euclaise/mathqa_programs huggingface dataset:
Problem: a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 52 , then how old is b ?
Options: a ) 17 years , b ) 20 years , c ) 29 years , d ) 10 years , e ) 12 years
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 52 5 x = 50 = > x = 10 hence , b ' s age = 2 x = 20 years . answer : b"
Answer: b
Python program:
a = 52 - 2
b = a * 2
c = 4 + 1 
d = b / c
Problem: a man ' s age is 125 % of what it was 10 years ago , but 83 x 1 / 3 % of what it will be after 10 years . what is his present age ?
Options: a ) 20 , b ) 60 , c ) 50 , d ) 70 , e ) 80
Rationale: c 50 let the age before 10 years = x then , 125 x / 100 = x + 10 ⇒ 125 x = 100 x + 1000 ⇒ x = 1000 / 25 = 40 present age = x + 10 = 40 + 10 = 50
Answer: c
Python program:
a = 125 / 100
b = a - 1
c = 10 / b
d = c + 10
Problem: when average age of 20 members are 0 , how many members greater than 0 ?
Options: a ) 17 , b ) 19 , c ) 21 , d ) 24 , e ) 25
Rationale: "average of 20 numbers = 0 . sum of 20 numbers ( 0 x 20 ) = 0 . it is quite possible that 19 of these numbers may be positive and if their sum is a then 20 th number is ( - a ) answer is 19 ( b )"
Answer: b
Python program:
a = 20 - 1
Problem: 5301 x 13 = ?
Options: a ) 89136 , b ) 31986 , c ) 68910 , d ) 53113 , e ) 68913
Rationale: "append 0 before and after : 053010 calculation : 1 x 3 + 0 = 3 ( take 3 as ones digit of the product ) 0 x 3 + 1 = 1 ( take 1 tens digit of the product ) 3 x 3 + 0 = 9 ( take 9 hundreds digit of the product ) 5 x 3 + 3 = 18 ( take 8 as thousands digit of the product , carry over 1 ) 0 x 3 + 5 = 5 ; 5 + 1 = 6 ( take 6 as ten thousands digits of the product ) so , 5301 x 13 = 68913 answer is e ."
Answer: e
Python program:
a = 5301 / 13
b = a * 100
Problem: a cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 9 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 4.5 hrs , b ) 5 hrs , c ) 6.5 hrs , d ) 7.2 hrs , e ) 9.2 hrs
Rationale: "net part filled in 1 hour = 1 / 3 - 1 / 9 = 2 / 9 therefore the cistern will be filled in 9 / 2 hours or 4.5 hours . answer : a"
Answer: a
Python program:
a = 1 / 3
b = 1 / 9
c = a - b
d = 1 / c
Problem: a river 8 m deep and 25 m wide is flowing at the rate of 8 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 26666 , b ) 26166 , c ) 29666 , d ) 22666 , e ) 26699
Rationale: "rate of water flow - 8 kmph - - 8000 / 60 - - 133.33 m / min depth of river - - 8 m width of river - - 25 m vol of water per min - - 133.33 * 8 * 25 - - - 26666 answer a"
Answer: a
Python program:
a = 8 * 25
b = 8 * 1000
c = a * b
d = 1 * const_60
e = c / d
Problem: among 400 students , 56 % study sociology , 44 % study mathematics and 40 % study biology . if 42 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ?
