euclaise/mathqa_programs huggingface dataset:
Problem: for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum s of all the even integers between 99 and 301 ?
Options: a ) 10,100 , b ) 20,200 , c ) 22,650 , d ) 40,200 , e ) 45,150
Rationale: "i would solve it in a different way . first of all , total number of even integers between 99 and 301 are , ( 301 - 99 ) / 2 = 202 / 2 = 101 average = ( 301 + 99 ) / 2 = 400 / 2 = 200 sum s = average * total count = 200 * 101 = 20,200 answer is b"
Answer: b
Python program:
a = 301 - 1
b = 99 + 1 
c = a - b
d = c / 2
e = d + 1
Problem: a can do a piece of work in 4 days . b can do it in 15 days . with the assistance of c they completed the work in 24 days . find in how many days can c alone do it ?
Options: a ) 0.391 days , b ) 0.491 days , c ) 0.331 days , d ) 1.391 days , e ) 0.301 days
Rationale: "c = 1 / 2 - 1 / 24 - 1 / 15 = 0.391 days answer : a"
Answer: a
Python program:
a = 4 * 15
b = 4 * 15
c = 4 * 15
d = c / 4
e = 4 * 15
f = e / 15
g = d + f 
h = g * 24
i = b - h
j = i / 24
k = a / j
Problem: find 10 / 11 = 110 / ?
Options: a ) 111 , b ) 1100 , c ) 121 , d ) 100 , e ) none of these
Rationale: "answer let 10 / 11 = 110 / n , then , 10 n = 11 x 110 ∴ n = ( 11 x 110 ) / 10 = 121 . option : c"
Answer: c
Python program:
a = 10 / 11
Problem: in a dairy farm , 46 cows eat 46 bags of husk in 46 days . in how many days one cow will eat one bag of husk ?
Options: a ) 1 , b ) 46 , c ) 20 , d ) 26 , e ) 30
Rationale: "explanation : one bag of husk = 46 cows per day ⇒ 46 × 1 × 46 = 1 × 46 × x for one cow = 46 days answer : b"
Answer: b
Python program:
a = 46 / 46
b = a * 46
Problem: [ ( 3.242 x 14 ) / 100 ] = ?
Options: a ) 0.045388 , b ) 4.5388 , c ) 453.88 , d ) 473.88 , e ) none of these
Rationale: "answer multiplying 3.242 x 14 = 4.5388 now divide 4.5388 by 100 so , 4.5388 ÷ 100 = 0.045388 ∴ shift the decimal two places to the left as 100 correct option : a"
Answer: a
Python program:
a = 3 * 242
b = a / 100
c = b / 10
Problem: i chose a number and divide it by 5 . then i subtracted 154 from the result and got 6 . what was the number i chose ?
Options: a ) 600 , b ) 700 , c ) 800 , d ) 900 , e ) none
Rationale: "solution : let xx be the number i chose , then x / 5 − 154 = 6 x / 5 = 160 x = 800 answer c"
Answer: c
Python program:
a = 154 + 6 
b = a * 5
Problem: a man rows his boat 80 km downstream and 45 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ?
Options: a ) 6 , b ) 8 , c ) 5 , d ) 7 , e ) 9
Rationale: "speed downstream = d / t = 80 / ( 2 1 / 2 ) = 32 kmph speed upstream = d / t = 45 / ( 2 1 / 2 ) = 18 kmph the speed of the stream = ( 32 - 18 ) / 2 = 7 kmph answer : d"
Answer: d
Python program:
a = 80 / 2
b = 45 / 2
c = a - b
d = c / 2
Problem: find out the c . i on rs . 6000 at 4 % p . a . compound half - yearly for 1 1 / 2 years
Options: a ) 367.25 , b ) 306.07 , c ) 306.04 , d ) 306.03 , e ) 306.01
Rationale: a = 6000 ( 51 / 50 ) 3 = 6367.248 6000 - - - - - - - - - - - 367.25 answer : a
Answer: a
Python program:
a = 4 / 100
b = 1 + a 
c = 3 / 2
d = b ** c
e = 6000 * d
f = e - 6000
Problem: a card is drawn from a pack of 52 cards . the probability of getting a queen club or a king of heart ?
