euclaise/mathqa_programs huggingface dataset:
Problem: evaluate : 11 + sqrt ( - 4 + 6 × 4 ÷ 3 ) = ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "according to order of operations , inner brackets first where 6 × 4 ÷ 3 is first calculated since it has a multiplication and a division . 6 × 4 ÷ 3 = 24 ÷ 3 = 8 hence 11 + sqrt ( - 4 + 6 × 4 ÷ 3 ) = 11 + sqrt ( - 4 + 8 ) = 11 + sqrt ( 4 ) = 11 + 2 = 13 correct answer d ) 13"
Answer: d
Python program:
a = 6 * 4
b = a / 3
c = b - 4
d = math.sqrt(c)
e = 11 + d
Problem: the lcm and hcf of two numbers are 1000 and 100 respectively . find the larger of the two numbers if their sum is 1100 .
Options: a ) 1000 , b ) 10 , c ) 567 , d ) 57 , e ) 678
Rationale: "there are 2 approaches in solving this . methode 1 . hcf * lcm = the actual number . 1000 * 100 = 100000 so the answer which we are looking for has to be a factor of 100000 . so among the options shortlist the answers by eliminating those numbers which is not divisible by 100000 . and then take the highest number as the answer as the question asks abt the highest number . answer is a"
Answer: a
Python program:
a = 1000 * 100
b = a / 1100
Problem: ramesh purchased a refrigerator for rs . 12500 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 15 % if no discount was offered ?
Options: a ) 17608 , b ) 17606 , c ) 17604 , d ) 18400 , e ) 117601
Rationale: "price at which the tv set is bought = rs . 12,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 15625 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 15625 + 375 = rs . 16000 the price at which the tv should be sold to get a profit of 15 % if no discount was offered = 16000 * 115 / 100 = rs . 18400 . answer : d"
Answer: d
Python program:
a = 100 + 15 
b = 12500 * 100
c = 100 - 20
d = b / c
e = 125 + 250 
f = d + e 
g = a * f
h = g / 100
Problem: in a school 10 % of the boys are same in number as 1 / 6 th of the girls . what is the ratio of boys to the girls in the school ?
Options: a ) 5 : 3 , b ) 2 : 3 , c ) 1 : 4 , d ) 3 : 7 , e ) 2 : 5
Rationale: "10 % of b = 1 / 6 g 10 b / 100 = g / 6 b = 5 g / 3 b / g = 5 / 3 b : g = 5 : 3 answer is a"
Answer: a
Python program:
a = 10 / 100
b = 1 / 6
c = a / b
Problem: the number of positive integer solutions for the equation x + y + z + t = 15 is
Options: a ) 654 , b ) 584 , c ) 384 , d ) 364 , e ) 394
Rationale: the number of positive integer solutions for the equatio fx 1 + x 2 + ⋯ + xn = k ( k - 1 ) c ( n - 1 ) - where k is the number and n is number of variable in the equation . 15 - 1 c 4 - 1 = 14 c 3 = 364 answer : d
Answer: d
Python program:
a = 15 - 1
b = math.factorial(a)
c = 4 - 1
d = math.factorial(c)
e = 15 - 1
f = 4 - 1
g = e - f
h = math.factorial(g)
i = d * h
j = b / i
Problem: in a certain pond , 50 fish were caught , tagged , and returned to the pond . a few days later , 50 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what ` s the approximate number of fish in the pond ?
Options: a ) 400 , b ) 625 , c ) 1250 , d ) 2500 , e ) 10 000
Rationale: "if x is total number of fish in the pond : 4 = 50 / x * 100 = > x = 1250 so answer is c"
Answer: c
Python program:
a = 2 / 50
b = 50 / a
Problem: if the cost price of 12 pencils is equal to the selling price of 8 pencils , the gain percent is :
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: c 50 % let c . p . of each pencil be $ 1 . then , c . p . of 8 pencils = $ 8 ; s . p . of 8 pencils = $ 12 . gain % = 4 / 8 * 100 = 50 %
Answer: c
Python program:
a = 12 - 8
b = 8 / a
c = 100 / b
Problem: a and b together can do a work in 9 days . if a alone can do it in 18 days . in how many days can b alone do it ?
