euclaise/mathqa_programs huggingface dataset:
Problem: find the average of first 15 natural numbers .
Options: a ) 10 , b ) 120 , c ) 15 , d ) 8 , e ) 16
Rationale: explanation : sum of first n natural numbers = n ( n + 1 ) / 2 hence , sum of first 15 natural numbers = ( 15 x 16 ) / 2 = 120 therefore , required average of = 120 / 15 = 8 answer : d
Answer: d
Python program:
a = 1 + 2 
b = a + 3 
c = b + 4 
d = 4 + 1 
e = c + d 
f = 1 + 2 
g = f + 3 
h = e + g 
i = 4 + 3 
j = h + i 
k = 4 + 4 
l = j + k 
m = 4 + 4 
n = m + 1 
o = l + n 
p = o + 10 
q = 10 + 1 
r = p + q 
s = r + 12 
t = 12 + 1 
u = s + t 
v = 12 + 1 
w = v + 1 
x = u + w 
y = x + 15 
z = y / 15
Problem: the “ a - number ” of a number x is defined as the ones digit of 2 ^ x . antony rolls a die with 6 sides labeled with the integers from 1 to 6 , each of which has an equal probability of landing face - up . he then takes 3 ^ a , where a is the a - number of the result of his die roll , and plots 3 ^ a on a number line as the point a . finally , he repeats this entire process , this time plotting the result as the point b . what is the probability that the distance between a and b is greater than the value of b ?
Options: a ) 3 / 8 , b ) 13 / 36 , c ) 17 / 36 , d ) 19 / 36 , e ) 23 / 36
Rationale: if you calculate 3 ^ a for 1 st roll , all 6 results will be 9 , 81 , 6561 , 729 , 9 , 81 . this result is the same for 2 nd roll . 9 , 81 , 6561 , 729 , 9 , 81 . about distance : if the first result is 9 and the second is also 9 , the distance is 9 - 9 = 0 which is smaller than 9 . if the first result is 9 and the second is 81 , the distance is 81 - 9 = 72 which is also smaller than b which has the value of 81 . if the first result is 81 and the second is 9 , the distance will be greater than b . distance 81 - 9 = 72 > 9 . on the first roll , the probability of getting result 9 is 2 / 6 . in this case no other alternative values for second roll which would make the distance greater than b . so probability is 0 . so next estimations are : probability of getting 81 on the first roll ( 2 / 6 ) * probability of getting 9 on the second roll ( 2 / 6 ) = 1 / 9 probability of getting 729 on the first roll ( 1 / 6 ) * probability of getting 9 , 81 on the second roll ( 4 / 6 ) = 1 / 9 probability of getting 6561 on the first roll ( 1 / 6 ) * probability of getting 9 , 81 , 729 on the first roll ( 5 / 6 ) = 5 / 36 all together : 1 / 9 + 1 / 9 + 5 / 36 = 13 / 36 = b
Answer: b
Python program:
a = 4 + 2 
b = a + 1 
c = b + 2 
d = c + 4 
e = 6 * 6
f = d / e
Problem: you and your friend spent a total of $ 17 for lunch . your friend spent $ 3 more than you . how much did your friend spend on their lunch ?
Options: a ) $ 9 , b ) $ 3 , c ) $ 4 , d ) $ 10 , e ) $ 5
Rationale: "my lunch = l , my friends lunch = l + 3 ( l ) + ( l + 3 ) = 17 l + l + 3 - 3 = 17 - 3 2 l = 14 l = 7 my friends lunch l + 3 = 7 + 3 = $ 10 , the answer is d"
Answer: d
Python program:
a = 17 - 3
b = a / 2
c = b + 3
Problem: a man buy a book in rs 50 & sale it rs 60 . what is the rate of profit ? ? ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 25 % , e ) 28 %
Rationale: "cp = 50 sp = 60 profit = 60 - 50 = 10 % = 10 / 50 * 100 = 20 % answer : b"
Answer: b
Python program:
a = 60 - 50
b = a / 50
c = b * 100
Problem: a man complete a journey in 1010 hours . he travels first half of the journey at the rate of 2121 km / hr and second half at the rate of 2424 km / hr . find the total journey in km .
Options: a ) 121 km , b ) 242 km , c ) 224 km , d ) 112 km , e ) 110 km
Rationale: "solution 1 average speed = 2 ã — 21 ã — 2421 + 24 = 22.4 km / hr = 2 ã — 21 ã — 2421 + 24 = 22.4 km / hr total distance = 22.4 ã — 10 = 224 km answer is c"
Answer: c
Python program:
a = 2121 * 2424
b = a * 1010
c = 2121 + 2424 
d = b / c
e = 2 * d
Problem: the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 10 . if p invested the money for 20 months , find for how much time did q invest the money ?