Options: a ) 30 , b ) 90 , c ) 120 , d ) 168 , e ) 188
Rationale: "i would just like to add a bit of explanation after the step where you calculate that the number of students studying both m and s = 168 using your analysis : we see that the total number of students who study either maths or sociology = 176 + 224 - 168 = 232 so , in the image we know that the number of students in the zone with the black boundary = 232 let ' s assume the number of students who studyonlybiology to beb ( this is the number that we have to maximize ) and , let ' s assume the number of students who study none of the three subjects , that is the number of students in the white space = w since the total number of students = 400 , we can write : 232 + b + w = 400 or , b + w = 400 - 232 = 168 that is , b = 168 - w so , the maximum value ofbwill happen forw = 0 this is how we get , the maximum value ofb = 168 d"
Answer: d
Python program:
a = 400 / 100
b = a * 56
c = 400 / 100
d = c * 44
e = b + d 
f = 400 / 100
g = f * 42
h = e - g
i = 400 - h
Problem: each of the 20 boxes in a certain shipment weighs either 10 pounds or 20 pounds , and the average ( arithmetic mean ) weight of the boxes in the shipment is 18 pounds . if the average weight of the boxes in the shipment is to be reduced to 12 pounds by removing some of the 20 - pound boxes , how many 20 - pound boxes must be removed ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "if the average of 10 - pound and 20 - pound boxes is 18 , the ratio of 10 - pound boxes : 20 - pound boxes is 1 : 4 . so out of 20 boxes , 4 are 10 - pound boxes and 16 are 20 - pound boxes . if the average of 10 and 20 - pound boxes is to be 12 , the ratio of 10 - pound boxes : 20 - pound boxes should be 4 : 1 . the number of 10 pound boxes remains the same so we still have 4 of them . to get a ratio of 4 : 1 , the number of 20 - pound boxes must be 1 . we need to remove 15 of the 20 - pound boxes . the answer is e ."
Answer: e
Python program:
a = 20 * 20
b = 20 * 18
c = a - b
d = 20 - 10
e = c / d
f = 10 * e
g = 20 * 20
h = 20 * 18
i = g - h
j = 20 - 10
k = i / j
l = 20 - k
m = 20 * l
n = f + m 
o = 20 * 12
p = n - o
q = 20 - 12
r = p / q
Problem: if n is a positive integer and n ^ 2 is divisible by 264 , then the largest positive integer that must divide n is
Options: a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48
Rationale: "the question asks aboutthe largest positive integer that must divide n , not could divide n . since the least value of n for which n ^ 2 is a multiple of 72 is 12 then the largest positive integer that must divide n is 12 . complete solution of this question is given above . please ask if anything remains unclear . i spent a few hours on this one alone and i ' m still not clear . i chose 12 at first , but then changed to 48 . i ' m not a native speaker , so here is how i interpreted this question : the largest positive integer that must divide n = the largest positive factor of n . since n is a variable ( i . e . n is moving ) , so is its largest factor . please correct if i ' m wrong here . i know that if n = 12 , n ^ 2 = 144 = 2 * 72 ( satisfy the condition ) . when n = 12 , the largest factor of n is n itself , which is 12 . check : 12 is the largest positive number that must divide 12 - - > true however if n = 48 , n ^ 2 = 48 * 48 = 32 * 72 ( satisfy the condition too ) . when n = 48 , the largest factor of n is n itself , which is 48 . check : 48 is the largest positive number that must divide 48 - - > true so , i also notice that the keyword ismust , notcould . the question is , why is 48 notmust divide 48 , but instead onlycould divide 48 ? i ' m not clear right here . why is 12 must divide 12 ? what ' s the difference between them ? only restriction we have on positive integer n is that n ^ 2 is divisible by 72 . the least value of n for which n ^ 2 is divisible by 72 is 12 , thus nmustbe divisible by 12 ( n is in any case divisible by 12 ) . for all other values of n , for which n ^ 2 is divisible by 72 , n will still be divisible by 12 . this means that n is always divisible by 12 if n ^ 2 is divisible by 72 . now , ask yourself : if n = 48 , is n divisible by 48 ? no . so , n is not always divisible by 48 . e"
Answer: e
Python program:
a = 264 / 2
b = math.sqrt(a)
c = b * 2
Problem: ramesh purchased a refrigerator for rs . 17500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 10 % if no discount was offered ?
Options: a ) 34778 , b ) 26888 , c ) 24475 , d ) 17600 , e ) 12778
Rationale: "price at which the tv set is bought = rs . 17,500 discount offered = 20 % marked price = 17500 * 100 / 80 = rs . 21875 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 21875 + 375 = rs . 22250 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 22250 * 110 / 100 = rs . 24475 answer : c"
Answer: c
Python program:
a = 100 + 10 
b = 17500 * 100
c = 100 - 20
d = b / c
e = 125 + 250 
f = d + e 
g = a * f
h = g / 100
Problem: harkamal purchased 3 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 700 , b ) b ) 1065 , c ) c ) 1070 , d ) d ) 1075 , e ) e ) 1080
Rationale: "cost of 3 kg grapes = 70 × 3 = 210 . cost of 9 kg of mangoes = 55 × 9 = 490 . total cost he has to pay = 210 + 490 = 700 a"
Answer: a
Python program:
a = 3 * 70
b = 9 * 55
c = a + b
Problem: the wages earned by robin is 35 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much % is the wages earned by charles more than that earned by robin ?
