euclaise/mathqa_programs huggingface dataset:
Problem: if a - b = 3 and a ^ 2 + b ^ 2 = 35 , find the value of ab .
Options: a ) 12 , b ) 13 , c ) 10 , d ) 18 , e ) 13
Rationale: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 35 - 9 = 26 ab = 13 . answer is b ."
Answer: b
Python program:
a = math.sqrt(35)
b = a - 3
c = b / 2
d = 3 + c 
e = math.sqrt(35)
f = e - 3
g = f / 2
h = d * g
i = h * 2
Problem: on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 320 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 600 , b ) 640 , c ) 500 , d ) 520 , e ) 720
Rationale: "let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 320 ) = 2 + 2 ( extra ) = > 2 x - 640 = x = > x = 640 . answer : b"
Answer: b
Python program:
a = 320 * 2
Problem: 45 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?
Options: a ) 17 , b ) 97 , c ) 18 , d ) 55 , e ) 72
Rationale: "( 45 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 100 100 – 45 = 55 answer : d"
Answer: d
Python program:
a = 45 * 8
b = a / 30
c = b * 50
d = c / 6
e = d - 45
Problem: one hour before john started walking from p to q , a distance of 38 miles , ann had started walking along the same road from q to p . ann walked at a constant speed of 3 miles per hour and john at 2 miles per hour . how many miles had ann walked when they met ?
Options: a ) 6 miles , b ) 8,4 miles , c ) 19 miles , d ) 19,6 miles , e ) 24 miles
Rationale: "ann walks from q to p at a speed of 3 miles / hr for one hour . she covers 3 miles in 1 hour and now distance between john and ann is 38 - 3 = 35 miles . ann walks at 3 mph and john at 2 mph so their relative speed is 3 + 2 = 5 mph . they have to cover 35 miles so it will take them 35 / 5 = 7 hours to meet . in 7 hrs , ann would have covered 7 hrs * 3 miles per hour = 21 miles . adding this to the 3 miles she covered before john , ann covered a total of 3 + 21 = 24 miles . answer ( e )"
Answer: e
Python program:
a = 3 + 2 
b = 38 / a
c = b * 2
Problem: simplify 586645 * 9999
Options: a ) 5865863355 , b ) 5665863355 , c ) 4865863355 , d ) 4665863355 , e ) none of these
Rationale: explanation : although it is a simple question , but the trick is to save time in solving this . rather than multiplying it we can do as follows : 586645 * ( 10000 - 1 ) = 5866450000 - 586645 = 5865863355 option a
Answer: a
Python program:
a = 586645 * 9999
Problem: the true discount on a bill due 9 months hence at 16 % per annum is rs . 189 . the amount of the bill is :
Options: a ) rs . 1386 , b ) rs . 1764 , c ) rs . 1575 , d ) rs . 2268 , e ) none of these
Rationale: "solution 32.5 let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 189 . ∴ x 16 x 9 / 12 x 1 / 100 = 189 or x = 1575 . ∴ p . w . = rs . 1575 . ∴ sum due = p . w . + t . d . = rs . ( 1575 + 189 ) = rs . 1764 . answer b"
Answer: b
Python program:
a = 4 * 3
b = 9 / a
c = b * 16
d = c / 100
e = 189 / d
f = e + 189
Problem: if the price of petrol increases by 30 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?
Options: a ) 25 % , b ) 23 % , c ) 16.67 % , d ) 33.33 % , e ) none of these
Rationale: "explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 30 ) i . e 130 . now , his consumption should be reduced to : - = ( 130 − 100 ) / 130 ∗ 100 . hence , the consumption should be reduced to 23 % . answer : b"
Answer: b
Python program:
a = 100 + 30 
b = 100 / a
c = 1 - b
d = c * 100
Problem: pipe a that can fill a tank in two hour and pipe b that can fill the tank in an hour are opened simultaneously when the tank is empty . pipe b is shut 30 minutes before the tank overflows . when will the tank overflow ?