Options: a ) 11 , b ) 40 , c ) 18 , d ) 16 , e ) 12
Rationale: "7 * 5 : 20 * x = 7 : 10 x = 40 answer : b"
Answer: b
Python program:
a = 7 / 5
b = 10 / 7
c = a * b
d = c * 20
Problem: pipe a fills a tank in 56 minutes . pipe b can fill the same tank 7 times as fast as pipe a . if both the pipes are kept open when the tank is empty , how many minutes will it take to fill the tank ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: a ' s rate is 1 / 56 and b ' s rate is 1 / 8 . the combined rate is 1 / 56 + 1 / 8 = 1 / 7 the pipes will fill the tank in 7 minutes . the answer is d .
Answer: d
Python program:
a = 1 / 56
b = 7 / 56
c = a + b 
d = 1/(c)
Problem: a contractor undertakes to built a walls in 50 days . he employs 20 peoples for the same . however after 25 days he finds that only 40 % of the work is complete . how many more man need to be employed to complete the work in time ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 30 , e ) none of these
Rationale: 20 men complete 0.4 work in 25 days . applying the work rule , m 1 × d 1 × w 2 = m 2 × d 2 × w 1 we have , 20 × 25 × 0.6 = m 2 × 25 × 0.4 or m 2 = 20 × 25 × 0.6 / 25 × 0.4 = 30 men answerd
Answer: d
Python program:
a = 100 - 40
b = a / 100
c = 20 * b
d = 4 / 10
e = c / d
Problem: find the value for m ? 19 ( m + n ) + 17 = 19 ( - m + n ) - 135
Options: a ) 0 , b ) - 1 , c ) 1 , d ) 2 , e ) - 4
Rationale: 19 m + 19 n + 17 = - 19 m + 19 n - 135 38 m = - 152 = > m = - 4 e
Answer: e
Python program:
a = 135 + 17
Problem: there are 720 students in a school . the ratio of boys and girls in this school is 3 : 5 . find the total of girls & boys are there in this school ?
Options: a ) 320 , b ) 345 , c ) 450 , d ) 380 , e ) 400
Rationale: "in order to obtain a ratio of boys to girls equal to 3 : 5 , the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys . the total number of boys and girls is 720 . hence 3 x + 5 x = 720 solve for x 8 x = 720 x = 90 number of boys 3 x = 3 × 90 = 270 number of girls 5 x = 5 × 90 = 450 c"
Answer: c
Python program:
a = 720 / 5
b = a * 3
Problem: the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 2500 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 140 , b ) 150 , c ) 160 , d ) 170 , e ) 200
Rationale: "given that the area of the square = 2500 sq . units = > side of square = √ 2500 = 50 units the radius of the circle = side of the square = 50 units length of the rectangle = 2 / 5 * 50 = 20 units given that breadth = 10 units area of the rectangle = lb = 20 * 10 = 200 sq . units answer : option e"
Answer: e
Python program:
a = math.sqrt(2500)
b = 10 / 2
c = a / b
d = 2 * c
e = 10 * d
Problem: convert 1.6 hectares in ares
Options: a ) 130 ares . , b ) 160 ares . , c ) 180 ares . , d ) 230 ares . , e ) 250 ares .
Rationale: "1.6 hectares in ares 1 hectare = 100 ares therefore , 1.6 hectares = 1.6 × 100 ares = 160 ares . answer - b"
Answer: b
Python program:
a = 3 + 2 
b = a * 2
c = 3 + 2 
d = c * 2
e = b * d
f = e * 1
g = 3 + 2 
h = g * 2
i = 3 + 2 
j = i * 2
k = h * j
l = f / k
Problem: the average of 7 numbers is 15 . if each number be multiplied by 5 . find the average of new set of numbers ?
Options: a ) a ) 110 , b ) b ) 122 , c ) c ) 90 , d ) d ) 85 , e ) e ) 75
Rationale: explanation : average of new numbers = 15 * 5 = 75 answer : option e
Answer: e
Python program:
a = 15 * 5
Problem: calculate the speed of a boat in still water ( in km / hr ) if in one hour , the boat goes 15 km / hr downstream and 7 km / hr upstream .
Options: a ) 12 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) 11 kmph
Rationale: "speed in still water = ( 15 + 7 ) 1 / 2 kmph = 11 kmph . answer : e"
Answer: e
Python program:
a = 15 + 7 
b = a / 2
Problem: a and b go around a circular track of length 400 m on a cycle at speeds of 36 kmph and 36 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 40 sec , b ) 198 sec , c ) 178 sec , d ) 665 sec , e ) 276 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 { 400 / ( 36 * 5 / 18 ) , 400 / ( 36 * 5 / 18 ) } = lcm ( 40 , 40 ) = 40 sec . answer : a"
Answer: a
Python program:
a = 36 * const_0_2778
b = 36 * const_0_2778
c = a - b
d = 400 / c
Problem: a circle graph shows how the megatech corporation allocates its research and development budget : 9 % microphotonics ; 14 % home electronics ; 10 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ?
