 41 / 45 , b ) 15 / 14 , c ) 4 / 5 , d ) 5 / 4 , e ) can not be determined
Rationale: "average speed of jack = distance / time = 41 / ( 9 / 2 ) = 82 / 9 average speed of jill = 41 / ( 4.1 ) = 10 ratio of average speed of jack to jill = ( 82 / 9 ) / 10 = 82 / 90 = 41 / 45 answer a"
Answer: a
Python program:
a = 41 / 4
b = 41 / 4
c = a / b
Problem: if the selling price of 100 articles is equal to the cost price of 40 articles , then the loss or gain percent is :
Options: a ) 25 % , b ) 40 % , c ) 60 % , d ) 65 % , e ) 50 %
Rationale: let c . p . of each article be re . 1 . then , c . p . of 100 articles = rs . 100 ; s . p . of 100 articles = rs . 40 . loss % = 60 / 100 * 100 = 60 % answer : c
Answer: c
Python program:
a = 100 - 40
Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 700 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?
Options: a ) 511 , b ) 546 , c ) 552 , d ) 562 , e ) 570
Rationale: "number of newborns that can die in first month = 1 / 10 * 700 = 70 survived = 630 number of newborns that can die in second month = 1 / 10 * 630 = 63 survived = 567 number of newborns that can die in third month = 1 / 10 * 567 = 56 survived = 511 answer : a"
Answer: a
Python program:
a = 1 / 10
b = 1 - a
c = 700 * b
d = 1 / 10
e = 1 - d
f = c * e
g = 1 / 10
h = 1 - g
i = f * h
Problem: the ratio , by volume , of bleach to detergent to water in a certain solution is 2 : 40 : 100 . the solution will be altered so that the ratio of bleach ( b ) to detergent is tripled while the ratio of detergent to water is halved . if the altered solution will contain 300 liters of water , how many liters of detergent will it contain ?
Options: a ) 40 , b ) 60 , c ) 50 , d ) 30 , e ) 70
Rationale: "b : d : w = 2 : 40 : 100 bnew / dnew = ( 1 / 3 ) * ( 2 / 40 ) = ( 1 / 60 ) dnew / wnew = ( 1 / 2 ) * ( 40 / 100 ) = ( 1 / 5 ) wnew = 300 dnew = wnew / 5 = 300 / 5 = 60 so , answer will be b b"
Answer: b
Python program:
a = 300 / 100
b = 40 / 2
c = a * b
Problem: in x game of billiards , x can give y 20 points in 60 and he can give z 50 points in 60 . how many points can y give z in x game of 100 ?
Options: a ) 30 , b ) 20 , c ) 25 , d ) 40 , e ) 75
Rationale: "x scores 60 while y score 40 and z scores 10 . the number of points that z scores when y scores 100 = ( 100 * 50 ) / 40 = 25 . in x game of 100 points , y gives ( 100 - 25 ) = 75 points to c . e"
Answer: e
Python program:
a = 60 - 20
b = a * 3
c = 60 - 50
d = c * 3
e = b - d
Problem: jack and jill work at a hospital with 5 other workers . for an internal review , 2 of the 7 workers will be randomly chosen to be interviewed . what is the probability that jack and jill will both be chosen ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 21 , d ) 3 / 8 , e ) 2 / 3
Rationale: "1 / 7 c 2 = 1 / 21 . answer : c ."
Answer: c
Python program:
a = math.factorial(7)
b = math.factorial(2)
c = math.factorial(5)
d = b * c
e = a / d
f = 1/(e)
Problem: the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 10 cm each . the radius of the sphere is
Options: a ) 3 cm , b ) 5 cm , c ) 6 cm , d ) 8 cm , e ) none
Rationale: "solution 4 î r 2 = 2 î 5 x 10 â ‡ ’ r 2 = ( 5 x 10 / 2 ) â ‡ ’ 25 â ‡ ’ r = 5 cm . answer b"
Answer: b
Python program:
a = 10 / 2
b = 10 * a
c = math.pi * b
d = c * 2
e = math.pi * 4
f = d / e
g = math.sqrt(f)
Problem: find a number such that it exceeds 18 by 3 times the number by which it is less than 86 ?
