euclaise/mathqa_programs huggingface dataset:
Problem: a sum of money is to be divided among ann , bob and chloe . first , ann receives $ 4 plus one - half of what remains . next , bob receives $ 4 plus one - third of what remains . finally , chloe receives the remaining $ 32 . how much money j did bob receive ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 52
Rationale: notice that we need not consider ann ' s portion in the solution . we can just let k = the money remaining after ann has received her portion and go from there . our equation will use the fact that , once we remove bob ' s portion , we have $ 32 for chloe . so , we getk - bob ' s $ = 32 bob received 4 dollars plus one - third of what remained once bob receives $ 4 , the amount remaining is k - 4 dollars . so , bob gets a 1 / 3 of that as well . 1 / 3 of k - 4 is ( k - 4 ) / 3 so altogether , bob receives 4 + ( k - 4 ) / 3 so , our equation becomes : k - [ 4 + ( k - 4 ) / 3 ] = 32 simplify to get : k - 4 - ( k - 4 ) / 3 = 32 multiply both sides by 3 to get : 3 k - 12 - k + 4 = 96 simplify : 2 k - 8 = 96 solve : k = 52 plug this k - value intok - bob ' s $ = 32 to get : 52 - bob ' s $ = 32 so , bob ' s $ j = 20 answer : b
Answer: b
Python program:
a = 32 * 2
b = a / 3
Problem: a certain junior class has 1,000 students and a certain senior class has 800 students . among these students , there are 40 siblings pairs , each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected at will be a sibling pair ?
Options: a ) 3 / 40,000 , b ) 1 / 3,600 , c ) 1 / 20,000 , d ) 1 / 60 , e ) 1 / 15
Rationale: total number of ways of choosing one student from each group is = 800 * 1000 number of cases in which a sibling pair will be got is = 40 thus the probability that the 2 students selected will be a sibling pair is = 40 / ( 800 * 1000 ) = 1 / 20,000 c
Answer: c
Python program:
a = 1 / 3
Problem: running at their respective constant rates , machine x takes 2 days longer to produce w widgets than machine y . at these rates , if the two machines together produce 5 / 4 w widgets in 3 days , how many days would it take machine x alone to produce 5 w widgets ?
Options: a ) 4 , b ) 30 , c ) 8 , d ) 10 , e ) 12
Rationale: "let y produce w widgets in y days hence , in 1 day y will produce w / y widgets . also , x will produce w widgets in y + 2 days ( given , x takes two more days ) hence , in 1 day x will produce w / y + 2 widgets . hence together x and y in 1 day will produce { w / y + w / y + 2 } widgets . together x and y in 3 days will produce = 3 * [ { w / y + w / y + 2 } ] widgets . it is given that in 3 days together they produce ( 5 / 4 ) w widgets . equating , 3 * [ { w / y + w / y + 2 } ] = ( 5 / 4 ) w take out w common and move 3 to denominator of rhs w { 1 / y + 1 / ( y + 2 ) } = ( 5 / 12 ) w canceling w from both sides { 1 / y + 1 / ( y + 2 ) } = 5 / 12 2 y + 2 / y ( y + 2 ) = 5 / 12 24 y + 24 = 5 y ^ 2 + 10 y 5 y ^ 2 - 14 y - 24 = 0 5 y ^ 2 - 20 y + 6 y - 24 = 0 5 y ( y - 4 ) + 6 ( y - 4 ) = 0 ( 5 y + 6 ) + ( y - 4 ) = 0 y = - 6 / 5 or y = 4 discarding y = - 6 / 5 as no of days can not be negative y = 4 hence it takes y , 4 days to produce w widgets . therefore , it will take x ( 4 + 2 ) = 6 days to produce w widgets . hence it will take x 5 * 6 = 30 days to produce 2 w widgets . answer : b"
Answer: b
Python program:
a = 3 * 4
b = a * 2
c = 3 * 4
d = b - c
e = d / 2
Problem: find value for x from below equation ? x + 1 = 2
Options: a ) - 5 , b ) 1 , c ) 4 , d ) 3 , e ) 2
Rationale: "1 . subtract 1 from both sides : x + 1 - 1 = 2 - 1 2 . simplify both sides : x = 1 b"
Answer: b
Python program:
a = 2 - 1
Problem: a person lent a certain sum of money at 4 % per annum at simple interest and in 8 years the interest amounted to rs . 170 less than the sum lent . what was the sum lent ?