Options: a ) 25.92 % , b ) 18.75 % , c ) 30 % , d ) 50 % , e ) 100 %
Rationale: "explanatory answer let the wages earned by erica be $ 100 then , wages earned by robin and charles will be $ 135 and $ 160 respectively . charles earns $ 35 more than robin who earns $ 135 . therefore , charles ' wage is 35 / 135 * 100 = 25.92 % . the correct choice is ( a )"
Answer: a
Python program:
a = 100 + 60 
b = 100 + 35 
c = a - b
d = 100 + 35 
e = c / d
f = e * 100
Problem: if log 1087.5 = 4.9421 , then the number of digits in ( 875 ) 10 is ?
Options: a ) 60 , b ) 28 , c ) 27 , d ) 26 , e ) 25
Rationale: "x = ( 875 ) 10 = ( 87.5 x 10 ) 10 therefore , log 10 x = 10 ( log 4087.5 + 1 ) = 10 ( 4.9421 + 1 ) = 10 ( 5.9421 ) = 59.421 x = antilog ( 59.421 ) therefore , number of digits in x = 60 . answer : a"
Answer: a
Python program:
a = 4 * 4
b = math.log(100)
c = math.log(10)
d = b / c
e = a + d
Problem: a soccer store typically sells replica jerseys at a discount of 30 percent to 70 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what percent of the list price is the lowest possible sale price ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50
Rationale: "let the list price be 2 x for min sale price , the first discount given should be 70 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which is 40 % of 80 hence , d is the answer"
Answer: d
Python program:
a = 80 / 2
Problem: speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph . a man rows to place at a distance of 210 km and comes back to the starting point . the total time taken by him is :
Options: a ) 12 hours , b ) 24 hours , c ) 36 hours , d ) 48 hours , e ) none
Rationale: "sol . speed upstream = 7.5 kmph ; speed downstream = 10.5 kmph . ∴ total time taken = [ 210 / 7.5 + 210 / 10.5 ] hours = 48 hours . answer d"
Answer: d
Python program:
a = 9 + 1 
b = 210 / a
c = 9 - 1
d = 210 / c
e = b + d
Problem: q ' = 3 q - 3 , what is the value of ( 4 ' ) ' ?
Options: a ) 48 , b ) 57 , c ) 66 , d ) 72 , e ) 81
Rationale: "( 4 ' ) ' = ( 3 * 4 - 3 ) ' = 9 ' = 9 * 9 - 9 = 72 answer d"
Answer: d
Python program:
a = 3 * 4
b = a - 3
c = b * 3
d = c - 3
e = 4 - 1
f = d * e
Problem: if the simple interest on a sum of money for 2 years at 5 % per annum is $ 50 , what is the compound interest on the same at the same rate and for the same time ?
Options: a ) $ 50 , b ) $ 51.5 , c ) $ 52 , d ) $ 52.5 , e ) $ 51.25
Rationale: "sum = 50 x 100 / ( 2 x 5 ) = 500 = 500 x ( 1 + 5 / 100 ) ^ 2 = 500 x 21 / 20 x 21 / 20 = 551.25 . c . i = 551.25 - 500 = 51.25 . answer e ) $ 51.25"
Answer: e
Python program:
a = 5 / 100
b = a * 2
c = 50 / b
d = c * 5
e = d / 100
f = 5 / 100
g = f * 2
h = 50 / g
i = e + h 
j = 5 / 100
k = j * 2
l = 50 / k
m = l * 5
n = m / 100
o = 5 / 100
p = o * 2
q = 50 / p
r = n + q 
s = r * 5
t = s / 100
u = i + t 
v = 5 / 100
w = v * 2
x = 50 / w
y = u - x
Problem: a train running at the speed of 180 km / hr crosses a pole in 9 seconds . find the length of the train .