Options: a ) 10 , b ) 99 , c ) 18 , d ) 55 , e ) 21
Rationale: "1 / 9 – 1 / 18 = 1 / 18 = > 18 answer : c"
Answer: c
Python program:
a = 1 / 9
b = 1 / 18
c = a - b
d = 1/(c)
e = 2 + 3 
f = 2 / e
g = d + f
Problem: solve below question 6 x - 1 = - 13
Options: a ) - 8 , b ) - 2 , c ) - 5 , d ) - 4 , e ) 1
Rationale: 1 . subtract 1 from both sides : 6 x - 1 + 1 = - 13 + 1 2 . simplify both sides : 6 x = - 12 3 . divide both sides by 6 : 4 . simplify both sides : x = - 2 b
Answer: b
Python program:
a = 13 + 1 
b = negate / (
Problem: if n = ( 32 ) ^ 43 + ( 43 ) ^ 33 what is the units digit of n ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "first of all , the units digit of ( 32 ) ^ 43 is the same as that of 3 ^ 43 and the units digit of ( 43 ) ^ 33 is the same as that of 3 ^ 33 . so , we need to find the units digit of 3 ^ 43 + 3 ^ 33 . next , the units digit of 3 in positive integer power repeats in blocks of four { 3 , 9 , 7 , 1 } : 3 ^ 1 = 3 ( the units digit is 3 ) 3 ^ 2 = 9 ( the units digit is 9 ) 3 ^ 3 = 27 ( the units digit is 7 ) 3 ^ 4 = 81 ( the units digit is 1 ) 3 ^ 5 = 243 ( the units digit is 3 again ! ) . . . thus : the units digit of 3 ^ 43 is the same as the units digit of 3 ^ 3 , so 7 ( 43 divided by the cyclicity of 4 gives the remainder of 3 ) . the units digit of 3 ^ 33 is the same as the units digit of 3 ^ 1 , so 3 ( 33 divided by the cyclicity of 4 gives the remainder of 1 ) . therefore the units digit of ( 23 ) ^ 43 + ( 43 ) ^ 33 is 5 + 3 = 0 . answer : e ."
Answer: e
Python program:
a = reminder ** (
b = a + reminder 
c = reminder - (
Problem: if 125 ( 5 ^ y ) = 1 then y =
Options: a ) – 2 , b ) – 1 , c ) 0 , d ) 1 , e ) - 3
Rationale: 5 ^ x = 1 / 125 5 ^ x = 1 / 5 ^ 3 5 ^ x = 5 ^ - 3 x = - 3 e
Answer: e
Python program:
a = 1 / 125
b = math.log(a)
c = math.log(5)
d = b / c
Problem: the salary of a , b , c , d , e is rs . 8000 , rs . 5000 , rs . 11000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is
Options: a ) rs . 7000 , b ) rs . 8000 , c ) rs . 8500 , d ) rs . 9000 , e ) none
Rationale: "answer average salary = 8000 + 5000 + 11000 + 7000 + 9000 / 5 = rs . 8000 correct option : b"
Answer: b
Python program:
a = 8000 + 5000 
b = a + 11000 
c = b + 7000 
d = c + 9000 
e = 4 + 1 
f = d / e
Problem: a car averages 75 mph for the first 4 hours of a trip and averages 60 mph for each additional hour . the average speed for the entire trip was 70 mph . how many hours long is the trip ?
Options: a ) 6 , b ) 78 , c ) 8 , d ) 9 , e ) 10
Rationale: "let the time for which car averages 60 mph = t 70 * ( t + 4 ) = 75 * 4 + 60 t = > 10 t = 20 = > t = 2 total duration of the trip = 4 + 2 = 6 answer a"
Answer: a
Python program:
a = 70 * 4
b = 75 * 4
c = a - b
d = 60 - 70
e = c / d
f = e + 4
Problem: linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 210 , what were her original savings ?