Options: a ) 3 / 26 , b ) 1 / 26 , c ) 4 / 26 , d ) 6 / 26 , e ) 10 / 26
Rationale: "n ( s ) = 52 let e = event of getting a queen of club or a king of heart . n ( e ) = 2 p ( e ) = n ( e ) / n ( s ) = 2 / 52 = 1 / 26 option : b"
Answer: b
Python program:
a = 4 * 4
b = 52 - a
c = b / 52
Problem: a , b and c run around a circular track starting from the same point simultaneously and in the same direction at speeds of 4 kmph , 6 kmph and 8 kmph respectively . if the length of the track is 400 meters , when will a , b and c meet at the starting point for the first time after they started the race ?
Options: a ) 1 minute , b ) 5 minutes , c ) 12 minutes , d ) 20 minutes , e ) 24 minutes
Rationale: 4 kmph , 6 kmph and 8 kmph is equal to 4000 / 60 mtrs / min , 6000 / 60 mtrs / min and 8000 / 60 mtrs / min or 200 / 3 , 100 , 400 / 3 mtrs / min respectively . seeing this we can infer that the answer should be at least divisible by 3 . ( minutes in options are integers . so if the answer is not divisible by 3 , we will have 200 / 3 * answer = distance traveled by a in fractions whereas 100 * answer = distance traveled by a as integer ) so , a , b and d are out . at 12 min a , b and c will travel 800 , 1200 and 1600 mtrs respectively . length of the circle is given as 400 mtrs . as 800 , 1200 and 1600 are divisible by 400 , we can say that a , b and c will be at starting point after 12 min . hence , c will be the answer .
Answer: c
Python program:
a = 400 / 1000
b = 6 / a
c = const_60 / b
d = 400 / 1000
e = 8 / d
f = const_60 / e
g = c * f
Problem: if 15 workers can build a wall in 48 hours , how many workers will be required to do the same work in 30 hours ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 25 , e ) 23
Rationale: let the number of workers employed to build the wall in 30 hours be y 48 * 15 = 30 * y ( 48 * 15 ) / 30 = y y = 24 answer : b
Answer: b
Python program:
a = 15 * 48
b = a / 30
Problem: the least number of 4 digits which is divisible by 15 , 25 , 40 and 75 is :
Options: a ) 9000 , b ) 9400 , c ) 9600 , d ) 9800 , e ) 9700
Rationale: greatest number of 4 digits is 9999 . l . c . m of 15 , 25 , 40 and 75 is 600 . on dividing 9999 by 600 , the remainder is 399 . required number = 9999 - 399 = 9600 answer : c
Answer: c
Python program:
a = 4 * 2
b = 75 * a
c = 4 * 2
d = b * c
e = d * 2
Problem: find the probability that a leap year chosen at random will have 53 sundays
Options: a ) 2 / 7 , b ) 2 / 6 , c ) 2 / 5 , d ) 2 / 3 , e ) 2 / 4
Rationale: "a leap year has 366 day which is 52 full weeks + 2 odd days . now these two odd days may be ( sun + mon ) , ( mon + tue ) , . . . . ( sat + sun ) . now there are total 7 ways . of which sunday appeared two times . so answer 2 / 7 answer : a"
Answer: a
Python program:
a = 3 + 4 
b = 2 / a
Problem: three pipes a , b and c can fill a tank from empty to full in 20 minutes , 20 minutes and 30 minutes respectively . when the tank is empty , all the three pipes are opened . a , b and c discharge chemical solutions p , q and r respectively . what is the proportion of solution r in the liquid in the tank after 3 minutes ?