Options: a ) 228 , b ) 278 , c ) 250 , d ) 500 , e ) 821
Rationale: "p - 170 = ( p * 4 * 8 ) / 100 p = 250 answer : c"
Answer: c
Python program:
a = 4 * 8
b = a / 100
c = 1 - b
d = 170 / c
Problem: little john had $ 10.50 . he spent $ 2.25 on sweets and gave to his two friends $ 2.20 each . how much money was left ?
Options: a ) $ 1.85 , b ) $ 3.85 , c ) $ 4.85 , d ) $ 6.85 , e ) $ 5.85
Rationale: "john spent and gave to his two friends a total of 2.25 + 2.20 + 2.20 = $ 6.65 money left 10.50 - 6.65 = $ 3.85 correct answer is b ) $ 3.85"
Answer: b
Python program:
a = 2 + 20 
b = 2 + 25 
c = 10 - 50
Problem: a and b can do a piece of work in 12 days and 16 days respectively . both work for 3 days and then a goes away . find how long will b take to complete the remaining work ?
Options: a ) 6 days , b ) 12 days , c ) 15 days , d ) 9 days , e ) 8 days
Rationale: "3 / 12 + ( 3 + x ) / 16 = 1 x = 9 days answer : d"
Answer: d
Python program:
a = 3 / 16
b = 3 / 12
c = a + b 
d = 3 - c
e = 3 / 16
f = d / e
Problem: a motorcycle importer is planning on increasing the price of a certain model by $ 1000 . at this new price 8 fewer motorcycles will be sold per month , but the total revenues will increase by $ 26000 to $ 594000 . what is the number of motorcycles the manufacturer will sell at this new price ?
Options: a ) 61 , b ) 62 , c ) 65 , d ) 63 , e ) 64
Rationale: responding to a pm : to solve this question , i will make an equation in x and then make educated guesses . here ' s how : assuming x motorcycles were sold every month initially . ( 568000 / x + 1000 ) ( x - 8 ) = 594000 ( 568 / x + 1 ) ( x - 8 ) = 594 now 568 = 8 * 71 assuming x = 71 ( we have all integers so it is obvious that 568 / x should be an integer . we get 9 * 66 = 594 ( matches ) so he will sell 71 - 8 = 63 bikes this month answer ( d )
Answer: d
Python program:
a = 8 + 1 
b = 8 - 1
c = a * b
Problem: 1 / 0.02 is equal to
Options: a ) 50 , b ) 2.5 , c ) 25 , d ) . 25 , e ) none of these
Rationale: explanation : 1 / 0.02 = ( 1 * 100 ) / 2 = 100 / 2 = 50 option a
Answer: a
Python program:
a = 1 / 0
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 10000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 14
Rationale: "solution let the toatl number of workers be x . then 8000 x = ( 10000 x 7 ) + 6000 ( x - 7 ) x = 14 . answer e"
Answer: e
Python program:
a = 10000 - 8000
b = 7 * a
c = 8000 - 6000
d = b / c
e = 7 + d
Problem: what is the remainder when 3 ^ 29 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the units digit of powers of 3 follow a repeating cycle of four : { 3 , 9 , 7 , 1 } 29 has the form 4 k + 1 , so the units digit of 3 ^ 29 is 3 . the remainder when dividing by 5 is 3 . the answer is d ."
Answer: d
Python program:
a = 5 / 2
b = 3 * 3
c = a - b
Problem: obra drove 200 π meters along a circular track . if the area enclosed by the circular track on which she drove is 57,600 π square meters , what percentage of the circular track did obra drive ?