Options: a ) $ 840 , b ) $ 800 , c ) $ 1000 , d ) $ 700 , e ) $ 1500
Rationale: "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 210 . so 1 / 4 of her savings is $ 210 . so her original savings are 4 times $ 210 = $ 840 correct answer a"
Answer: a
Python program:
a = 3 / 4
b = 1 - a
c = 210 / b
Problem: the duplicate ratio of 1 : 4 is ?
Options: a ) 1 : 2 , b ) 1 : 4 , c ) 1 : 8 , d ) 1 : 18 , e ) 1 : 13
Rationale: "1 ^ 2 : 4 ^ 2 = 2 : 16 = 1 : 8 answer : c"
Answer: c
Python program:
a = 1 ** 2
b = 4 ** 2
c = a / b
Problem: find the cost of fencing around a circular field of diameter 20 m at the rate of rs . 1.50 a meter ?
Options: a ) 287 , b ) 94.2 , c ) 156 , d ) 158 , e ) 267
Rationale: "2 * 22 / 7 * 10 = 62.8 62.8 * 1 1 / 2 = rs . 94.2 answer : b"
Answer: b
Python program:
a = 20 / 2
b = circumface * (
Problem: a 60 kg metal bar made of alloy of tin and silver lost 6 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ?
Options: a ) 1 / 4 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3
Rationale: "you can simply use this formula to avoid confusion : w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2 . we have an overall loss ( average loss ) . the average loss is 6 kg when 60 kg alloy is immersed . this is a loss of ( 6 / 60 ) * 100 = 10 % . this is aavg the loss of tin is 1.375 kg for every 10 kg . this means it loses ( 1.375 / 10 ) * 100 = 13.75 % of its weight in water . this is a 1 . the loss of silver is . 375 kg for every 5 kg . this means it loses ( . 375 / 5 ) * 100 = 7.5 % of its weight in water . this is a 2 . weight of tin / weight of silver = ( silver ' s loss - avg loss ) / ( avg loss - tin ' s loss ) x / y = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2 / 3 e"
Answer: e
Python program:
a = 0 / 375
b = a * 60
c = 6 - b
d = 1 / 375
e = 0 / 375
f = d - e
g = c / f
h = 0 / 375
i = h * 60
j = 6 - i
k = 1 / 375
l = 0 / 375
m = k - l
n = j / m
o = 60 - n
p = g / o
Problem: a walks at 10 kmph and 10 hours after his start , b cycles after him at 20 kmph . how far from the start does b catch up with a ?
Options: a ) 100 km , b ) 150 km , c ) 50 km , d ) 120 km , e ) 200 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 10 hours . x / 10 - x / 20 = 10 x = 200 km answer is e"
Answer: e
Python program:
a = 10 * 20
Problem: the sum of the non - prime numbers between 60 and 70 , non - inclusive , is
Options: a ) 387 , b ) 429 , c ) 457 , d ) 499 , e ) 536
Rationale: "sum of consecutive integers from 61 to 69 , inclusive = = = = > ( a 1 + an ) / 2 * # of terms = ( 61 + 69 ) / 2 * 9 = 65 * 9 = 585 sum of non - prime numbers b / w 60 and 70 , non inclusive = = = > 585 - 128 ( i . e . , 61 + 67 , being the prime # s in the range ) = 457 answer : c"
Answer: c
Python program:
a = 60 + 1 
b = 60 + 1 
c = b + 1 
d = a + c 
e = 60 + 1 
f = e + 1 
g = f + 2 
h = d + g 
i = 60 + 1 
j = i + 1 
k = j + 2 
l = k + 1 
m = h + l 
n = 60 + 1 
o = n + 1 
p = o + 2 
q = p + 1 
r = q + 1 
s = m + r 
t = 60 + 1 
u = t + 1 
v = u + 2 
w = v + 1 
x = w + 1 
y = x + 1 
z = s + y 
A = 60 + 1 
B = A + 1 
C = B + 2 
D = C + 1 
E = D + 1 
F = E + 1 
G = F + 1 
H = z + G
Problem: how many seconds will a 500 meter long train moving with a speed of 63 km / hr , take to cross a man walking with a speed of 3 km / hr in the direction of the train ?