Options: a ) 36 mins , b ) 35 mins , c ) 40 mins , d ) 32 mins , e ) 30 mins
Rationale: the last 30 minutes only pipe a was open . since it needs 2 hour to fill the tank , then in 30 minutes it fills 1 / 4 th of the tank , thus 3 / 4 of the tank is filled with both pipes open . the combined rate of two pipes is 1 + 2 = 3 tanks / hour , therefore to fill 3 / 4 th of the tank they need ( time ) = ( work ) / ( rate ) = ( 3 / 4 ) / 3 = 1 / 4 hours = 15 minutes . total time = 15 + 15 = 30 minutes . answer : e
Answer: e
Python program:
a = 1 / const_60
b = a / 2
c = 30 * b
d = 1 - c
e = 1 / const_60
f = 1 / const_60
g = f / 2
h = e + g 
i = d / h
Problem: two family reunions are happening at the taj hotel , the oates reunion and the hall reunion . all 150 guests at the hotel attend at least one of the reunions . if 70 people attend the oates reunion and 52 people attend the hall reunion , how many people attend both reunions ?
Options: a ) 2 , b ) 5 , c ) 10 , d ) 16 , e ) 28
Rationale: no of people in oates reunion = 70 no of people in hall reunion = 52 attending both = x all guests attend at least one . therefore , 150 = 70 + 52 - ( both ) both = 28 answer e
Answer: e
Python program:
a = 52 + 70 
b = 150 - a
Problem: you buy a piece of land with an area of â ˆ š 1024 , how long is one side of the land plot ?
Options: a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 32
Rationale: "try filling the numbers into the answer y x y = find the closest to 1024 . answer e"
Answer: e
Python program:
a = math.sqrt(1024)
Problem: divide rs . 720 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ?
Options: a ) s . 800 , b ) s . 400 , c ) s . 600 , d ) s . 180 , e ) s . 900
Rationale: "a + b + c = 720 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 720 = > 180 answer : d"
Answer: d
Python program:
a = 720 / 3
Problem: the least common multiple of positive integer e and 3 - digit integer n is 690 . if n is not divisible by 3 and e is not divisible by 2 , what is the value of n ?
Options: a ) 115 , b ) 230 , c ) 460 , d ) 575 , e ) 690
Rationale: the lcm of n and e is 690 = 2 * 3 * 5 * 23 . e is not divisible by 2 , thus 2 goes to n n is not divisible by 3 , thus 3 goes to e . from above : n must be divisible by 2 and not divisible by 3 : n = 2 * . . . in order n to be a 3 - digit number it must take all other primes too : n = 2 * 5 * 23 = 230 . answer : b .
Answer: b
Python program:
a = 3 * 10
b = 690 / a
c = 2 + 3 
d = 2 * c
e = b * d
Problem: half a number plus 5 is 15 . what is the number ?
Options: a ) 8 , b ) 20 , c ) 10 , d ) 11 , e ) 12
Rationale: "let x be the number . always replace ` ` is ' ' with an equal sign ( 1 / 2 ) x + 5 = 15 ( 1 / 2 ) x = 15 - 5 ( 1 / 2 ) x = 10 x = 20 correct answer is b"
Answer: b
Python program:
a = 15 - 5
b = a * 2
Problem: a car takes 6 hours to cover a distance of 630 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 48 kmph , b ) 50 kmph , c ) 52 kmph , d ) 56 kmph , e ) 70 kmph
Rationale: "time = 6 distence = 630 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 630 / 9 = 70 kmph e"
Answer: e
Python program:
a = 6 * 3
b = a / 2
c = 630 / b
Problem: population of a city in 20004 was 1100000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45 % , then find the population of city atthe end of the year 2007
Options: a ) 354354 , b ) 545454 , c ) 465785 , d ) 456573 , e ) 2384525 / 2
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 2384525 / 2 e"
Answer: e
Python program:
a = 15 / 100
b = 1 + a 
c = 35 / 100
d = 1 - c
e = b * d
f = 35 / 100
g = 1 + f 
h = e * g
i = 1100000 * h
Problem: a man walking at a rate of 15 km / hr crosses a bridge in 15 minutes . the length of the bridge is ?
