euclaise/mathqa_programs huggingface dataset:
Problem: ron cycles his way up on a hill side and back . he takes the exact same route both ways . on the trip out he cycles an average speed of 5 miles per hour . on the trip back , downhill cycling at an average speed of 100 miles per hour , he is quick to return back . what is his approximate average speed for the round trip in miles per hour ?
Options: a ) 8 , b ) 9.52 , c ) 10 , d ) 11.7 , e ) 20
Rationale: average speed = total distance / total time here distance to hill top and back is same as he takes the same route . d = 5 t 1 and d = 100 t 2 therefore , t 1 = d / 5 and t 2 = d / 100 t 1 + t 2 = 21 d / 100 therefore , average speed = 2 d / 21 d / 100 = 2 d * 100 / 21 d answer is 9.52 since , the options are far away we need not solve till the decimal points so correct answer is option b
Answer: b
Python program:
a = 100 * 2
b = a / 5
c = b * 5
d = 100 * 2
e = d / 100
f = e * 100
g = c + f 
h = 100 * 2
i = h / 100
j = 100 * 2
k = j / 5
l = i + k 
m = g / l
Problem: two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability q that jane will be on the same committee as albert ?
Options: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %
Rationale: "total number of ways to choose 3 member committee - 6 c 3 = ( 6 ! / 3 ! 3 ! ) = 20 no . of ways albert n jane are in same committee : - ( 4 c 1 * 2 ) = 8 probability q = ( 8 / 20 ) * 100 = 40 % . + 1 for me . . : d"
Answer: d
Python program:
a = math.comb(4, 1)
b = a * 2
c = math.comb(6, 3)
d = b / c
e = 5 * 5
f = e * 4
g = d * f
Problem: how many 3 digit positive integers q exist that when divided by 7 leave a remainder of 5 ?
Options: a ) 128 , b ) 142 , c ) 143 , d ) 141 , e ) 129
Rationale: minimum three digit number is 100 and maximum three digit number is 999 . the first three digit number that leaves remainder 5 when divided by 7 is 103 . 14 * 7 = 98 + 5 = 103 the second three digit number that leaves remainder 5 when divided by 7 is 110 . 15 * 7 = 105 + 5 = 110 the third three digit number that leaves remainder 5 when divided by 7 is 117 and so on the last three digit number that leaves remainder 5 when divided by 7 is 999 142 * 7 = 994 + 5 = 999 therefore , we identify the sequence 103 , 110,117 . . . . . 999 use the formula of last term last term = first term + ( n - 1 ) * common difference you will get the answer 129 that is definitely e .
Answer: e
Python program:
a = 100 * 10
b = a - 1
c = 10 + 4 
d = c * 7
e = d + 5 
f = b - e
g = f / 7
Problem: a ' and ' b ' are positive integers such that their lcm is 20 and their hcf is 1 . what is the addition between the maximum and minimum possible values of ' a - b ' ?
Options: a ) 0 , b ) 12 , c ) 24 , d ) 26 , e ) 18
Rationale: "possible values of a and b can be 5,4 ; 4,5 and 1,20 ; 20,1 maximum possible value for a - b is 20 - 1 = 19 minimum possible value for a - b is 1 - 20 = - 19 19 - 19 = 0 ans is a"
Answer: a
Python program:
a = 20 + 20 
b = 1 + 1 
c = a - b
Problem: alice , benjamin , and carol each try independently to win a carnival game . if their individual probabilities for success are 1 / 5 , 3 / 8 , and 2 / 7 , respectively , what is the probability that exactly two of the 3 players will win but one will lose ?
Options: a ) 3 / 140 , b ) 1 / 28 , c ) 3 / 56 , d ) 3 / 35 , e ) 7 / 40
Rationale: p = p ( a wins , b wins , c loses ) + p ( a wins , b loses , c wins ) + p ( a loses , b wins , c wins ) = 1 / 5 * 3 / 8 * 5 / 7 + 1 / 5 * 5 / 8 * 2 / 7 + 4 / 5 * 3 / 8 * 2 / 7 = 7 / 40 . answer : e .