Options: a ) 1 / 2 , b ) 1 / 5 , c ) 1 / 3 , d ) 1 / 4 , e ) 1 / 6
Rationale: part filled by ( a + b + c ) in 3 minutes = 3 ( 1 / 20 + 1 / 20 + 1 / 30 ) = 6 / 15 part filled by c in 3 minutes = 3 / 30 required ratio = 3 / 30 * 15 / 6 = 1 / 4 answer : d
Answer: d
Python program:
a = 3 / 30
b = 1 / 30
c = 1 / 20
d = 1 / 20
e = c + d 
f = b + e 
g = 3 * f
h = 1 / g
i = a * h
Problem: a man ' s speed with the current is 25 km / hr and the speed of the current is 2.5 km / hr . the man ' s speed against the current is ?
Options: a ) 10 , b ) 80 , c ) 50 , d ) 30 , e ) 20
Rationale: "man ' s speed with the current = 25 km / hr = > speed of the man + speed of the current = 25 km / hr speed of the current is 2.5 km / hr hence , speed of the man = 25 - 2.5 = 22.5 km / hr man ' s speed against the current = speed of the man - speed of the current = 22.5 - 2.5 = 20 km / hr answer is e ."
Answer: e
Python program:
a = 25 - 2
b = a - 2
Problem: in a fraction , if numerator is added by 2 and denominator by 1 it results 1 , and if numerator added again by 4 and denominator by 2 it results 1 / 2 . find the fraction ?
Options: a ) 3 / 4 , b ) 5 / 4 , c ) 7 / 4 , d ) 9 / 4 , e ) 11 / 4
Rationale: x + 2 / y + 1 = 1 i . e , x - y + 1 = 0 ; - - - - - - - - ( 1 ) x + 4 / y + 2 = 1 / 2 i . e . , 2 x - y + 6 = 0 ; - - - - - - - - - ( 2 ) solving 1 and 2 . . . we get x = - 5 and y = - 4 answer is 5 / 4 . . . answer : b
Answer: b
Python program:
a = 4 + 1 
b = a / 4
Problem: a rectangular room has the rectangular shaped rug shown as above figure such that the rug ’ s area is 180 square feet and its length is 8 feet longer than its width . if the uniform width between the rug and room is 8 feet , what is the area of the region uncovered by the rug ( shaded region ) , in square feet ?
Options: a ) 32
b ) 36
c ) 704
d ) 46
e ) 104
Rationale: rug ' s area = 180 which is ( x ) x ( 8 + x ) = 180 so x = 10 rug maintains a uniform distance of 8 feet so room has dimension 10 + 16 and 18 + 16 i . e . 26 and 34 area of room 26 x 34 = 884 area covered is 180 so uncovered area is 884 - 180 = 704 ( answer c )
Answer: c
Python program:
a = const_180 / 10
b = a - 2
c = b + 10 
d = const_180 / 10
e = const_180 / 10
f = e - 2
g = d + f 
h = c * g
i = h - 180
Problem: 7 people average age is 30 . youngest person age is 4 . find average of the people when youngest was born .
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27
Rationale: "average age of people = 30 so have total age = 210 before 7 years we have to deduct each person age by seven years 210 - 32 = 182 so average age would be 182 / 7 = 26 answer : d"
Answer: d
Python program:
a = 30 * 7
b = 4 * 7
c = a - b
d = c / 7
Problem: in a group of cows and chickens , the number of legs was 10 more than twice the number of heads . the number of cows was :
Options: a ) 5 , b ) 7 , c ) 10 , d ) 12 , e ) 14
Rationale: "let the number of cows be x and their legs be 4 x . let the number of chicken be y and their legs be 2 x . total number of legs = 4 x + 2 y . total number of heads = x + y . the number of legs was 10 more than twice the number of heads . therefore , 2 × ( x + y ) + 10 = 4 x + 2 y . or , 2 x + 2 y + 10 = 4 x + 2 y . or , 2 x + 10 = 4 x [ subtracting 2 y from both sides ] . or , 10 = 4 x – 2 x [ subtracting 2 x from both sides ] . or , 10 = 2 x . or , x = 5 [ dividing by 2 on both sides ] . therefore , the number of cows = 5 . correct answer : a ) 5"
Answer: a
Python program:
a = 4 - 2
b = 10 / a
Problem: the cash difference between the selling prices of an article at a profit of 4 % and 6 % is rs . 3 . the ratio of the two selling prices is :
Options: a ) 51 : 52 , b ) 52 : 53 , c ) 51 : 53 , d ) 52 : 55 , e ) 52 : 56
Rationale: "let c . p . of the article be rs . x . then , required ratio = 104 % of x / 106 % of x = 104 / 106 = 52 / 53 = 52 : 53 answer : b"
Answer: b
Python program:
a = 100 + 4 
b = 100 + 6 
c = a / b
Problem: the area of a circle is increased by 300 % . by what percent has the radius of the circle increased ?