Options: a ) 1250 m , b ) 1110 m , c ) 950 m , d ) 750 m , e ) 1300 m
Rationale: "speed = 15 * 5 / 18 = 15 / 18 m / sec distance covered in 15 minutes = 15 / 18 * 15 * 60 = 750 m answer is d"
Answer: d
Python program:
a = 15 * 1000
b = a / const_60
c = b * 15
Problem: a room 4 m 47 cm long and 7 m 77 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 38636 , b ) 38640 , c ) 38647 , d ) 38591 , e ) 38675
Rationale: "explanation : area of the room = ( 447 x 777 ) cm 2 . size of largest square tile = h . c . f . of 447 cm and 777 cm = 3 cm . area of 1 tile = ( 3 x 3 ) cm 2 . number of tiles required = ( 447 × 777 ) / ( 3 × 3 ) = 38591 answer : option d"
Answer: d
Python program:
a = 4 * 100
b = a + 47 
c = 7 * 100
d = c + 77 
e = b * d
f = 2 * 4
g = f + 2 
h = 47 - g
i = 2 * 4
j = i + 2 
k = 47 - j
l = h * k
m = e / l
Problem: the cost price of an book is 64 % of the marked price . calculate the gain percent after allowing a discount of 13 % ?
Options: a ) 31.5 % , b ) 35.9 % , c ) 37.5 % , d ) 39.5 % , e ) 30.5 %
Rationale: "let marked price = $ 100 . then , c . p . = $ 64 , s . p . = $ 87 gain % = 23 / 64 * 100 = 35.9 % . b"
Answer: b
Python program:
a = 100 / 64
b = 100 - 13
c = b / 100
d = a * c
e = d - 1
f = e * 100
Problem: the two lines y = x and x = - 4 intersect on the coordinate plane . if z represents the area of the figure formed by the intersecting lines and the x - axis , what is the side length r of a cube whose surface area is equal to 6 z ?
Options: a ) r = 16 , b ) r = 8 √ 2 , c ) r = 8 , d ) r = 2 √ 2 , e ) ( √ 2 ) / 3
Rationale: "800 score official solution : the first step to solving this problem is to actually graph the two lines . the lines intersect at the point ( - 4 , - 4 ) and form a right triangle whose base length and height are both equal to 4 . as you know , the area of a triangle is equal to one half the product of its base length and height : a = ( 1 / 2 ) bh = ( 1 / 2 ) ( 4 × 4 ) = 8 ; so z = 8 . the next step requires us to find the length of a side of a cube that has a face area equal to 8 . as you know the 6 faces of a cube are squares . so , we can reduce the problem to finding the length of the side of a square that has an area of 8 . since the area of a square is equal to s ² , where s is the length of one of its side , we can write and solve the equation s ² = 8 . clearly s = √ 8 = 2 √ 2 , oranswer choice ( d ) ."
Answer: d
Python program:
a = 4 * 4
b = a / 2
c = math.sqrt(b)
Problem: a candidate got 25 % of the votes polled and he lost to his rival by 4000 votes . how many votes were cast ?
Options: a ) 7500 , b ) 2028 , c ) 2775 , d ) 5496 , e ) 8000
Rationale: "25 % - - - - - - - - - - - l 75 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 50 % - - - - - - - - - - 4000 100 % - - - - - - - - - ? = > 8000 answer : e"
Answer: e
Python program:
a = 25 / 100
b = 1 - a
c = 25 / 100
d = b - c
e = 4000 / d
Problem: 8 , 24 , 12 , 36 , 18 , 54 , ( . . . . )
Options: a ) 27 , b ) 68 , c ) 107 , d ) 108 , e ) 28
Rationale: "8 × 3 = 24 24 ÷ 2 = 12 12 × 3 = 36 36 ÷ 2 = 18 18 × 3 = 54 54 ÷ 2 = 27 answer is a"
Answer: a
Python program:
a = negate - (
Problem: the ratio 5 : 20 expressed as percent equals to
Options: a ) 50 % , b ) 125 % , c ) 25 % , d ) none of above , e ) 30 %
Rationale: "explanation : actually it means 5 is what percent of 20 , which can be calculated as , ( 5 / 20 ) * 100 = 5 * 5 = 25 option c"
Answer: c
Python program:
a = 5 / 20
b = a * 100
Problem: a sum of money becomes 7 / 6 of itself in 2 years at a certain rate of simple interest . the rate per annum is ?