Options: a ) 150 meter , b ) 286 meter , c ) 186 meter , d ) 288 meter , e ) 450 meter
Rationale: "speed = 180 * ( 5 / 18 ) m / sec = 50 m / sec length of train ( distance ) = speed * time ( 50 ) * 9 = 450 meter answer : e"
Answer: e
Python program:
a = 180 * 1000
b = a / 3600
c = b * 9
Problem: the cost of 2 chairs and 3 tables is rs . 1700 . the cost of 3 chairs and 2 tables is rs . 1200 . the cost of each table is more than that of each chair by ?
Options: a ) 228 , b ) 287 , c ) 277 , d ) 188 , e ) 500
Rationale: "explanation : 2 c + 3 t = 1700 - - - ( 1 ) 3 c + 2 t = 1200 - - - ( 2 ) subtracting 2 nd from 1 st , we get - c + t = 500 = > t - c = 500 answer : e"
Answer: e
Python program:
a = 3 * 1700
b = 2 * 3
c = a - b
d = 3 * 3
e = 2 * 2
f = d - e
g = c / f
h = 3 * 1700
i = 2 * 3
j = h - i
k = 3 * 3
l = 2 * 2
m = k - l
n = j / m
o = 2 * n
p = 3 - o
q = p / 3
r = g - q
Problem: the speed of a subway train is represented by the equation z = s ^ 2 + 2 s for all situations where 0 ≤ s ≤ 7 , where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving . in kilometers per hour , how much faster is the subway train moving after 5 seconds than it was moving after 3 seconds ?
Options: a ) 4 , b ) 9 , c ) 15 , d ) 20 , e ) 63
Rationale: "given : z = s ^ 2 + 2 s for 0 ≤ s ≤ 7 z ( 3 ) = 3 ^ 2 + 2 * 3 = 15 z ( 5 ) = 5 ^ 2 + 2 * 5 = 35 therefore z ( 7 ) - z ( 3 ) = 35 - 15 = 20 km / hr option d"
Answer: d
Python program:
a = 5 ** 2
b = 5 * 2
c = a + b 
d = 3 ** 2
e = 3 * 2
f = d + e 
g = c - f
Problem: consider the word rotor . whichever way you read it , from left to right or from right to left , you get the same word . such a word is known as palindrome . find the maximum possible number of 5 - letter palindromes ?
Options: a ) 56678 , b ) 16789 , c ) 17576 , d ) 35142 , e ) none of these
Rationale: "explanation : the first letter from the right can be chosen in 26 ways because there are 26 alphabets . having chosen this , the second letter can be chosen in 26 ways . = > the first two letters can be chosen in 26 * 26 = 676 wayshaving chosen the first two letters , the third letter can be chosen in 26 ways . = > all the three letters can be chosen in 676 * 26 = 17576 ways . it implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter . answer : c"
Answer: c
Python program:
a = 10 + 10 
b = a + 3 
c = b + 3 
d = 5 - 2
e = c ** d
Problem: the present ages of reena and usha are 24 and 36 yr . respectively . what was the ratio between the ages of usha and reena respectively 8 yr ago ?
Options: a ) 7 : 4 , b ) 4 : 7 , c ) 11 : 8 , d ) 8 : 11 , e ) 9 : 12
Rationale: required ratio = ( 36 - 8 ) / ( 24 - 8 ) = 28 / 16 = 7 : 4 answer : a
Answer: a
Python program:
a = 36 - 8
b = 24 - 8
c = a / b
Problem: a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 24 gallons of gasoline ?
Options: a ) 190 , b ) 284.6 , c ) 300 , d ) 292 , e ) 312
Rationale: so 12.2 * 24 = 292 . . imo option d is correct answer . .
Answer: d
Python program:
a = 12 * 2
Problem: a train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 20 seconds . what is the length of the platform in meters ?
Options: a ) 200 meters , b ) 360 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined
Rationale: "speed of the train in metres / sec = 72000 / 3600 = 20 distance travelled by train to cross the platform = 30 * 20 = 600 = length of train + length of platform distance travelled by train to cross the man = 20 * 20 = 400 = length of train length of platform = 600 - 400 = 200 answer : a"
Answer: a
Python program:
a = 72 * 1000
b = a / 3600
c = b * 30
d = 72 * 1000
e = d / 3600
f = e * 20
g = c - f
Problem: what is the 20 - fourth decimal to the right in the fraction 35 / 36 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: 35 / 36 = 0.97222222222 . . . the answer is b .