Options: a ) 400 % , b ) 200 % , c ) 100 % , d ) 600 % , e ) 800 %
Rationale: "the area of the circle is increased by 300 % , thus the area is increased 4 times . the area of a circle it proportional to the square of the radius ( area = π r ^ 2 ) , therefore the radius must increase 2 times ( diameter increase 2 times = area increase 4 times ) , which is increase by 100 % . answer : c"
Answer: c
Python program:
a = 2 / 2
b = 100 * a
Problem: the total number of digits used in numbering the pages of a book having 356 pages is
Options: a ) 732 , b ) 990 , c ) 1098 , d ) 960 , e ) 1405
Rationale: "total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 257 ) = ( 9 + 180 + 771 ) = 960 . answer : d"
Answer: d
Python program:
a = 356 * 3
b = 100 - 1
c = a - b
d = 10 - 1
e = c - d
Problem: working alone at their respective constant rates , a can complete a task in ‘ a ’ days and b in ‘ b ’ days . they take turns in doing the task with each working 2 days at a time . if a starts they finish the task in exact 8 days . if b starts , they take a day more . how long does it take to complete the task if they both work together ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 4 , e ) 2
Rationale: "work done by ab in a day = xy respectively . when a starts : no . of days when a works = 4 no . of days when b works = 4 → 4 x + 4 y = 1 when b starts : no . of days when a works = 5 no . of days when b works = 3 → 5 x + 3 y = 1 solving the above two equations for xy x = 1 / 8 y = 1 / 8 → total work done by ab in a day = 1 / 8 + 1 / 8 = 1 / 4 → no . of days to complete the work when both work together = 4 answer : d"
Answer: d
Python program:
a = 8 - 1
b = 1/(a)
c = 8 + 2 
d = 1/(c)
e = b + d 
f = 1/(e)
Problem: a thief goes away with a santro car at a speed of 40 kmph . the theft has been discovered after half an hour and the owner sets off in a bike at 45 kmph when will the owner over take the thief from the start ?
Options: a ) a ) 2 , b ) b ) 5 , c ) c ) 7 , d ) d ) 4 , e ) e ) 8
Rationale: "explanation : | - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - | 45 40 d = 20 rs = 45 – 40 = 5 t = 20 / 5 = 4 hours answer : option d"
Answer: d
Python program:
a = 1 / 2
b = a * 40
c = 45 - 40
d = b / c
e = 1 / 2
f = d - e
Problem: the area of a right triangle pcm is 18 . length of smallest side cm is 3 units . find the length of the other two sides .
Options: a ) 12 , 9
b ) 18 , 3
c ) 15.16 , 6
d ) 12 , 12.37
e ) 12 , 15.16
Rationale: cm = 3 area = pm * cm / 2 , thus pm = 12 by pythagorean theorem , we can now find the value of pc . d is the correct option .
Answer: d
Python program:
a = 18 * 2
b = a / 3
c = b ** 2
d = 3 ** 2
e = c + d 
f = 1/(2)
g = e ** f
Problem: each machine of type a has 2 steel parts and 2 chrome parts . each machine of type b has 6 steel parts and 5 chrome parts . if a certain group of type a and type b machines has a total of 20 steel parts and 22 chrome parts , how many machines are in the group
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 7
Rationale: "look at the below representation of the problem : steel chrome total a 2 2 20 > > no . of type a machines = 20 / 4 = 5 b 6 5 22 > > no . of type b machines = 22 / 11 = 2 so the answer is 7 i . e e . hope its clear ."