Options: a ) 50 / 9 , b ) 50 / 7 , c ) 50 / 6 , d ) 50 / 8 , e ) 50 / 3
Rationale: "let sum = x . then , amount = 7 x / 6 s . i . = 7 x / 6 - x = x / 6 ; time = 2 years . rate = ( 100 * x ) / ( x * 6 * 2 ) = 50 / 6 % . answer : c"
Answer: c
Python program:
a = 7 / 6
b = a - 1
c = b / 2
d = c * 100
Problem: a train travels 325 km in 3.5 hours and 470 km in 4 hours . find the average speed of train ?
Options: a ) 116 kmph , b ) 106 kmph , c ) 186 kmph , d ) 126 kmph , e ) 176 kmph
Rationale: explanation : as we know that speed = distance / time for average speed = total distance / total time taken thus , total distance = 325 + 470 = 795 km thus , total speed = 7.5 hrs average speed = 795 / 7.5 = > 106 kmph . answer : b
Answer: b
Python program:
a = 325 + 470 
b = 3 + 5 
c = a / b
Problem: a bucket full of nuts was discovered by the crow living in the basement . the crow eats a sixth of the total number of nuts in 8 hours . how many hours in total will it take the crow to finish a quarter of the nuts ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "in one hour , the crow eats 1 / 48 of the nuts . ( 1 / 4 ) / ( 1 / 48 ) = 12 hours the answer is b ."
Answer: b
Python program:
a = 1 / 4
b = 2 + 3 
c = 1 / b
d = c / 8
e = a / d
Problem: speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph . a man rows to a place at a distance of 7560 km and comes back to the starting point . the total time taken by him is :
Options: a ) 914.2 hours , b ) 900 hours , c ) 915 hours , d ) 905 hours , e ) 960 hours
Rationale: "explanation : speed downstream = ( 16 + 2 ) = 18 kmph speed upstream = ( 16 - 2 ) = 14 kmph total time taken = 7560 / 18 + 7560 / 14 = 420 + 540 = 960 hours answer : option e"
Answer: e
Python program:
a = 16 + 2 
b = 7560 / a
c = 16 - 2
d = 7560 / c
e = b + d
Problem: jennifer had $ 150 to spend on herself . she spent 1 / 5 of the money on a sandwich , 1 / 6 for a ticket to a museum , and 1 / 2 of it on a book . how much money does jennifer have left over ?
Options: a ) $ 4 , b ) $ 14 , c ) $ 5 , d ) $ 15 , e ) $ 20
Rationale: "1 / 5 x $ 150 = $ 30 for sandwich 1 / 6 x $ 150 = $ 25 for museum 1 / 2 x $ 150 = $ 75 for book $ 30 + $ 25 + $ 75 = $ 130 spent $ 150 - $ 130 = $ 20 left over correct answer e"
Answer: e
Python program:
a = 1 / 5
b = 150 * a
c = 1 / 6
d = 150 * c
e = b + d 
f = 1 / 2
g = 150 * f
h = e + g 
i = 150 - h
Problem: excluding the stoppages , the speed of a bus is 32 km / hr and including the stoppages the speed of the bus is 16 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 15 min , b ) 10 min , c ) 12 min , d ) 30 min , e ) 18 min
Rationale: "speed of the bus without stoppage = 32 km / hr speed of the bus with stoppage = 16 km / hr difference in speed = 16 km / hr so , the time taken in the stoppages = time taken to cover 16 km = ( 16 / 32 ) hr = 1 / 2 hr = 30 min answer : d"
Answer: d
Python program:
a = 16 / 32
b = a * const_60
c = const_60 - b
Problem: what is the sum of all the multiples of 10 between 0 and 75 ?