Options: a ) 6.67 % , b ) 12.5 % , c ) 41.66 % , d ) 25 % , e ) 33.3 %
Rationale: "area enclosed by the circular track on which she drove is 57,600 π square meters so , π ( r ^ 2 ) = 57,600 π - - - > ( r ^ 2 ) = 57,600 - - - > r = 240 circumference of the circular track = 2 π r = 480 π therefore , part of circumference covered = 200 π / 480 π = 41.66 % hence , answer is c ."
Answer: c
Python program:
a = circumface / (
b = a * 200
c = b * 3
d = c - 2
e = d - 4
Problem: if the price of a certain computer increased 20 percent from d dollars to 351 dollars , then 2 d =
Options: a ) 540 , b ) 585 , c ) 619 , d ) 649 , e ) 700
Rationale: "before price increase price = d after 30 % price increase price = d + ( 20 / 100 ) * d = 1.2 d = 351 ( given ) i . e . d = 351 / 1.3 = $ 292,5 i . e . 2 d = 2 * 292.5 = 585 answer : option b"
Answer: b
Python program:
a = 100 + 20 
b = a / 100
c = 351 / b
d = c * 2
Problem: two pipes can fill the cistern in 10 hr and 12 hr respectively , while the third empty it in 20 hr . if all pipes are opened simultaneously , then the cistern will be filled in
Options: a ) 7.5 hr , b ) 8 hr , c ) 8.5 hr , d ) 10 hr , e ) none of these
Rationale: "solution : work done by all the tanks working together in 1 hour . 1 / 10 + 1 / 12 − 1 / 20 = 2 / 15 hence , tank will be filled in 15 / 2 = 7.5 hour option ( a )"
Answer: a
Python program:
a = 1 / 10
b = 1 / 12
c = a + b 
d = 1 / 20
e = c - d
f = 1/(e)
Problem: what must be added to each term of the ratio 2 : 3 , so that it may become equal to 4 : 5 ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 9 , e ) 8
Rationale: let the number to be added be x , then ( 2 + x ) : ( 3 + x ) = 4 : 5 ⇒ ( 2 + x ) / ( 5 + x ) = 4 / 5 5 ( 2 + x ) = 4 ( 3 + x ) 10 + 5 x = 12 + 4 x 5 x - 4 x = 12 - 10 x = 2 answer : 2
Answer: a
Python program:
a = 4 * 3
b = 5 * 2
c = a - b
d = 5 - 4
e = c / d
Problem: obra drove 180 π meters along a circular track . if the area enclosed by the circular track on which she drove is 57,600 π square meters , what percentage of the circular track did obra drive ?
Options: a ) 37.5 % , b ) 12.5 % , c ) 18.75 % , d ) 25 % , e ) 33.3 %
Rationale: "area enclosed by the circular track on which she drove is 57,600 π square meters so , π ( r ^ 2 ) = 57,600 π - - - > ( r ^ 2 ) = 57,600 - - - > r = 240 circumference of the circular track = 2 π r = 480 π therefore , part of circumference covered = 180 π / 480 π = 37.5 % hence , answer is a ."
Answer: a
Python program:
a = circumface / (
b = a * 180
c = b * 3
d = c - 2
e = d - 4
Problem: the average of 8 numbers is 21 . if each of the number is multiplied by 8 , the average of the new set of numbers is :
Options: a ) 168 , b ) 667 , c ) 288 , d ) 1991 , e ) 111
Rationale: "average of new numbers = ( 21 × 8 ) = 168 answer : a"
Answer: a
Python program:
a = 21 * 8
Problem: if 14 men do a work in 80 days , in how many days will 20 men do it ?