Answer: e
Python program:
a = 4 / 5
b = 3 / 8
c = a * b
d = 2 / 7
e = c * d
f = 1 / 5
g = 5 / 8
h = f * g
i = 2 / 7
j = h * i
k = e + j 
l = 1 / 5
m = 3 / 8
n = l * m
o = 5 / 7
p = n * o
q = k + p
Problem: a person takes 10 minutes more to cover a certain distance by decreasing his speed by 20 % . what is the time taken to cover the distance at his original speed ?
Options: a ) 50 minutes , b ) 20 minutes , c ) 40 minutes , d ) 60 minutes , e ) 80 minutes
Rationale: let the distance and original speed be d km and k kmph respectively . d / 0.8 k - d / k = 10 / 60 = > 5 d / 4 k - d / k = 1 / 6 = > ( 5 d - 4 d ) / 4 k = 1 / 6 = > d = 4 / 6 k = 2 / 3 k time taken to cover the distance at original speed = d / k = 2 / 3 hours = 40 minutes . answer : c
Answer: c
Python program:
a = 100 - 20
b = a / 20
c = 10 * b
Problem: victor gets 92 % marks in examinations . if these are 184 marks , find the maximum marks .
Options: a ) 334 , b ) 500 , c ) 200 , d ) 288 , e ) 271
Rationale: "let the maximum marks be m then 92 % of m = 184 ⇒ 92 / 100 × m = 184 ⇒ m = ( 184 × 100 ) / 92 ⇒ m = 18400 / 92 ⇒ m = 200 therefore , maximum marks in the examinations are 200 . answer : c"
Answer: c
Python program:
a = 92 / 100
b = 184 / a
Problem: by selling 8 pencils for a rupee a man loses 60 % . how many for a rupee should he sell in order to gain 60 % ?
Options: a ) 8 , b ) 9 , c ) 2 , d ) 6 , e ) 4
Rationale: "40 % - - - 8 160 % - - - ? 40 / 160 * 12 = 2 answer : c"
Answer: c
Python program:
a = 100 + 60 
b = 100 - 60
c = 1 / b
d = a * c
e = 1 / d
f = e * 8
Problem: a specialized type of sand consists of 40 % mineral x by volume and 60 % mineral y by volume . if mineral x weighs 3.5 grams per cubic centimeter and mineral y weighs 3 grams per cubic centimeter , how many grams does a cubic meter of specialized sand combination weigh ? ( 1 meter = 100 centimeters )
Options: a ) 5 , 500,000 , b ) 3 , 200,000 , c ) 55,000 , d ) 28,000 , e ) 280
Rationale: "let the volume be 1 m ^ 3 = 1 m * 1 m * 1 m = 100 cm * 100 cm * 100 cm = 1 , 000,000 cm ^ 3 by volume 40 % is x = 400,000 cm ^ 3 60 % is y = 600,000 cm ^ 3 by weight , in 1 cm ^ 3 , x is 3.5 gms in 400,000 cm ^ 3 , x = 3.5 * 400,000 = 1 , 400,000 grams in 1 cm ^ 3 , y is 3 gms in 600,000 cm ^ 3 , y = 3 * 600,000 = 1 , 800,000 gms total gms in 1 m ^ 3 = 1 , 400,000 + 1 , 800,000 = 3 , 200,000 answer : b"
Answer: b
Python program:
a = volume_cube / (
b = a * 10
c = b * 3
d = c + 3 
e = volume_cube / (
f = e * 10
g = 2 * 3
h = f * g
i = d - h
Problem: for any integer k > 1 , the term “ length of an integer ” refers to the number of positive prime factors , not necessarily distinct , whose product is equal to k . for example , if k = 24 , the length of k is equal to 4 , since 24 = 2 × 2 × 2 × 3 . if x and y are positive integers such that x > 1 , y > 1 , and x + 3 y < 1000 , what is the maximum possible sum of the length of x and the length of y ?