Answer: b
Python program:
a = 12 - 1
b = a * 2
c = b - 20
Problem: a and b walk around a circular track . they start at 9 a . m . from the same point in the opposite directions . a and b walk at a speed of 2 rounds per hour and 3 rounds per hour respectively . how many times shall they cross each other before 10 : 00 a . m . ?
Options: a ) 8 , b ) 7 , c ) 6 , d ) 5 , e ) 10
Rationale: sol . relative speed = ( 2 + 3 ) = 5 rounds per hour . so , they cross each other 5 times in an hour and 5 times in next hour . hence , they cross each other 10 times before 10 : 00 a . m . answer e
Answer: e
Python program:
a = 2 + 3 
b = 2 + 3 
c = a + b
Problem: a regular hexagon is there . the mid points of the sides were joined and formed another hexagon . then what is the percentage reduction in area .
Options: a ) 25 % , b ) 35 % , c ) 45 % , d ) 55 % , e ) 65 %
Rationale: let abcdef be the regular hexagon with sides ab and ed parallel . p and q are mid points of af and ef resp . ae = root ( 3 ) * s ( s is side of hexagon ) then pq = ( root ( 3 ) * s ) / 2 mid point theorem now u know side of inner hexagon use formula area of hexagon = ( 3 * root ( 3 ) ) 2 * s ^ 2 and find diff in area of two hexagon multiply by 100 and divide the product by area of bigger hexagon ans 25 % answer : a
Answer: a
Python program:
a = 3 / 4
b = 1 - a
c = b * 100
Problem: in the faculty of reverse - engineering , 226 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 85 % of the total ?
Options: a ) 515 . , b ) 545 . , c ) 606 . , d ) 644 . , e ) 666 .
Rationale: "answer is c : 606 solution : total number of students studying both are 423 + 226 - 134 = 515 ( subtracting the 134 since they were included in the both the other numbers already ) . so 85 % of total is 515 , so 100 % is approx . 606 ."
Answer: c
Python program:
a = 226 + 423
Problem: if the length of the longest chord of a certain circle is 20 , what is the radius of that certain circle ?
Options: a ) 2.5 , b ) 5 , c ) 10 , d ) 15 , e ) 20
Rationale: "longest chord of a circle is the diameter of the circle diameter = 2 * radius if diameter of the circle is given as 20 = 2 * 10 so radius of the circle = 10 correct answer - c"
Answer: c
Python program:
a = 20 / 2
Problem: carl is facing very difficult financial times and can only pay the interest on a $ 10,000 loan he has taken . the bank charges him a quarterly compound rate of 6 % . what is the approximate interest he pays annually ?
Options: a ) $ 1200 , b ) $ 2000 , c ) $ 2150 , d ) $ 2500 , e ) $ 12000
Rationale: "an easy way too attempt this is by approximation : for the first quarter , he pays 6 % of 10,000 which is $ 600 . so for the four quarters in the year , he will approximately play 600 * 4 = 2400 over the entire year . the compound interest will be more than 2400 . all other options are not right except d . answer : d"
Answer: d
Python program:
a = 100 * 100
b = 6 / 100
c = 1 + b 
d = c ** 4
e = a * d
f = 100 * 100
g = e - f
Problem: in a certain game of dice , the player ’ s score is determined as a sum of four throws of a single die . the player with the highest score wins the round . if more than one player has the highest score , the winnings of the round are divided equally among these players . if jim plays this game against 26 other players , what is the probability of the minimum score that will guarantee jim some monetary payoff ?
Options: a ) 41 / 50 , b ) 1 / 221 , c ) 1 / 1296 , d ) 1 / 84 , e ) 1 / 42
Rationale: "toguaranteethat jim will get some monetary payoff he must score the maximum score of 6 + 6 + 6 + 6 = 24 , because if he gets even one less than that so 23 , someone can get 24 and jim will get nothing . p ( 24 ) = 1 / 6 ^ 4 = 1 / 1296 . answer : c ."