Options: a ) 500 , b ) 620 , c ) 450 , d ) 340 , e ) 280
Rationale: "the multiples of 10 between 0 and 99 are 10 , 20 , 30 , 40 , 50 , 60 , 70 . if these are all added together , the result is 280 . final answer : e"
Answer: e
Python program:
a = 12 + 2 
b = a + 1 
c = 12 + 2 
d = 2 + 4 
e = d + 4 
f = 10 - 1
g = e + f 
h = 2 + 4 
i = h + 4 
j = g + i 
k = 10 + 2 
l = j + k 
m = c + l 
n = b + m 
o = 12 + 2 
p = o + 1 
q = p + 1 
r = n + q 
s = r + 10 
t = 2 + 4 
u = s + t
Problem: the sum of the non - prime numbers between 10 and 20 , non - inclusive , is
Options: a ) 60 , b ) 75 , c ) 90 , d ) 105 , e ) 120
Rationale: "sum of consecutive integers from 11 to 19 , inclusive = = = = > ( a 1 + an ) / 2 * # of terms = ( 11 + 19 ) / 2 * 9 = 15 * 9 = 135 sum of non - prime numbers b / w 10 and 20 , non inclusive = = = > 135 - 60 ( i . e . , 11 + 13 + 17 + 19 , being the prime # s in the range ) = 75 answer : b"
Answer: b
Python program:
a = 10 + 1 
b = 10 + 1 
c = b + 1 
d = a + c 
e = 10 + 1 
f = e + 1 
g = f + 2 
h = d + g 
i = 10 + 1 
j = i + 1 
k = j + 2 
l = k + 1 
m = h + l 
n = 10 + 1 
o = n + 1 
p = o + 2 
q = p + 1 
r = q + 1 
s = m + r 
t = 10 + 1 
u = t + 1 
v = u + 2 
w = v + 1 
x = w + 1 
y = x + 1 
z = s + y 
A = 10 + 1 
B = A + 1 
C = B + 2 
D = C + 1 
E = D + 1 
F = E + 1 
G = F + 1 
H = z + G
Problem: the length of a rectangular plot is 10 mtr more than its width . the cost of fencing the plot along its perimeter at the rate of rs . 6.5 mtr is rs . 2210 . the perimeter of the plot is ?
Options: a ) 126 , b ) 156 , c ) 340 , d ) 321 , e ) 260
Rationale: "sol . let width = x , length = ( 10 + x ) perimeter = 2 ( x + ( 10 + x ) ) = 2 ( 2 x = 10 ) & 2 ( 2 x + 10 ) * 6.5 = 2210 x = 80 required perimeter = 2 ( 80 + 90 ) = 340 c"
Answer: c
Python program:
a = 2210 / 6
b = a / 2
c = b - 10
d = c / 2
e = 2210 / 6
f = e / 2
g = f - 10
h = g / 2
i = h + 10 
j = d + i 
k = j * 2
Problem: the ratio of the volumes of two cubes is 729 : 1331 . what is the ratio of their total surface areas ?
Options: a ) 81 : 121 , b ) 81 : 126 , c ) 81 : 189 , d ) 81 : 176 , e ) 81 : 117
Rationale: "ratio of the sides = ³ √ 729 : ³ √ 1331 = 9 : 11 ratio of surface areas = 92 : 112 = 81 : 121 answer : a"
Answer: a
Python program:
a = 729 / 1331
b = 1 / 3
c = a ** b
Problem: at what rate percent on simple interest will rs . 1750 amount to rs . 2000 in 4 years ?
Options: a ) 4 % , b ) 3.57 % , c ) 2 6 / 7 % , d ) 5 % , e ) 6 %
Rationale: "explanation : 250 = ( 1750 x 4 xr ) / 100 r = 3.57 % answer : option b"
Answer: b
Python program:
a = 2000 - 1750
b = a / 1750
c = b / 4
d = c * 100
Problem: roy is now 8 years older than julia and half of that amount older than kelly . if in 2 years , roy will be three times as old as julia , then in 2 years what would be roy ’ s age multiplied by kelly ’ s age ?