Options: a ) 5 , b ) 6 , c ) 15 , d ) 16 , e ) 18
Rationale: basically the length of an integer is the sum of the powers of its prime factors . for example the length of 24 is 4 because 24 = 2 ^ 3 * 3 ^ 1 - - > 3 + 1 = 4 . given : x + 3 y < 1,000 . now , to maximize the length of x or y ( to maximize the sum of the powers of their primes ) we should minimize their prime bases . minimum prime base is 2 : so if x = 2 ^ 9 = 512 then its length is 9 - - > 512 + 3 y < 1,000 - - > y < 162.7 - - > maximum length of y can be 7 as 2 ^ 7 = 128 - - > 9 + 7 = 16 . answer : d .
Answer: d
Python program:
a = 4 + 3 
b = 4 + 4 
c = b + 1 
d = a + c
Problem: there 3 kinds of books in the library physics , chemistry and biology . ratio of physics to chemistry is 3 to 2 ; ratio of chemistry to biology is 4 to 3 , and the total of the books is more than 3000 . which one of following can be the total t of the book ?
Options: a ) 3003 , b ) 3027 , c ) 3024 , d ) 3021 , e ) 3018
Rationale: "first , you have to find the common ratio for all 3 books . you have : p : c : b 3 : 2 - - > multiply by 2 ( gives you row 3 ) 4 : 6 6 : 4 : 3 hence : p : c : b : t ( total ) t 6 : 4 : 3 : 13 - - - - > this means , the total number must be a multiple of 13 . answer a is correct since 299 is divisible by 13 , hence is 2990 and so is 3003 ( 2990 + 13 ) ."
Answer: a
Python program:
a = 3000 + 3
Problem: a jogger running at 9 kmph along side a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ?
Options: a ) 3.6 sec , b ) 18 sec , c ) 36 sec , d ) 72 sec , e ) none
Rationale: category formulae examples directions : problems based on trains . 11 . a train 280 m long , running with a speed of 63 km / hr will pass a tree in a . 15 sec . b . 16 sec . c . 18 sec . d . 20 sec . solution speed = ( 63 x 5 / 18 ) m / sec = 35 / 2 msec time taken = ( 280 x 2 / 35 ) m / sec = 16 sec . 12 . a train running at the speed of 60 km / hr crosses a pole in 9 seconds . what is ihe length of the train ? a . 120 metres b . 180 metres c . 324 metres d . none of these solution 13 . a jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ? a . 3.6 sec b . 18 sec c . 36 sec d . 72 sec solution speed of train relative to jogger = ( 45 - 9 ) km / hr = 36 km / hr = ( 36 x 5 / 18 ) m / sec = 10 m / sec distance covered = ( 240 + 120 ) m = 360 m time taken = ( 360 / 10 ) sec = 36 sec . answer c
Answer: c
Python program:
a = 240 + 120 
b = a / 1000
c = 45 - 9
d = b / c
e = d * const_60
f = e * const_60
Problem: of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 100 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
Options: a ) 280 , b ) 400 , c ) 540 , d ) 500 , e ) 840
Rationale: "of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month : 2 / 3 * 3 / 4 = 1 / 2 survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year : ( 1 - 3 / 5 ) * 1 / 2 = 1 / 5 survived the first year . 100 geese survived the first year : 1 / 5 * ( total ) = 100 - - > ( total ) = 500 . answer : d ."