Options: a ) 15 s , b ) 20 s , c ) 25 s , d ) 30 s , e ) 35 s
Rationale: distance = 500 m speed = 63 - 3 km / hr = 60 km / hr = 600 / 36 m / s = 50 / 3 m / s time taken = distance / speed = 500 / ( 50 / 3 ) = 30 s answer is d .
Answer: d
Python program:
a = 63 - 3
b = a * const_0_2778
c = 500 / b
Problem: evaluate 50 % of 450 + 45 % of 500
Options: a ) 232 , b ) 450 , c ) 252 , d ) 262 , e ) 272
Rationale: "explanation : = ( 50 / 100 ) * 450 + ( 45 / 100 ) * 500 = 450 option b"
Answer: b
Python program:
a = 450 / 50
b = 50 / a
Problem: ifaequals the sum of the even integers from 2 to 20 , inclusive , andbequals the sum of the odd integers from 1 to 19 , inclusive , what is the value of b - a ?
Options: a ) - 10 , b ) 10 , c ) - 19 , d ) 20 , e ) 21
Rationale: "yes ! there is really a faster way to solve it . sum of consecutive odd or even integers = ( no . of odd or even ints ) * ( first int + last int ) / 2 here a = sum of even ints from 2 to 20 , inclusive number of even ints = 10 , first int + last int = 2 + 20 = 22 a = 10 * 22 / 2 = 110 b = sum of odd ints from 1 to 19 , inclusive number of odd ints = 10 , first int + last int = 1 + 19 = 20 a = 10 * 20 / 2 = 100 b - a = 100 - 110 = - 10 ans : a"
Answer: a
Python program:
a = 20 / 2
b = 20 / 2
c = b + 1 
d = a * c
e = 19 + 1 
f = e / 2
g = 19 - 1
h = g / 2
i = h + 1 
j = f * i
k = d - j
Problem: the angle of elevation of a ladder leaning against a wall is 60 º and the foot of the ladder is 4.6 m away from the wall . the length of the ladder is :
Options: a ) 2.3 m , b ) 4.6 m , c ) 7.8 m , d ) 9.2 m , e ) 10.1
Rationale: "let ab be the wall and bc be the ladder . then , acb = 60 º and ac = 4.6 m . ac / bc = cos 60 º = 1 / 2 bc = 2 x ac = ( 2 x 4.6 ) m = 9.2 m . answer : option d"
Answer: d
Python program:
a = 4 * 6
Problem: what is the cost of leveling the field in the form of parallelogram at the rate of rs . 50 / 10 sq . metre , whose base & perpendicular distance from the other side being 94 m & 54 m respectively ?
Options: a ) s . 6420 , b ) s . 3563 , c ) s . 2400 , d ) s . 5480 , e ) s . 5076
Rationale: "area of the parallelogram = length of the base * perpendicular height = 94 * 54 = 5076 m . total cost of levelling = rs . 5076 e"
Answer: e
Python program:
a = 94 * 54
b = 50 / 10
c = a * b
Problem: what is the minimum value of | x - 4 | + | x + 8 | + | x - 5 | ?