Options: a ) 18 days , b ) 38 days , c ) 42 days , d ) 48 days , e ) 56 days
Rationale: "14 * 80 = 20 * x x = 56 days answer : e"
Answer: e
Python program:
a = 14 * 80
b = a / 20
Problem: in what proportion must flour at $ 0.8 per pound be mixed with flour at $ 0.9 per pound so that the mixture costs $ 0.855 per pound ?
Options: a ) 1 : 3 , b ) 1 : 2 , c ) 1 : 1 , d ) 2 : 1 , e ) 4 : 5
Rationale: "using weighted average method : let x be the proportion in which the $ 0.8 per pound flour is mixed with $ 0.9 per pound flour . thus 0.8 * x + 0.9 * ( 1 - x ) = 0.855 0.9 – 0.1 x = 0.855 x = 0.45 thus ratio of both flours is 4 : 5 e"
Answer: e
Python program:
a = 0 + 8 
b = 0 / 855
Problem: two terms are in 3 : 4 , if 10 is added to each of the terms , they will be 4 : 5 . find second term ?
Options: a ) 10 , b ) 30 , c ) 20 , d ) 40 , e ) 35
Rationale: solution : let the two numbers be 3 x and 4 x . then , ( 3 x + 10 ) / ( 4 x + 10 ) = 4 / 5 . = > 15 x + 50 = 16 x + 40 = > x = 10 . . ' . second term = 4 * 10 = 40 . answer is d
Answer: d
Python program:
a = 5 * 10
b = 4 * 10
c = a - b
d = c * 4
Problem: two pipes a and b can fill a tank in 18 hours and 24 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?
Options: a ) 20 hours , b ) 15 hours , c ) 10 hours , d ) 10 2 / 7 hours , e ) 8 hours
Rationale: "part filled by a in 1 hour = 1 / 18 part filled by b in 1 hour = 1 / 24 part filled by ( a + b ) in 1 hour = 1 / 18 + 1 / 24 = 7 / 72 both the pipes together fill the tank in 72 / 7 = 10 2 / 7 hours answer is d"
Answer: d
Python program:
a = 1 / 18
b = 1 / 24
c = a + b 
d = 1 / c
Problem: the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 75 sq . cm . what is the length of the rectangle
Options: a ) 18 cm , b ) 16 cm , c ) 40 cm , d ) 20 cm , e ) 28 cm
Rationale: "explanation : let breadth = x cm then , length = 2 x cm area = x × 2 x = 2 x ^ 2 sq . cm . new length = ( 2 x − 5 ) cm new breadth = ( x + 5 ) cm new area = ( 2 x − 5 ) ( x + 5 ) sq . cm . given that , new area = initial area + 75 sq . cm . ⇒ ( 2 x − 5 ) ( x + 5 ) = 2 x ^ 2 + 75 ⇒ 2 x ^ 2 + 10 x − 5 x − 25 = 2 x ^ 2 + 75 ⇒ 5 x − 25 = 75 ⇒ 5 x = 75 + 25 = 100 ⇒ x = 1005 = 20 cm length = 2 x = 2 × 20 = 40 cm answer : option c"
Answer: c
Python program:
a = 100 / 3
Problem: the list price of an article is rs . 70 . a customer pays rs . 59.85 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
Options: a ) 8 % , b ) 7 % , c ) 10 % , d ) 6 % , e ) 5 %
Rationale: "option e explanation : 70 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 59.85 x = 5 %"
Answer: e
Python program:
a = 10 / 100
b = 70 * a
c = 70 - b
d = c - 59
e = 10 / 100
f = 70 * e
g = 70 - f
h = d / g
i = h * 100
Problem: for every x , the action [ x ] is defined : [ x ] is the greatest integer less than or equal to x . what is the value of [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 9.8 ?
Options: a ) 12.6 . , b ) 14.4 . , c ) 15.8 . , d ) 16.2 . , e ) 16.4 .