Options: a ) 67 , b ) 68 , c ) 69 , d ) 70 , e ) 71
Rationale: x - 18 = 3 [ 86 - x ] x = 69 answer : c
Answer: c
Python program:
a = 3 * 86
b = 18 + a 
c = b / 4
Problem: of the 3600 employees of company x , 12 / 25 are clerical . if the clerical staff were to be reduced by 1 / 4 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 40 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %
Rationale: let ' s see , the way i did it was 12 / 25 are clerical out of 3600 so 1728 are clerical 1728 reduced by 1 / 4 is 1728 * 1 / 4 so it reduced 432 people , so there is 1296 clerical people left but since 432 people left , it also reduced from the total of 3600 so there are 3168 people total since 1296 clerical left / 3168 people total you get ( a ) 40 %
Answer: a
Python program:
a = 3600 * 12
b = a / 25
c = 3600 * 12
d = c / 25
e = d / 4
f = b - e
g = 3600 * 12
h = g / 25
i = h / 4
j = 3600 - i
k = f / j
l = k * 100
Problem: for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 25 percent of the seeds in the first plot germinated and exactly 40 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?
Options: a ) 12 % , b ) 26 % , c ) 29 % , d ) 31 % , e ) 60 %
Rationale: "in the first plot 25 % of 300 seeds germinated , so 0.25 x 300 = 75 seeds germinated . in the second plot , 40 % of 200 seeds germinated , so 0.4 x 200 = 80 seeds germinated . since 75 + 80 = 155 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 155 / 500 ) x 100 % , or 31 % . answer : d ."
Answer: d
Python program:
a = 25 / 100
b = a * 300
c = 40 / 100
d = c * 200
e = b + d 
f = 300 + 200 
g = e / f
h = g * 100
Problem: an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 60 cm , find the sum of the perimeters of all the triangles .
Options: a ) 180 cm , b ) 220 cm , c ) 240 cm , d ) 270 cm , e ) 360 cm
Rationale: "we have 60 for first triangle , when we join mid - points of first triangle we get the second equilateral triangle then the length of second one is 30 and continues . so we have 60 , 30,15 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 60 / 1 - ( 1 / 2 ) = 120 equilateral triangle perimeter is 3 a = 3 * 120 = 360 . so option e ."
Answer: e
Python program:
a = triangle_perimeter + (
Problem: in an election , candidate douglas won 66 percent of the total vote in counties x and y . he won 74 percent of the vote in county x . if the ratio of people who voted in county x to county y is 2 : 1 , what percent of the vote did candidate douglas win in county y ?
Options: a ) 25 % , b ) 30 % , c ) 50 % , d ) 75 % , e ) 80 %
Rationale: given voters in ratio 2 : 1 let x has 200 votersy has 100 voters for x 66 % voted means 74 * 200 = 148 votes combined for xy has 300 voters and voted 66 % so total votes = 198 balance votes = 198 - 148 = 50 as y has 100 voters so 50 votes means 50 % of votes required ans c
Answer: c
Python program:
a = 66 / 100
b = 74 / 100
c = 2 / 3
d = b * c
e = a - d
f = 1 / 3
g = e / f
h = g * 100
Problem: amithab ' s average expenditure for the january to june is rs . 4200 and he spends rs . 1200 in january and rs . 1500 in july . the average expenditure for the months of febraury to july is
Options: a ) rs . 4250 , b ) rs . 4228 , c ) rs . 4128 , d ) rs . 4988 , e ) rs . 4192
Rationale: amithab ' s total expenditure for jan - june = 4200 x 6 = 25200 expenditure for feb - june = 25200 - 1200 = 24000 expenditure for the months of feb - july = 24000 + 1500 = 25500 the average expenditure = { 25500 } / { 6 } = 4250 answer : a
Answer: a
Python program:
a = 1500 - 1200
b = 2 * 3
c = a / b
d = 4200 + c
Problem: one week , a certain truck rental lot had a total of 20 trucks , all of which were on the lot monday morning . if 50 % of the trucks that were rented out during the week were returned to the lot on or before saturday morning of that week , and if there were at least 16 trucks on the lot that saturday morning , what is the greatest number of different trucks that could have been rented out during the week ?
Options: a ) 18 , b ) 16 , c ) 12 , d ) 14 , e ) 8
Rationale: "n - not rented trucks ; r - rented trucks n + r = 20 n + r / 2 = 16 r = 8 e"
Answer: e
Python program:
a = 50 / 100
b = 20 * a
c = 16 + b
Problem: a person walks from one end to the other of a 80 - meter long moving walkway at a constant rate in 40 seconds , assisted by the walkway . when this person reaches the end , they reverse direction and continue walking with the same speed , but this time it takes 120 seconds because the person is traveling against the direction of the moving walkway . if the walkway were to stop moving , how many seconds would it take this person to walk from one end of the walkway to the other ?