Options: a ) - 13 , b ) 13 , c ) 5 , d ) 7 , e ) 8
Rationale: "a can not be the answer as all the three terms are in modulus and hence the answer will be non negative . | x - 4 | > = 0 - - > minimum occurs at x = 4 | x + 8 | > = 0 - - > minimum occurs at x = - 8 | x - 5 | > = 0 - - > minimum occurs at x = 5 x = - 8 - - > result = 12 + 0 + 13 = 25 . also any negative value will push the combined value of | x - 4 | + | x - 5 | to a value > 9 . x = 4 - - > result = 0 + 12 + 1 = 13 x = 5 - - > result = 1 + 13 + 0 = 14 x = 8 - - > result = 4 + 16 + 3 = 23 so minimum value of the expression occurs at x = 4 and the resultant value = 13 answer : b"
Answer: b
Python program:
a = 8 + 5
Problem: divide rs . 1600 among a , b and c so that a receives 1 / 4 as much as b and c together and b receives 3 / 4 as a and c together . a ' s share is ?
Options: a ) 350 , b ) 375 , c ) 320 , d ) 530 , e ) 230
Rationale: "a + b + c = 1600 a = 1 / 4 ( b + c ) ; b = 3 / 4 ( a + c ) a / ( b + c ) = 1 / 4 a = 1 / 5 * 1600 = > 320 answer : c"
Answer: c
Python program:
a = 1600 / 3
Problem: the population of a town is 10000 . it increases annually at the rate of 15 % p . a . what will be its population after 2 years ?
Options: a ) 13300 , b ) 13350 , c ) 13225 , d ) 13500 , e ) 13600
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 10000 ã — 115 / 100 ã — 115 / 100 = 13225 c"
Answer: c
Python program:
a = 10000 * 15
b = a / 100
c = b * 2
d = 10000 + c
Problem: a man ' s speed with the current is 16 km / hr and the speed of the current is 3.2 km / hr . the man ' s speed against the current is
Options: a ) 9 , b ) 9.6 , c ) 11 , d ) 12 , e ) 13
Rationale: "man ' s rate in still water = ( 16 - 3.2 ) km / hr = 12.8 km / hr . man ' s rate against the current = ( 12.8 - 3.2 ) km / hr = 9.6 km / hr . answer : b"
Answer: b
Python program:
a = 16 - 3
b = a - 3
Problem: a card game called “ high - low ” divides a deck of 52 playing cards into 2 types , “ high ” cards and “ low ” cards . there are an equal number of “ high ” cards and “ low ” cards in the deck and “ high ” cards are worth 2 points , while “ low ” cards are worth 1 point . if you draw cards one at a time , how many ways can you draw “ high ” and “ low ” cards to earn 6 points if you must draw exactly 3 “ low ” cards ?
Options: a ) 1 , b ) 20 , c ) 3 , d ) 4 , e ) 5
Rationale: "great question ravih . this is a permutations problem ( order matters ) with repeating elements . given thatlowcards are worth 1 pt andhigh cards 2 pts , and you must draw 3 low cards , we know that you must also draw 1 high card . the formula for permutations problems with repeating elements isn ! / a ! b ! . . . where n represents the number of elements in the group and a , b , etc . represent the number of times that repeating elements are repeated . here there are 4 elements and thelowcard is repeated 3 times . as a result , the formula is : 5 ! / 3 ! which represents ( 5 * 4 * 3 * 2 * 1 ) / ( 3 * 2 * 1 ) which simplifies to just 20 , giving you answer b ."
Answer: b
Python program:
a = 4 * 3
b = a * 2
c = b * 1
d = 3 * 2
e = d * 1
f = c / e
Problem: a card is drawn from a pack of 52 cards . the probability of not getting a face card ?
Options: a ) 9 / 13 , b ) 5 / 12 , c ) 3 / 13 , d ) 6 / 17 , e ) 1 / 13
Rationale: clearly in the 52 cards other than face cards = 52 - 16 = 36 probability of not getting a face card = 36 / 52 = 9 / 13 correct option is a
Answer: a
Python program:
a = 4 * 4
b = 52 - a
c = b / 52
Problem: what number is 64 more than two - fourth of itself ?