Rationale: "[ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 9.8 = 6 * 0 + 2 * 7.2 + 8 - 9.8 = 0 + 14.4 - 1.8 12.6 answer a"
Answer: a
Python program:
a = 2 * 7
b = 4 / 10
c = 8 - 4
d = a + c 
e = d - 9
Problem: two persons start running simultaneously around a circular track of length 250 m from the same point at speeds of 20 kmph and 40 kmph . when will they meet for the first time any where on the track if they are moving in the opposite direction ?
Options: a ) 144 , b ) 15 , c ) 18 , d ) 32 , e ) 38
Rationale: time taken to meet the first time = length of track / relative speed = 250 / ( 20 + 40 ) ( 5 / 18 ) = 250 / 60 * ( 18 / 5 ) = 15 sec . answer : b
Answer: b
Python program:
a = 20 + 40 
b = a * const_0_2778
c = 250 / b
Problem: sixteen percent of the programmers in a startup company weigh 200 pounds or more . 20 - 5 percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less . what percent of the programmers in the startup company weigh between 100 and 200 pounds ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 63 % , e ) 75 %
Rationale: initially 84 % and 16 % split 80 % is further divided as 25 % and 75 % q is asking about that 75 % let total be ' 100 ' then that 75 % is ( 3 / 4 ) ∗ 84 so , the required % is [ ( 3 / 4 ) ∗ 84 / 100 ] ∗ 100 = 63 % answer : d
Answer: d
Python program:
a = 20 + 5 
b = 100 - a
c = b / 100
d = 20 - 4
e = 100 - d
f = c * e
Problem: pipes a and b can fill a tank in 3 and 4 hours . pipe c can empty it in 4 hours . if all pipes are opened together , then the tank will be filled in ?
Options: a ) 3 hr , b ) 1 / 2 hr , c ) 1 hr , d ) 9 / 7 hr , e ) 5 / 3 hr
Rationale: "net part filled in 1 hour = 1 / 3 + 1 / 4 - 1 / 4 = 1 / 3 the tank will be full in 3 hr answer is a"
Answer: a
Python program:
a = 1 / 3
b = 1 / 4
c = a + b 
d = 1 / 4
e = c - d
f = 1/(e)
Problem: a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 3 : 5 . the ratio of economy cars to sport utility vehicles is 4 : 3 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 9 : 8 , b ) 8 : 9 , c ) 3 : 2 , d ) 20 : 9 , e ) 1 : 2
Rationale: "the ratio of economy to luxury cars is 3 : 5 - - > e : l = 3 : 5 = 12 : 20 . the ratio of economy cars to sport utility vehicles is 4 : 3 - - > e : s = 4 : 3 = 12 : 9 . thus , l : s = 20 : 9 . answer : d ."
Answer: d
Python program:
a = 4 * 3
b = 3 * 3
c = a / b
d = 3 * 4
e = 5 * 4
f = d / e
g = c / f
Problem: in a graduating class , the difference between the highest and lowest salaries is $ 100000 . the median salary is $ 50000 higher than the lowest salary and the average salary is $ 20000 higher than the median . what is the minimum number of students r in the class ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 20 , e ) e ) 25
Rationale: the difference between the highest and lowest salaries is $ 100000 . so there are at least 2 people - say one with salary 0 and the other with 100 k . no salary will be outside this range . median = 50 k more than lowest . so median is right in the center of lowest and highest since lowest and highest differ by 100 k . in our example , median = 50 k . since there are more than 2 people , there would probably be a person at 50 k . mean = 20 k more than median so in our example , mean salary = 70 k on the number line , 0 . . . . . . . . 50 k ( median ) . . . . . . . . 100 k mean = 70 k so there must be people more toward 100 k to bring the mean up to 70 k . since we want to add minimum people , we will add people at 100 k to quickly make up the right side deficit . 0 and 50 k are ( 70 k + 20 k ) = 90 k away from 70 k . 100 k is 30 k away from 70 k . to bring the mean to 70 k , we will add two people at 100 k each to get : 0 . . . . 