Options: a ) 56 , b ) 60 , c ) 64 , d ) 68 , e ) 72
Rationale: "let v be the speed of the person and let x be the speed of the walkway . 40 ( v + x ) = 80 then 120 ( v + x ) = 240 120 ( v - x ) = 80 when we add the two equations : 240 v = 320 v = 4 / 3 time = 80 / ( 4 / 3 ) = 60 seconds the answer is b ."
Answer: b
Python program:
a = 80 / 40
b = 80 / 120
c = a + b 
d = c / 2
e = 80 / d
Problem: neha ' s mother was 4 times her age 12 years ago . she will be twice as old as neha 12 years from now . what is the present age of neha ' s mother ?
Options: a ) 60 years , b ) 33 , c ) 77 , d ) 66 , e ) 101
Rationale: explanation : let neha ' s present age be ' x ' years . her age 12 years ago = ( x – 12 ) years therefore , her mother ' s age 12 years ago = 4 ( x – 12 ) her mother ' s present age = 4 x – 48 + 12 = 4 x – 36 neha ' s age after 12 years = x + 12 her mother ' s age after 12 years = 4 x – 36 + 12 = 4 x – 24 4 x – 24 = 2 ( x + 12 ) 4 x – 2 x = 24 + 24 x = 24 therefore , neha ' s present age = 24 her mother ' s present age = 4 x – 36 = 4 ( 24 ) – 36 = 60 years answer : a
Answer: a
Python program:
a = 12 + 12 
b = 2 * a
c = 12 + 12 
d = b - c
e = 4 - 2
f = d / e
g = 4 * f
h = g + 12
Problem: what is the measure of the radius of the circle that circumscribes a triangle whose sides measure 3 , 4 , and 5 ?
Options: a ) 3.5 , b ) 3 , c ) 5 , d ) 4 , e ) 2.5
Rationale: "some of pyhtagron triplets we need to keep it in mind . like { ( 2 , 3,5 ) , ( 5 , 12,13 ) , ( 7 , 24,25 ) , ( 11 , 60,61 ) . so now we know the triangle is an right angle triangle . the circle circumscribes the triangle . the circum raduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 5 / 2 = 2.5 ans . e"
Answer: e
Python program:
a = triangle_area_three_edges / (
Problem: what is the sum of the numbers between 1 and 5 , inclusive ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: "sol . add numbers between 1 and 5 . answer = c , 15 ."
Answer: c
Python program:
a = 1 * 5
b = a / 4
Problem: a mathematics teacher tabulated the marks secured by 35 students of 8 th class . the average of their marks was 72 . if the marks secured by reema was written as 46 instead of 96 then find the correct average marks up to two decimal places .
Options: a ) 73.41 , b ) 74.31 , c ) 73.42 , d ) 73.43 , e ) can not be determined
Rationale: "total marks = 35 x 72 = 2520 corrected total marks = 2520 - 46 + 96 = 2570 correct average = 2570 / 35 = 73.42 answer : c"
Answer: c
Python program:
a = 35 * 72
b = 96 - 46
c = a - b
d = c / 35
Problem: if the sides of a triangle are 36 cm , 34 cm and 20 cm , what is its area ?
Options: a ) 320 cm 2 , b ) 360 cm 2 , c ) 340 cm 2 , d ) 310 cm 2 , e ) 300 cm 2
Rationale: "the triangle with sides 36 cm , 34 cm and 20 cm is right angled , where the hypotenuse is 36 cm . area of the triangle = 1 / 2 * 34 * 20 = 340 cm 2 answer : c"
Answer: c
Python program:
a = 34 * 20
b = a / 2
Problem: a group of hikers is planning a trip that will take them up a mountain using one route and back down using another route . they plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up , but the time each route will take is the same . if they will go up the mountain at a rate of 3 miles per day and it will take them two days , how many miles long is the route down the mountain ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "on the way down , the rate is 1.5 * 3 = 4.5 miles per day . the distance of the route down the mountain is 2 * 4.5 = 9 miles . the answer is c ."
Answer: c
Python program:
a = 3 * 2
b = 3 / 2
c = a * b