Options: a ) 128 , b ) 225 , c ) 288 , d ) 324 , e ) 336
Rationale: "2 / 4 x + 64 = x that means 64 = 2 / 4 x x = 64 * 2 = 128 a is the answer"
Answer: a
Python program:
a = 1 / 4
b = 1 - a
c = 64 / b
Problem: in 10 years , a will be twice as old as b was 10 years ago . if a is now 6 years older than b the present age of b is
Options: a ) 37 , b ) 36 , c ) 39 , d ) 40 , e ) 41
Rationale: "let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 6 = > 2 b - b - 6 = 30 b = 36 so the present age of b is 36 years answer : b"
Answer: b
Python program:
a = 2 * 10
b = a + 10 
c = b + 6
Problem: a train running at the speed of 56 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 140 m , b ) 786 m , c ) 566 m , d ) 546 m , e ) 445 m
Rationale: "speed = 56 * 5 / 18 = 140 / 9 m / sec length of the train = speed * time = 140 / 9 * 9 = 140 m answer : a"
Answer: a
Python program:
a = 56 * 1000
b = a / 3600
c = b * 9
Problem: the cross - section of a cannel is a trapezium in shape . if the cannel is 11 m wide at the top and 9 m wide at the bottom and the area of cross - section is 960 sq m , the depth of cannel is ?
Options: a ) 69 , b ) 92 , c ) 94 , d ) 49 , e ) 96
Rationale: "1 / 2 * d ( 11 + 9 ) = 960 d = 96 answer : e"
Answer: e
Python program:
a = 11 + 9 
b = a / 2
c = 960 / b
d = c / 9
e = d / 2
Problem: suppose 6 monkeys take 6 minutes to eat 6 bananas . how many monkeys would it take to eat 18 bananas in 18 minutes ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 6 , e ) 13
Rationale: "one monkey takes 6 min to eat 1 banana , so in 18 mins 1 monkey will eat 3 bananas , so for 18 bananas in 18 min we need 18 / 3 = 6 monkeys answer : d"
Answer: d
Python program:
a = 18 / 6
b = 18 / a
Problem: 6 ) a marketing firm determined that , of 240 households surveyed , 80 used neither brand a nor brand b soap . 60 used only brand a soap and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 household surveyed used both brands of soap ?
Options: a ) a ) 15 , b ) b ) 20 , c ) c ) 25 , d ) d ) 40 , e ) e ) 45
Rationale: "160 = at least one of soap a or b both brands = x brand b = 3 x = > 60 + x + 3 x = 160 = > 4 x = 100 = > x = 25 answer - c"
Answer: c
Python program:
a = 240 - 80
b = a - 60
c = b / 4
Problem: if 20 % of a number is equal to three - fifth of another number , what is the ratio of first number to the second number ?
Options: a ) 3 : 1 , b ) 2 : 1 , c ) 1 : 3 , d ) 1 : 2 , e ) 2 : 3
Rationale: "let 20 % of a = 3 / 5 b . then , 20 a / 100 = 3 b / 5 = > 1 a / 5 = 3 b / 5 a / b = ( 3 / 5 * 5 / 1 ) = 3 / 1 a : b = 3 : 1 . answer : a"
Answer: a
Python program:
a = 1 / 4
b = 20 / 100
c = a / b
Problem: the sum of the ages of 5 children born at the intervals of 3 years each is 80 years . what is the age of the youngest child ?
Options: a ) 2 years , b ) 4 years , c ) 6 years , d ) 8 years , e ) 10 years
Rationale: "let the ages of the children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 80 5 x = 50 = > x = 10 . age of youngest child = x = 10 years . answer : e"
Answer: e
Python program:
a = 5 / 3
b = 80 / a
c = 5 - 1
d = c * 3
e = b - d
f = e / 3
Problem: a runs 1 2 ⁄ 3 times as fast as b . if a gives b a start of 80 m , how far must the winning post be so that a and b might reach it at the same time ?