50 k . . . . . 100 k , 100 k , 100 k but when we add more people to the right of 70 k , the median will shift to the right . we need to keep the median at 50 k . so every time we add people to the right of 70 k , we need to add people at 50 k too to balance the median . 50 k is 20 k less than 70 k while 100 k is 30 k more than 70 k . to keep the mean same , we need to add 2 people at 100 k for every 3 people we add at 50 k . so if we add 3 people at 50 k and 2 people at 100 k , we get : 0 , . . . 50 k , 50 k , 50 k , 50 k , . . . 100 k , 100 k , 100 k , 100 k , 100 k the median is not at 50 k yet . add another 3 people at 50 k and another 2 at 100 k to get 0 , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k now the median is 50 k and mean is 70 k . total number of people is 15 . answer ( c )
Answer: c
Python program:
a = 100000 / 20000
b = a * 3
Problem: if 10 people contributed a total of $ 20.00 toward a gift and each of them contributed at least $ 1.00 , then the maximum possible amount any one person could have contributed is
Options: a ) $ 11.00 , b ) $ 1.25 , c ) $ 5.00 , d ) $ 6.00 , e ) $ 20.00
Rationale: "a for me 9 people with 1 $ each - > maximum = 11"
Answer: a
Python program:
a = 10 - 1
b = a * 1
c = 20 - 0
Problem: the average salary of workers in an industry is rs . 200 the average salary of technicians being rs . 400 and that of non - technicians being rs . 125 . what is the total number of workers ?
Options: a ) 277 , b ) 665 , c ) 662 , d ) 552 , e ) 281
Rationale: "8 * 84 = 672 – 7 = 665 answer : b"
Answer: b
Python program:
a = 200 - 125
b = 400 / 200
c = a * b
d = c + 1 
e = math.floor(d)
Problem: two trains of equal lengths take 10 sec and 8 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 22 , b ) 12 , c ) 9 , d ) 99 , e ) 21
Rationale: speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 8 = 15 m / sec . relative speed = 12 + 15 = 27 m / sec . required time = ( 120 + 120 ) / 27 = 9 sec . answer : c
Answer: c
Python program:
a = 120 * 2
b = speed + ( 
c = a / b
Problem: reema took a loan of rs 1200 with simple interest for as many years as the rate of interest . if she paid rs . 432 as interest at the end of the loan period , what was the rate of interest .
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "explanation : let rate = r % then time = r years . = > 1200 ∗ r ∗ r / 100 = 432 = > r 2 = 36 = > r = 6 % option b"
Answer: b
Python program:
a = 1200 / 100
b = 432 / a
c = math.sqrt(b)
Problem: each of the dogs in a certain kennel is a single color . each of the dogs in the kennel either has long fur or does not . of the 45 dogs in the kennel , 26 have long fur , 22 are brown , and 8 are neither long - furred nor brown . how many long - furred dogs are brown ?
Options: a ) 26 , b ) 19 , c ) 11 , d ) 8 , e ) 6
Rationale: "no of dogs = 45 long fur = 26 brown = 22 neither long fur nor brown = 8 therefore , either long fur or brown = 45 - 8 = 37 37 = 26 + 22 - both both = 11 answer c"
Answer: c
Python program:
a = 26 + 22 
b = 45 - 8
c = a - b
Problem: evaluate : 6202.5 + 620.25 + 62.025 + 6.2025 + 0.62025
Options: a ) 6819.59775 , b ) 6981.59775 , c ) 6918.59775 , d ) 6198.59775 , e ) 6891.59775
Rationale: "6202.5 620.25 62.025 6.2025 + 0.62025 - - - - - - - - - - - - - - - 6891.59775 answer is e ."
Answer: e
Python program:
a = 620 * 25
b = a * 6
c = 6202 - 5
Problem: a van takes 5 hours to cover a distance of 465 km . what speed in kph should the van maintain to cover the same distance in 3 / 2 of the previous time ?
Options: a ) 56 , b ) 58 , c ) 60 , d ) 62 , e ) 64
Rationale: "( 3 / 2 ) * 5 = 7.5 hours 465 / 7.5 = 62 kph the answer is d ."