Options: a ) 72 , b ) 84 , c ) 88 , d ) 96 , e ) 108
Rationale: "r = j + 8 = k + 4 r + 2 = 3 ( j + 2 ) ( j + 8 ) + 2 = 3 j + 6 j = 2 r = 10 k = 6 in 2 years ( r + 2 ) ( k + 2 ) = 12 * 8 = 96 the answer is d ."
Answer: d
Python program:
a = 8 - 2
b = 8 + a 
c = b + 2 
d = 8 - 2
e = 8 + d 
f = 8 / 2
g = e - f
h = g + 2 
i = c * h
Problem: having scored 95 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ?
Options: a ) 28 , b ) 27 , c ) 23 , d ) 22 , e ) 24
Rationale: "explanation : let the average score of the first 18 innings be n 18 n + 95 = 19 ( n + 4 ) = > n = 19 so , average score after 19 th innings = x + 4 = 23 . answer : c"
Answer: c
Python program:
a = 19 * 4
b = 95 - a
c = b + 4
Problem: if a rectangular billboard has an area of 104 square feet and a perimeter of 42 feet , what is the length of each of the shorter sides ?
Options: a ) 4
b ) 7
c ) 8
d ) 13
e ) 26
Rationale: assume the sides to be x and y . perimeter = 2 x + 2 y = 42 hence x + y = 21 - ( i ) area = xy = 104 - ( ii ) since these are the sides of a billboard , we are dealing with positive numbers only and the options tell us that they are integers . 104 can be written as a product of two numbers as 104 * 1 or 52 * 2 or 26 * 4 or 13 * 8 of these , only 13 * 8 satisfies the equation ( i ) hence the lengths are 13 and 8 length of shorter side = 8 answer : c
Answer: c
Python program:
a = 42 / 2
b = 42 / 2
c = b ** 2
d = 4 * 104
e = c - d
f = math.sqrt(e)
g = a - f
h = g / 2
Problem: in a village of 2,700 people , 900 people are over 70 years old and 1200 people are female . it is known that 40 percent of the females are younger than 70 years old . if no one in the village is 70 years old , what is the probability that a person chosen at random is either a male or younger than 70 years old ?
Options: a ) 3 / 5 , b ) 7 / 10 , c ) 11 / 15 , d ) 23 / 30 , e ) 31 / 45
Rationale: "the number of people younger than 70 years old is 2700 - 900 = 1800 the number of females older than 70 years old is 0.6 * 1200 = 720 the number of males older than 70 years old is 900 - 720 = 180 the number of people who are either male or younger than 70 is 1800 + 180 = 1980 . p ( a person is younger than 70 or male ) = 1980 / 2700 = 11 / 15 the answer is c ."
Answer: c
Python program:
a = 5 * 5
b = a / const_0_25
c = const_26 * b
d = 5 * 5
e = d / const_0_25
f = 40 / e
g = 1 - f
h = 1200 * g
i = c - h
j = 5 * 5
k = j / const_0_25
l = const_26 * k
m = i / l
Problem: the marks obtained by vijay and amith are in the ratio 4 : 4 and those obtained by amith and abhishek in the ratio of 3 : 2 . the marks obtained by vijay and abhishek are in the ratio of ?
Options: a ) 3 : 2 , b ) 6 : 1 , c ) 6 : 5 , d ) 6 : 2 , e ) 6 : 3
Rationale: "4 : 4 3 : 2 - - - - - - - 12 : 12 : 8 12 : 8 3 : 2 answer : a"
Answer: a
Python program:
a = 4 * 3
b = 4 * 2
c = a / b
Problem: 5 x + y = 19 , and x + 3 y = 1 . find the value of 3 x + 2 y
Options: a ) 20 , b ) 18 , c ) 11 , d ) 10 , e ) 5
Rationale: add these two equations 6 x + 4 y = 20 divide by 2 ( to get 3 x + 2 y ) answer will be d . 10
Answer: d
Python program:
a = 19 + 1 
b = a / 2
Problem: a number is increased by 50 % and then decreased by 50 % . find the net increase or decrease per cent .