Answer: e
Python program:
a = 5 + 2 
b = 22 / a
c = 2 + 2 
d = 20 / c
e = b + d
Problem: a boat can travel with aspeed of 30 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 70 km downstream .
Options: a ) 1 hr , b ) 2 hrs , c ) 3 hrs , d ) 4 hrs , e ) 5 hrs
Rationale: "speed downstream = ( 30 + 5 ) km / hr = 35 km / hr . time taken to travel 68 km downstream = 70 / 35 hrs = 2 hrs . b"
Answer: b
Python program:
a = 30 + 5 
b = 70 / a
Problem: the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 46 years , was replaced by a new person . find the age of the new person ?
Options: a ) 18 , b ) 56 , c ) 16 , d ) 17 , e ) 14
Rationale: "initial average age of the 10 persons be p . age of the new person q . sum of the ages of the initial 10 persons = 10 p new average = ( p - 3 ) 10 ( p - 3 ) = 10 p - 46 + q = > q = 16 answer : c"
Answer: c
Python program:
a = 10 * 3
b = 46 - a
Problem: a number whose fifth part increased by 4 is equal to its fourth part diminished by 10 , is :
Options: a ) 240 , b ) 260 , c ) 270 , d ) 280 , e ) 290
Rationale: let the number be x . then , ( ( 1 / 5 ) x + 4 ) = ( ( 1 / 4 ) x − 10 ) < = > x / 20 < = > x = 14 * 20 = 280 . answer : d
Answer: d
Python program:
a = 10 + 4 
b = 1 / 4
c = 1 + 4 
d = 1 / c
e = b - d
f = a / e
Problem: if 0.60 : x : : 6 : 2 , then x is equal to
Options: a ) 0.2 , b ) 0.5 , c ) 2.5 , d ) 1.8 , e ) none
Rationale: "sol . ( x × 6 ) = ( 0.60 × 2 ) ⇒ x = 0.60 / 6 = 0.2 . answer a"
Answer: a
Python program:
a = 0 * 60
b = a / 6
Problem: a and b together can do a piece of work in 6 days and a alone can do it in 12 days . in how many days can b alone can do it ?
Options: a ) 11 days , b ) 15 days , c ) 12 days , d ) 21 days , e ) 22 days
Rationale: "explanation : a and b can do work 1 / 6 in 1 day a alone can do 1 / 12 work in 1 day b alone can do ( 1 / 6 - 1 / 12 ) = 1 / 12 work in 1 day = > complete work can be done in 12 days by b answer : option c"
Answer: c
Python program:
a = 1/(6)
b = 1/(12)
c = a - b
d = 1/(c)
Problem: in a certain town , the ratio of ny yankees fans to ny mets fans is 2 : 1 , and the ratio of ny mets fans to boston red sox fans is 3 : 7 . if there are 352 baseball fans in the town , each of whom is a fan of exactly one of those three teams , how many ny mets fans are there in this town ?
Options: a ) 58 , b ) 66 , c ) 74 , d ) 82 , e ) 90
Rationale: "the ratio of yankees : mets : red sox = 6 : 3 : 7 the mets fans are 3 / 16 of the population . ( 3 / 16 ) * 352 = 66 the answer is b ."
Answer: b
Python program:
a = 2 * 1
b = a + 3 
c = b + 7 
d = 352 / c
e = d * 3
Problem: in a certain neighborhood , 60 percent of the student are going to school ( a ) , and the rest are going to school ( b ) . a new school ( c ) is opened , if 30 percent of student of school ( a ) and 40 percent of student of school ( b ) are expected to go to the new school ( c ) , what percent of student are expected to go to the new school ( c ) ?
Options: a ) 30 % , b ) 34 % , c ) 38 % , d ) 42 % , e ) 46 %
Rationale: say there are total of 100 students in the neighborhood , 60 students are going to school ( a ) and 40 student are going to school ( b ) 60 * 0.3 = 18 student of school ( a ) are expected to go to the new school ( c ) 40 * 0.4 = 16 student of school ( b ) are expected to go to the new school ( c ) thus total of 18 + 16 = 34 student are expected to go to the new school ( c ) , which is 34 % of students . answer : b .