Answer: d
Python program:
a = 3 / 5
b = 1 - a
c = 100 / b
d = 3 / 4
e = c / d
f = 2 / 3
g = e / f
Problem: a shopkeeper sold an article for rs 2524.36 . approximately what was his profit percent if the cost price of the article was rs 2400
Options: a ) 4 % , b ) 5 % , c ) 6 % , d ) 7 % , e ) 8 %
Rationale: "explanation : gain % = ( 125.36 * 100 / 2400 ) = 5.2 % = 5 % approx option b"
Answer: b
Python program:
a = 2524 - 36
b = a / 2400
c = 100 * b
d = math.floor(c)
Problem: at a particular graduation party with 300 guests , 70 % of the guests brought gifts , and 40 % of the female guests brought gifts . if 30 males did not bring gifts to the party , how many females did bring gifts ?
Options: a ) 18 , b ) 28 , c ) 40 , d ) 68 , e ) 70
Rationale: "the correct method total = 300 . . 70 % of 300 = 210 got gifts . . 90 did not get gift , out of which 30 are males , so remaining 90 - 30 = 60 are females . . but 40 % females brought gift , so 60 % did not get it . . so 60 % = 60 , 100 % = 60 * 100 / 60 = 100 . ans 40 % of 100 = 40 c"
Answer: c
Python program:
a = 70 * 300
b = a / 100
c = 300 - b
d = c - 30
e = d * 100
f = 100 - 40
g = e / f
h = g * 40
i = h / 100
Problem: how many multiples of 5 are there between 1 and 36 , exclusive ?
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "7 multiples of 5 between 1 and 36 exclusive . from 5 * 1 upto 5 * 7 , ( 1,2 , 3,4 , . . . , 7 ) . hence , 7 multiples ! correct option is d"
Answer: d
Python program:
a = 36 - 1
b = a / 5
c = b + 1
Problem: a cave is going to explode . a family is trapped inside that cave . the only way to get outside is a narrow tunnel . but the tunnel is weak and thus only two people can go at one time . also , everybody is afraid of going alone . the father takes one minute to go through till the end , the mother takes two , the son takes 4 and the daughter takes 5 . the cave and tunnel will explode in 12 minutes . can they make it to the other end in that time frame ? ps : keep in mind that when two people are moving , the total time taken will be as per the slower one .
Options: a ) 10 minutes , b ) 12 minutes , c ) 18 minutes , d ) 19 minutes , e ) 16 minutes
Rationale: b 12 minutes explanation : yes , surely they can all make it out of the cave . first , father and mother will go . time taken = 2 minutes . father comes back . time taken = 2 + 1 = 3 minutes . both children go . time taken = 3 + 5 = 8 minutes . mother comes back . time taken = 8 + 2 = 10 minutes . mother and father go . time taken = 10 + 2 = 12 minutes . thus in 12 minutes , all of them will be out of the cave through the tunnel .
Answer: b
Python program:
a = 12 / 4
b = a * 5
c = b - 3
Problem: a bag contains 10 balls numbered from 0 to 9 . the balls are such that the person picking a ball out of the bag is equally likely to pick anyone of them . a person picked a ball and replaced it in the bag after noting its number . he repeated this process 2 more times . what is the probability that the ball picked first is numbered higher than the ball picked second and the ball picked second is numbered higher than the ball picked third ?
Options: a ) 72 / 100 , b ) 3 / 25 , c ) 4 / 5 , d ) 1 / 6 , e ) 1 / 9
Rationale: explanation : let , the number of the ball picked first = a , second = b and third = c and these three numbers a , b and c are distinct . three distinct ball can be picked in ( 10 × 9 × 8 ) ways . the order of a , b and c can be as follows : - ( i ) a > b > c . ( ii ) a > c > b . ( iii ) b > c > a . ( iv ) b > a > c . ( v ) c > a > b . ( vi ) c > b > a . they will occur equal number of times . so , the number of ways in which ( a > b > c ) are : - = > 1 / 6 x 10 x 9 x 8 . = > 120 . hence , the required probability is : - = > 120 / ( 10 x 10 x 10 ) . = > 3 / 25 . answer : b
Answer: b
Python program:
a = 10 * 9
b = 4 + 4 
c = a * b
d = 4 + 2 
e = c / d
f = 10 ** 3
g = e / f
Problem: what sum of money will produce rs . 70 as simple interest in 3 years at 3 1 / 2 percent ?