Options: a ) 200 m , b ) 250 m , c ) 450 m , d ) 350 m , e ) 270 m
Rationale: speed of a : speed of b = 5 ⁄ 3 : 1 = 5 : 3 i . e . , in a race of 5 m , a runs 5 m and b runs 3 m i . e . , a gains 2 m over b in a race of 5 m = > a gains 80 m over b in a race of 52 × 80 = 200 m hence , winning point should be 200 m away from the starting point . answer : a
Answer: a
Python program:
a = 1 * 3
b = a + 2 
c = b / 3
d = 80 * c
e = 1 * 3
f = e + 2 
g = f / 3
h = g - 1
i = d / h
Problem: in a division , a student took 42 as divisor instead of 36 . his answer was 24 . the correct answer is -
Options: a ) 42 , b ) 32 , c ) 48 , d ) 28 , e ) 38
Rationale: "x / 42 = 24 . x = 24 * 42 . so correct answer would be , ( 24 * 42 ) / 36 = 38 . answer : e"
Answer: e
Python program:
a = 42 * 24
b = a / 36
Problem: hyderabad chennai mumbai delhi bangalore trivandram ; hyderabad chennai mumbai delhi bangalore trivandram in the table above , what is the least number of table entries that are needed to show the mileage between each city and each of the other 5 cities ?
Options: a ) 20 , b ) 18 , c ) 14 , d ) 15 , e ) 16
Rationale: easy way to go about this problem is we have 6 * 6 = 36 enteries in table the least number of enteries would be ( 36 - 6 ) / 2 since 6 enteries represent the distances between same points . alternatively this can be solved as combination problem . correct answer d
Answer: d
Python program:
a = 5 * 3
Problem: the speed of a boat in still water in 20 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 24 minutes is :
Options: a ) 10.6 , b ) 10.2 , c ) 10.8 , d ) 10.4 , e ) 10.0
Rationale: "speed downstream = ( 20 + 5 ) = 25 kmph time = 24 minutes = 24 / 60 hour = 2 / 5 hour distance travelled = time × speed = 2 / 5 × 25 = 10.0 km answer is e ."
Answer: e
Python program:
a = 20 + 5 
b = 24 / const_60
c = a * b
Problem: the average weight of 8 person ' s increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg . what is the weight of the new person ?
Options: a ) 93 kg , b ) 50 kg , c ) 85 kg , d ) 80 kg , e ) 60 kg
Rationale: "explanation : total increase in weight = 8 ã — 3.5 = 28 if x is the weight of the new person , total increase in weight = x â ˆ ’ 65 = > 28 = x - 65 = > x = 28 + 65 = 93 answer : option a"
Answer: a
Python program:
a = 8 * 3
b = a + 65
Problem: a river 5 m deep and 19 m wide is flowing at the rate of 4 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 4500 , b ) 6333 , c ) 6576 , d ) 6345 , e ) 2882
Rationale: "( 4000 * 5 * 19 ) / 60 = 6333 m 3 answer : b"
Answer: b
Python program:
a = 5 * 19
b = 4 * 1000
c = a * b
d = 1 * const_60
e = c / d
Problem: if the number is divided by 3 , it reduced by 24 . the number is
Options: a ) a ) 51 , b ) b ) 50 , c ) c ) 45 , d ) d ) 40 , e ) e ) 36
Rationale: "explanation : let the number be x . then , x - ( x / 3 ) = 24 = > 2 x / 3 = 24 = > x = 36 answer : option e"
Answer: e
Python program:
a = 24 * 3
b = 3 - 1
c = a / b
Problem: at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 120 . at the same place it would cost $ 158.50 for 4 burgers , 10 shakes , and one cola . how much would it cost for a meal of one burger , one shake , and one cola ?
Options: a ) $ 21 , b ) $ 27 , c ) $ 31 , d ) $ 43 , e ) it can not be determined
Rationale: "let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 120 4 b + 10 s + c = 158.5 subtracting the first equation from the second gives us b + 3 s = 38.5 now if we subtract the new equation two times from first or 3 times from second we will get b + s + c = 43 . in any case , there is no necessity to know each item ' s price , just the sum . answer : d"
Answer: d
Python program:
a = 158 - 50
b = 120 + a 
c = 158 - 50
d = c * 3
e = b - d