Answer: c
Python program:
a = 26 / 3
b = a - 1
c = b ** 2
d = 1 / c
Problem: 3 candidates in an election and received 4136 , 7636 and 11628 votes respectively . what % of the total votes did the winning candidate got in that election ?
Options: a ) 45 % , b ) 49 % , c ) 50 % , d ) 59 % , e ) 61 %
Rationale: "total number of votes polled = ( 4136 + 7636 + 11628 ) = 23400 so , required percentage = 11628 / 23400 * 100 = 50 % c"
Answer: c
Python program:
a = 4136 + 7636 
b = a + 11628 
c = 11628 / b
d = c * 100
Problem: a piece of paper is in the shape of a right angled triangle and is cut along a line that is parallel to the hypotenuse , leaving a smaller triangle . there was a 35 % reduction in the length of the hypotenuse of the triangle . if the area of the original triangle was 34 square inches before the cut , what is the area ( in square inches ) of the smaller triangle ?
Options: a ) 16.665
b ) 16.565
c ) 15.465
d ) 14.365
e ) 14.378
Rationale: explanation : smaller triangle and original triangle will be similar to each other . ratio of area = ( ratio of side ) 2 area of smaller triangle = area of original triangle * ( 65 / 100 ) 2 = 14.365 . answer : d
Answer: d
Python program:
a = 35 / 100
b = 1 - a
c = b ** 2
d = c * 34
Problem: in x game of billiards , x can give y 20 points in 60 and he can give z 30 points in 60 . how many points can y give z in x game of 80 ?
Options: a ) 30 , b ) 20 , c ) 25 , d ) 40 , e ) 50
Rationale: "x scores 60 while y score 40 and z scores 30 . the number of points that z scores when y scores 80 = ( 80 * 30 ) / 40 = 60 . in x game of 100 points , y gives ( 80 - 60 ) = 20 points to c . b"
Answer: b
Python program:
a = 60 - 20
b = a * 3
c = 60 - 30
d = c * 3
e = b - d
Problem: a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 110 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 28 sec , b ) 16 sec , c ) 35 sec , d ) 18 sec , e ) 17 sec
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 110 = 350 m . time taken = 350 / 10 = 35 sec . answer : c"
Answer: c
Python program:
a = 240 + 110 
b = 45 - 9
c = 10 / 2
d = 45 - 9
e = d / 2
f = c / e
g = b * f
h = a / g
Problem: a marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each . there can be no less than 8 musicians per row and no more than 30 musicians per row . how many different rectangular formations f are possible ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) f = 8
Rationale: "the combinations could be f { ( 1,240 ) , ( 2,120 ) , ( 3,80 ) , ( 4,60 ) , ( 5,48 ) , ( 6,40 ) , ( 8,30 ) , ( 10,24 ) , ( 12,20 ) , ) 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) , ( 40,6 ) , ( 48,5 ) , ( 60,4 ) , ( 80,3 ) , ( 120,2 ) , ( 240,1 ) } of these we are told 8 < = t < = 30 so we can remove these pairs , and we are left only with . { ( 8,30 , ( 10,24 ) , ( 12,20 ) , ( 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) } hence 8 . . e"
Answer: e
Python program:
a = 240 / 30
Problem: by travelling at 50 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what speed should he maintain for the remaining distance to reach his destination on time ?
Options: a ) 23 kmph , b ) 24 kmph , c ) 25 kmph , d ) 26 kmph , e ) 27 kmph
Rationale: "let the time taken to reach the destination be 3 x hours . total distance = 50 * 3 x = 150 x km he covered 2 / 3 * 150 x = 100 x km in 1 / 3 * 3 x = x hours so , the remaining 50 x km , he has to cover in 2 x hours . required speed = 50 x / 2 x = 25 kmph . answer : c"
Answer: c
Python program:
a = 50 * 3
b = 50 * 3
c = b * 2
d = c / 3
e = a - d
f = 3 - 1
g = e / f
Problem: what is the 29 th digit to the right of the decimal point in the decimal form of 4 / 11 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "4 / 11 = 0.363636 . . . the odd numbered positions in the decimal expansion are all 3 . the answer is c ."
Answer: c
Python program:
a = 4 / 11