Answer: d
Python program:
a = 3 / 2
b = a * 5
c = 465 / b
Problem: the product of two numbers is 120 and the sum of their squares is 289 . the sum is :
Options: a ) 23 , b ) 21 , c ) 43 , d ) 56 , e ) 30
Rationale: "xy = 120 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 120 ) = 529 x + y = 529 = 23 . answer a"
Answer: a
Python program:
a = 2 * 120
b = 289 - a
c = math.sqrt(b)
d = c ** 2
e = 4 * 120
f = d + e 
g = math.sqrt(f)
Problem: in what time will a railway train 60 m long moving at the rate of 54 kmph pass a telegraph post on its way ?
Options: a ) 4 sec , b ) 7 sec , c ) 2 sec , d ) 6 sec , e ) 9 sec
Rationale: "t = 60 / 54 * 18 / 5 = 4 sec answer : a"
Answer: a
Python program:
a = 54 * const_0_2778
b = 60 / a
Problem: a person walks at a speed of 4 km / hr and runs at a speed of 8 km / hr . how many hours will the person require to cover a distance of 4 km , if the person completes half of the distance by walking and the other half by running ?
Options: a ) 0.25 , b ) 0.5 , c ) 0.75 , d ) 1 , e ) 1.25
Rationale: "time = 2 / 4 + 2 / 8 = 6 / 8 = 0.75 hours the answer is c ."
Answer: c
Python program:
a = 4 / 2
b = a / 4
c = 4 / 2
d = c / 8
e = b + d
Problem: mary passed a certain gas station on a highway while traveling west at a constant speed of 50 miles per hour . then , 15 minutes later , paul passed the same gas station while traveling west at a constant speed of 60 miles per hour . if both drivers maintained their speeds and both remained on the highway for at least 4 hours , how long after he passed the gas station did paul catch up with mary ?
Options: a ) 2 , b ) 1.5 , c ) 1.6 , d ) 1.7 , e ) 1.25
Rationale: "d = rt m : r = 50 mph , t = t + 1 / 4 hr d = 50 ( t + 1 / 4 ) p : r = 60 , t = t d = 60 t since they went the same distance : 50 t + 50 / 4 = 60 t 10 t = 50 / 4 t = 1.25 or 1 hr , 15 min e"
Answer: e
Python program:
a = 15 / const_60
b = 50 * a
c = 60 - 50
d = b / c
e = const_60 * d
Problem: the sum of three consecutive even numbers is 36 . find the middle number of the three ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 24 , e ) 36
Rationale: "three consecutive even numbers ( 2 p - 2 ) , 2 p , ( 2 p + 2 ) . ( 2 p - 2 ) + 2 p + ( 2 p + 2 ) = 36 6 p = 36 = > p = 6 . the middle number is : 6 p = 36 . answer : e"
Answer: e
Python program:
a = 36 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 36 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 36 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 36 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: the average of runs of a cricket player of 10 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 87 , b ) 16 , c ) 10 , d ) 76 , e ) 17
Rationale: "average after 11 innings = 36 required number of runs = ( 36 * 11 ) - ( 32 * 10 ) = 396 - 320 = 76 . answer : d"
Answer: d
Python program:
a = 10 + 1 
b = 4 + 32 
c = a * b
d = 10 * 32
e = c - d
Problem: the guests at a football banquet consumed a total of 323 pounds of food . if no individual guest consumed more than 2 pounds of food , what is the minimum number of guests that could have attended the banquet ?
Options: a ) 160 , b ) 161 , c ) 162 , d ) 163 , e ) 164
Rationale: "to minimize one quantity maximize other . 161 * 2 ( max possible amount of food a guest could consume ) = 322 pounds , so there must be more than 161 guests , next integer is 162 . answer : c ."
Answer: c
Python program:
a = 323 / 2
b = math.floor(a)
c = b + 1