Answer: b
Python program:
a = 30 / 100
b = a * 60
c = 40 / 100
d = 100 - 60
e = c * d
f = b + e
Problem: two trains of equal length , running with the speeds of 60 and 100 kmph , take 50 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 10 , b ) 6.25 , c ) 7.35 , d ) 2.62 , e ) 2.28
Rationale: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 50 d = 50 * 100 / 18 = 2500 / 9 rs = 60 + 100 = 160 * 5 / 18 t = 2500 / 9 * 18 / 800 = 6.25 sec . answer : b"
Answer: b
Python program:
a = 60 - 100
b = const_0_2778 * a
c = b * 50
d = 60 + 100 
e = const_0_2778 * d
f = 1/(e)
g = c * f
Problem: find the number of elements in the power set of { 1,2 }
Options: a ) 4 , b ) 0 , c ) 2 , d ) 3 , e ) 5
Rationale: "power set is the set of subsets of { 1,2 } that is { { 1,2 } , { 1 } , { 2 } , f } answer : a"
Answer: a
Python program:
a = 2 + 2
Problem: 64 + 5 * 12 / ( 180 / 3 ) = ?
Options: a ) 22 , b ) 77 , c ) 29 , d ) 65 , e ) 21
Rationale: 64 + 5 * 12 / ( 180 / 3 ) = 64 + 5 * 12 / ( 60 ) = 64 + ( 5 * 12 ) / 60 = 64 + 1 = 65 . answer : d
Answer: d
Python program:
a = 5 * 12
b = 180 / 3
c = a / b
d = 64 + c
Problem: alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 1021 . find the cost of each ice - cream cup ?
Options: a ) 35 , b ) 66 , c ) 77 , d ) 99 , e ) 91
Rationale: "let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1021 96 + 225 + 490 + 6 x = 1021 6 x = 210 = > x = 35 . answer : a"
Answer: a
Python program:
a = 16 * 6
b = 1021 - a
c = 5 * 45
d = b - c
e = 7 * 70
f = d - e
g = f / 6
Problem: the length of a train and that of a platform are equal . if with a speed of 54 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ?
Options: a ) 227 , b ) 299 , c ) 450 , d ) 750 , e ) 211
Rationale: "speed = [ 54 * 5 / 18 ] m / sec = 15 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 15 è x = 15 * 60 / 2 = 450 answer : c"
Answer: c
Python program:
a = 54 * 1000
b = const_60 / 1
c = a / b
d = c / 2
Problem: jack went on a diet 6 months ago when he weighed 222 pounds . if he now weighs 198 pounds and continues to lose at the same average monthly rate , in approximately how many months will he weigh 180 pounds ?
Options: a ) 3 , b ) 35 , c ) 4 , d ) 45 , e ) 5
Rationale: joe lost his weigh 24 pounds during 6 months . that means that he lost 4 pounds per month . he should lose more 18 pounds to be 180 pounds . so it would take 18 / 4 = 4.5 months . correct answer is d
Answer: d
Python program:
a = 198 - 180
b = 222 - 198
c = 6 / b
d = a * c
e = d * 10
Problem: if 2 x = 3 y = 10 , then 3 xy = ?
Options: a ) 100 , b ) 200 , c ) 120 , d ) 50 , e ) 20
Rationale: "2 x = 10 ; x = 5 3 y = 10 ; y = 10 / 3 multiply : 3 xy = 3 * 5 * 10 / 3 = 50 answer : d ."
Answer: d
Python program:
a = 2 * 100
b = a / 2
c = b - 2
d = 2 * 100
e = d / 2
f = e + 2 
g = c / f
Problem: b completes a work in 7 days . a alone can do it in 10 days . if both work together , the work can be completed in how many days ?