Options: a ) 25 % , b ) 18 % , c ) 17 % , d ) 13 % , e ) 16 %
Rationale: "let the number be 100 . increase in the number = 50 % = 50 % of 100 = ( 50 / 100 ã — 100 ) = 50 therefore , increased number = 100 + 50 = 150 this number is decreased by 50 % therefore , decrease in number = 50 % of 150 = ( 50 / 100 ã — 150 ) = 7500 / 100 = 75 therefore , new number = 150 - 75 = 75 thus , net decreases = 100 - 75 = 25 hence , net percentage decrease = ( 25 / 100 ã — 100 ) % = ( 2500 / 100 ) % = 25 % answer : a"
Answer: a
Python program:
a = 50 + 100 
b = 100 - 50
c = a * b
d = c / 100
Problem: the unit digit in the product ( 115 * 297 * 196 * 108 ) is :
Options: a ) 2 , b ) 7 , c ) 6 , d ) 0 , e ) 8
Rationale: "explanation : unit digit in the given product = unit digit in ( 5 * 7 * 6 * 8 ) = 0 answer : d"
Answer: d
Python program:
a = 115 * 297
b = a * 196
c = b * 108
d = 115 * 297
e = d * 196
f = e * 108
g = 4 + 4 
h = f - g
i = c - h
Problem: if 0.75 : x : : 5 : 8 , then x is equal to :
Options: a ) 1.12 , b ) 1.2 , c ) 1.25 , d ) 1.3 , e ) none
Rationale: "( x * 5 ) = ( 0.75 * 8 ) x = 6 / 5 x = 1.20 answer = b"
Answer: b
Python program:
a = 0 * 75
b = a / 5
Problem: the effective annual rate of interest corresponding to a nominal rate of 6 % per annum payable half - yearly is :
Options: a ) 6.09 % , b ) 6.08 % , c ) 6.1 % , d ) 6.07 % , e ) 6.05 %
Rationale: "amount of rs . 100 for 1 year when compounded half - yearly = 100 x ( 1 + 3 / 100 ) ^ 2 = 106.09 therefore effective rate = ( 106.09 - 100 ) % = 6.09 % answer a ) 6.09 %"
Answer: a
Python program:
a = 6 / 2
b = 6 / 2
c = a + b 
d = 6 / 2
e = 6 / 2
f = d * e
g = f / 100
h = c + g
Problem: a reduction of 25 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 1200 , what is the reduced price for kg ?
Options: a ) s . 40 , b ) s . 46 , c ) s . 49 , d ) s . 41 , e ) s . 60
Rationale: "1200 * ( 25 / 100 ) = 300 - - - - 5 ? - - - - 1 = > rs . 60 answer : e"
Answer: e
Python program:
a = 1200 * 25
b = a / 100
c = b / 5
Problem: if 50 % of ( x - y ) = 20 % of ( x + y ) then what percent of x is y ?
Options: a ) 2.5 % , b ) 10 % , c ) 5 % , d ) 15 % , e ) 43 %
Rationale: "50 % of ( x - y ) = 20 % of ( x + y ) ( 50 / 100 ) ( x - y ) = ( 20 / 100 ) ( x + y ) 5 ( x - y ) = 2 ( x + y ) 3 x = 7 y x = 7 / 3 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / ( 7 / 3 ) y ) x 100 ) = 43 % answer is e ."
Answer: e
Python program:
a = 50 - 20
b = 50 + 20 
c = a / b
d = c * 100
Problem: ashwin rented a power tool from a rental shop . the rent for the tool was $ 25 for the first hour and $ 10 for each additional hour . if ashwin paid a total of $ 125 , excluding sales tax , to rent the tool , for how many hours did she rent it ?
Options: a ) 11 , b ) 12 , c ) 15 , d ) 18 , e ) 16
Rationale: 25 + 10 n = 125 n = 10 total time = n + 1 hrs = 10 + 1 hrs = 11 hrs answer : a
Answer: a
Python program:
a = 10 + 1
Problem: on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 390 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 237 , b ) 780 , c ) 197 , d ) 287 , e ) 720
Rationale: "explanation : let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 390 ) = 2 + 2 ( extra ) = > 2 x - 780 = x = > x = 780 . answer : b"
Answer: b
Python program:
a = 390 * 2