Options: a ) 263 , b ) 500 , c ) 367 , d ) 368 , e ) 666.7
Rationale: "70 = ( p * 3 * 7 / 2 ) / 100 p = 666.7 answer : e"
Answer: e
Python program:
a = 1 / 2
b = 3 + a 
c = 3 * b
d = c / 100
e = 70 / d
Problem: a person x working alone can complete a work in 5 days . a person y completes the same amount of work in 20 days , and a person z when working alone can complete the same amount of work in 30 days . all 3 people work together for 2 days but then x and y leave . how many more days does z need to complete the work after x and y leave ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: the fraction of work completed in two days is 2 / 5 + 2 / 20 + 2 / 30 = 17 / 30 the fraction of work remaining is 1 - 17 / 30 = 13 / 30 the number of days required for z is 13 days . the answer is a .
Answer: a
Python program:
a = 1 / 5
b = 1 / 20
c = a + b 
d = 1 / 30
e = c + d 
f = e * 2
g = 1 - f
h = 1 / 30
i = g / h
Problem: a train 100 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is :
Options: a ) 46 , b ) 50 , c ) 40 , d ) 36 , e ) 41
Rationale: "speed of the train relative to man = 100 / 10 m / sec = 10 m / sec . = 10 x 18 / 5 km / hr = 36 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 36 = 41 km / hr . answer : e"
Answer: e
Python program:
a = 5 * const_0_2778
b = a * 5
c = 100 - b
d = c / 5
e = d / const_0_2778
Problem: in what time will a train 200 meters long completely pass an electric pole , if it travels at a speed of 80 kmph .
Options: a ) 7 , b ) 9 , c ) 5 , d ) 10 , e ) 3
Rationale: sol . speed = [ 80 x 5 / 18 ] m / sec = 22.2 m / sec . time taken = ( 200 / 22.2 ) sec = 9 sec . answer b
Answer: b
Python program:
a = 80 * const_0_2778
b = 200 / a
Problem: a company organzied a help desk . there have been done 24 hrs work on software , 17 hrs on help user nd 40 % on other services . find the total no . of hrs have been worked on that day ?
Options: a ) 68 , b ) 69 , c ) 70 , d ) 67 , e ) 76
Rationale: let total no of hrs = x they have done 24 + 17 = 41 40 % of x is 40 / 100 = 2 / 5 x = 41 + 2 x / 5 x = 68.3 answer : a
Answer: a
Python program:
a = 1 + 4 
b = 24 + 17 
c = a * b
d = c / 3
Problem: the true discount on a bill of rs . 2360 is rs . 360 . what is the banker ' s discount ?
Options: a ) rs . 432 , b ) rs . 425 , c ) rs . 412 , d ) rs . 442 , e ) none of these
Rationale: "explanation : f = rs . 2360 td = rs . 360 pw = f - td = 2360 - 360 = rs . 2000 true discount is the simple interest on the present value for unexpired time = > simple interest on rs . 2000 for unexpired time = rs . 360 banker ' s discount is the simple interest on the face value of the bill for unexpired time = simple interest on rs . 2360 for unexpired time = 360 / 2000 × 2360 = 0.18 × 2160 = rs . 425 answer : option b"
Answer: b
Python program:
a = 2360 - 360
b = 360 / a
c = b * 2360
Problem: a and b go around a circular track of length 600 m on a cycle at speeds of 18 kmph and 48 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 176 sec , c ) 360 sec , d ) 187 sec , e ) 189 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 600 / ( 18 * 5 / 18 ) , 600 / ( 48 * 5 / 18 ) } = 360 sec . answer : c"
Answer: c
Python program:
a = 48 * const_0_2778
b = 18 * const_0_2778
c = a - b
d = 600 / c
Problem: 15 litres of mixture contains 20 % alcohol and the rest water . if 2 litres of water be mixed with it , the percentage of alcohol in the new mixture would be ?