Options: a ) 3.75 days , b ) 4.11 days , c ) 5.11 days , d ) 6.75 days , e ) 7.33 days
Rationale: "1 / 7 + 1 / 10 = 17 / 70 70 / 17 = 4.11 days answer : b"
Answer: b
Python program:
a = 10 * 7
b = 7 + 10 
c = a / b
Problem: excluding the stoppages , the speed of a bus is 48 km / hr and including the stoppages the speed of the bus is 24 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 30 min , b ) 10 min , c ) 12 min , d ) 20 min , e ) 18 min
Rationale: "speed of the bus without stoppage = 48 km / hr speed of the bus with stoppage = 24 km / hr difference in speed = 24 km / hr so , the time taken in the stoppages = time taken to cover 24 km = ( 24 / 48 ) hr = 1 / 2 hr = 30 min answer : a"
Answer: a
Python program:
a = 24 / 48
b = a * const_60
c = const_60 - b
Problem: what is the % change in the area of a rectangle when its length increases by 20 % and its width decreases by 20 % ?
Options: a ) 0 % , b ) 20 % increase , c ) 20 % decrease , d ) 4 % decrease , e ) insufficient data
Rationale: "( 12 / 10 ) * ( 8 / 10 ) = 96 / 100 of original area 96 / 100 is a 4 % decrease from 100 / 100 - > d"
Answer: d
Python program:
a = 100 + 20 
b = 100 - 20
c = a * b
d = c / 100
e = 100 - d
Problem: 5 pieces of wood have an average length of 128 cm and a median length of 140 cm . what is the maximum possible length , in cm , of the shortest piece of wood ?
Options: a ) a ) 90 , b ) b ) 100 , c ) c ) 110 , d ) d ) 130 , e ) e ) 140
Rationale: c . 110 sum of all lengths of all 5 pieces of wood = 128 * 5 = 640 3 rd piece ( sorted in increasing length ) length = 140 ( median ) for sum of first 2 wood length to become max , last two should be least . let 4 th , 5 th wood also have length 140 each . total of last 3 = 140 * 3 = 420 sum of first 2 = 640 - 420 = 220 each of these 2 will have length 220 / 2 = 110 answer c
Answer: c
Python program:
a = 5 * 128
b = 140 * 3
c = a - b
d = c / 2
Problem: if a certain toy store ' s revenue in november was 4 / 5 of its revenue in december and its revenue in january was 3 / 4 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 ) 1 / 4 , b ) 1 / 2 , c ) 2 / 3 , d ) 2 , e ) 4
Rationale: "let dec rev = 100 then nov rev is 4 / 5 ( 100 ) = > 80 therefore jan rev = 3 / 4 ( nov rev ) = 3 / 4 ( 80 ) = > 60 hence dec rev = x * ( nov rev + jan rev ) / 2 100 = x * ( 80 + 60 ) / 2 x = 100 / 70 = > 1.42 = 2 ans ) d"
Answer: d
Python program:
a = 4 / 5
b = 4 / 5
c = 3 / 4
d = b * c
e = a + d 
f = e / 2
g = 3 / f
Problem: a car started running at a speed of 34 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 10 hours of the journey .
Options: a ) 43 km , b ) 76 km , c ) 25 km , d ) 15 km , e ) 30 km
Rationale: "a 43 km the total distance covered by the car in the first 10 hours = 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 + 50 + 52 = sum of 10 terms in ap whose first term is 34 and last term is 52 = 10 / 2 [ 34 + 52 ] = 430 km ."
Answer: a
Python program:
a = 2 * 10
b = 34 + a 
c = b + 34 
d = c / 2
Problem: two boys starts from the same place walking at the rate of 4 kmph and 5.5 kmph respectively in the same direction . what time will they take to be 10.5 km apart ?
Options: a ) 8 , b ) 5 , c ) 7 , d ) 9 , e ) 6
Rationale: "explanation : relative speed = 5.5 - 4 = 1.5 kmph ( because they walk in the same direction ) distance = 10.5 km time = distance / speed = 10.5 / 1.5 = 7 hr answer : c"
Answer: c
Python program:
a = 5 - 5
b = 10 / 5