Options: a ) 16.67 % , b ) 23 % , c ) 18.3 % , d ) 17.64 % , e ) 21.23 %
Rationale: "alcohol in the 15 litres of mix . = 20 % of 15 litres = ( 20 * 15 / 100 ) = 3 litres water in it = 15 - 3 = 12 litres new quantity of mix . = 15 + 2 = 17 litres quantity of alcohol in it = 3 litres percentage of alcohol in new mix . = 3 * 100 / 17 = 17.64 % answer is d"
Answer: d
Python program:
a = 15 + 2 
b = 100 - 20
c = b / 100
d = c * 15
e = d + 2 
f = a - e
g = 15 + 2 
h = f / g
i = h * 100
Problem: two pipes p and q can fill a cistern in 10 and 15 minutes respectively . both are opened together , but at the end of 2 minutes the first is turned off . how many more minutes will it take for the cistern to fill after the first pipe is turned off ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "let x be the total time it takes for the cistern to fill . 2 / 10 + x / 15 = 1 x / 15 = 4 / 5 x = 12 after the first pipe is turned off , it takes 10 more minutes to fill the cistern . the answer is e ."
Answer: e
Python program:
a = 1 / 10
b = 1 / 15
c = a + b 
d = c * 2
e = 1 - d
f = e * 15
Problem: there are 16 teams in the hockey league , and each team faces all the other teams 10 times each . how many games are played in the season ?
Options: a ) 750 , b ) 900 , c ) 1050 , d ) 1200 , e ) 1350
Rationale: the number of ways to choose two teams is 16 c 2 = 16 * 15 / 2 = 120 the total number of games in the season is 10 * 120 = 1200 . the answer is d .
Answer: d
Python program:
a = 16 - 1
b = 16 * a
c = b * 10
d = c / 2
Problem: in an examination , the percentage of students qualified to the number of students appeared from school a is 70 % . in school b , the number of students appeared is 20 % more than the students appeared from school a and the number of students qualified from school b is 50 % more than the students qualified from school a . what is the percentage of students qualified to the number of students appeared from school b ?
Options: a ) 30 % , b ) 70 % , c ) 80 % , d ) 87.5 % , e ) none
Rationale: solution let number of students appeared from school a = 100 . then , number of students qualified from school a = 70 . number of students appeared from school b = 120 . number of students qualified from school b = [ 150 / 100 x 70 ] = 105 . required percentage = [ 105 / 120 x 100 ] % = 87.5 % answer d
Answer: d
Python program:
a = 70 - 20
b = const_0_25 * 2
c = 50 - b
d = c - 12
e = a + d
Problem: a man sitting in a train which is travelling at 20 kmph observes that a goods train , travelling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed ?
Options: a ) 52 kmph . , b ) 62 kmph . , c ) 72 kmph . , d ) 92 kmph . , e ) none
Rationale: "solution relative speed = ( 280 / 9 ) m / sec = ( 280 / 9 x 18 / 5 ) = 112 kmph . speed of the train = ( 112 - 20 ) kmph = 92 kmph . answer d"
Answer: d
Python program:
a = 280 / 9
b = a * const_3_6
c = b - 20
Problem: the area of one square is x ^ 2 + 6 x + 9 and the area of another square is 4 x ^ 2 − 20 x + 25 . if the sum of the perimeters of both squares is 52 , what is the value of x ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "the areas are ( x + 3 ) ^ 2 and ( 2 x - 5 ) ^ 2 . the lengths of the sides are x + 3 and 2 x - 5 . if we add the two perimeters : 4 ( x + 3 ) + 4 ( 2 x - 5 ) = 52 12 x = 60 x = 5 the answer is c ."
Answer: c
Python program:
a = 6 / 2
b = 4 * a
c = b - 20
d = 52 - c
e = d / 6
Problem: a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 130 m long ?
Options: a ) 39.2 sec , b ) 35 sec , c ) 44 sec , d ) 40 sec , e ) none of these
Rationale: "speed = 45 km / hr = 45 ã — ( 5 / 18 ) m / s = 150 / 12 = 50 / 4 = 25 / 2 m / s total distance = length of the train + length of the platform = 360 + 130 = 490 meter time taken to cross the platform = 490 / ( 25 / 2 ) = 490 ã — 2 / 25 = 39.2 seconds answer : a"
Answer: a
Python program:
a = 130 / 1000
b = 360 / 1000
c = a + b 
d = c / 45
e = d * 3600
Problem: if g is to be chosen at random from the set { 5,8 , 7,1 } and k is to be chosen at random from the set { 14 , 8,3 } , what is the probability that gk will be even ?
Options: a ) 1 , b ) 5 , c ) 8 , d ) 4 , e ) 3
Rationale: method - 1 gk will be even when 1 ) g is even and k is odd , probability of g even is ( 1 / 4 ) and probability of k odd is ( 1 / 3 ) , so probability of case ( 1 ) = ( 1 / 4 ) * ( 1 / 3 ) = ( 1 / 12 ) 2 ) g is odd and k is even , probability of g odd is ( 3 / 4 ) and probability of k even is ( 2 / 3 ) , so probability of case ( 2 ) = ( 3 / 4 ) * ( 2 / 3 ) = ( 6 / 12 ) 3 ) g is even and k is even , probability of g even is ( 1 / 4 ) and probability of k even is ( 2 / 3 ) , so probability of case ( 1 ) = ( 1 / 4 ) * ( 2 / 3 ) = ( 2 / 12 ) total favorable probability = ( 1 / 12 ) + ( 6 / 12 ) + ( 2 / 12 ) = ( 12 / 12 ) = 1 answer : option a
Answer: a
Python program:
a = 4 * 3
b = 4 * 3
c = a / b
Problem: a man can row 8 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and back . what is the total distance traveled by the man ?
Options: a ) 7.82 km , b ) 6 km , c ) 5.76 km , d ) 5.66 km , e ) 10 km
Rationale: "m = 8 s = 1.2 ds = 9.2 us = 6.8 x / 9.2 + x / 6.8 = 1 x = 3.91 d = 3.91 * 2 = 7.82 answer : a"
Answer: a
Python program:
a = 8 + 1 
b = 8 - 1
c = a * b
d = 8 + 1 
e = 8 - 1
f = d + e 
g = c / f
h = g * 2
Problem: the difference between the place values of two fives in the numerical 86510529 is
Options: a ) 0 , b ) 4905 , c ) 49050 , d ) 490500 , e ) none of them
Rationale: "required difference = ( 500000 - 500 ) = 490500 . answer is d"
Answer: d
Python program:
a = 86510529 + 1 
b = a / 2
Problem: if 45 - [ 28 - { 37 - ( 15 - * ) } ] = 56 , then * is equal to :
Options: a ) - 29 , b ) - 19 , c ) 17 , d ) 29 , e ) 39
Rationale: "45 - [ 28 - { 37 - ( 15 - * ) } ] = 56 = > 45 - [ 28 - { 37 - 15 + * } ] = 56 45 - [ 28 - 37 + 15 - * ] = 56 = > 45 [ 43 - 37 - * ] = 56 45 - [ 6 - * ] = 56 = > 45 - 6 + * = 56 39 + * = 56 = > * = 56 - 39 = 17 answer : c"
Answer: c
Python program:
a = 28 - 37
b = a + 15 
c = 45 - b
d = 56 - c