Options: a ) 108 ° , b ) 10 ° , c ) 18 ° , d ) 36 ° , e ) 52 °
Rationale: "9 % microphotonics ; 14 % home electronics ; 10 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; 100 - ( 9 + 14 + 10 + 29 + 8 ) = 30 % basic astrophysics . 30 % of 360 ° is 108 ° . answer : a ."
Answer: a
Python program:
a = 9 + 14 
b = a + 10 
c = b + 29 
d = c + 8 
e = 100 - d
f = 3600 / 10
g = e * f
h = g / 100
Problem: a mixture of 40 liters of milk and water contains 10 % water . how much water should be added to this so that water may be 20 % in the new mixture ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: 4 ltr - water 36 ltr - milk let x water be added then the new mixture must have 20 % water then 4 + x = 20 / 100 ( 40 + x ) x = 5 answer : c
Answer: c
Python program:
a = 20 / 100
b = 40 * a
c = 10 / 100
d = 40 * c
e = b - d
f = 100 - 20
g = f / 100
h = e / g
Problem: in the number 11,0 ab , a and b represent the tens and units digits , respectively . if 11,0 ab is divisible by 50 , what is the greatest possible value of b × a ?
Options: a ) 0 , b ) 5 , c ) 20 , d ) 15 , e ) 25
Rationale: "you should notice that 50 * 2 = 110 so 11,000 is divisible by 55 : 55 * 200 = 11,000 ( or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55 ) - - > b * a = 0 * 0 = 0 . next number divisible by 55 is 11,000 + 55 = 11,055 : b * a = 5 * 4 = 20 ( next number wo n ' t have 110 as the first 3 digits so we have only two options 0 and 25 ) . answer : c . ! please post ps questions in the ps subforum : gmat - problem - solving - ps - 140 / please post ds questions in the ds subforum : gmat - data - sufficiency - ds - 141 / no posting of ps / ds questions is allowed in the mainmath forum . c"
Answer: c
Python program:
a = 11 ** 0
b = a + 1000 
c = b / 50
d = c + 1 
e = d * 50
f = reminder * (
g = f - 10
Problem: a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 5 x km .
Options: a ) 16 , b ) 18 , c ) 24 , d ) 40 , e ) 12
Rationale: "total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 5 x / ( x / 8 ) = 40 kmph answer : d"
Answer: d
Python program:
a = 40 * 5
b = 40 / 40
c = 2 * 40
d = c / 20
e = b + d 
f = a / e
Problem: riya and priya set on a journey . riya moves eastward at a speed of 21 kmph and priya moves westward at a speed of 22 kmph . how far will be priya from riya after 60 minutes
Options: a ) 43 kms , b ) 45 kms , c ) 50 kms , d ) 30 kms , e ) 40 kms
Rationale: "total eastward distance = 21 kmph * 1 hr = 21 km total westward distance = 22 kmph * 1 hr = 22 km total distn betn them = 21 + 22 = 43 km ans 43 km answer : a"
Answer: a
Python program:
a = 21 + 22 
b = speed * (
Problem: a family had dinner in a restaurant and paid $ 30 for food . they also had to pay 9.5 % sale tax and 10 % for the tip . how much did they pay for the dinner ?
Options: a ) $ 35.83 , b ) $ 35.84 , c ) $ 35.85 , d ) $ 35.86 , e ) $ 35.87
Rationale: solution they paid for food , sales tax and tip , hence total paid = $ 30 + 9.5 % * 30 + 10 % * 30 = $ 35.85 answer c
Answer: c
Python program:
a = 9 - 5
b = a * 9
c = b - const_0_25
d = c + const_0_25 
e = d - 12
f = e - 12
g = f - 2
Problem: a man is 26 years older than his son . in two years , his age will be twice the age of his son . the present age of this son is
Options: a ) 78 years , b ) 22 years , c ) 88 years , d ) 66 years , e ) 24 years
Rationale: "let ' s son age is x , then father age is x + 26 . = > 2 ( x + 2 ) = ( x + 26 + 2 ) = > 2 x + 4 = x + 28 = > x = 24 years answer : e"
Answer: e
Python program:
a = 2 * 2
b = a - 2
c = 26 - b
d = 2 - 1
e = c / d
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 40 cm and breadth 20 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) ?
Options: a ) 47.14 , b ) 45.15 , c ) 43.23 , d ) 41.44 , e ) 41.51
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 40 + 20 ) = 120 cm parameter of the square = 120 cm i . e . 4 a = 120 a = 30 diameter of the semicircle = 30 cm circimference of the semicircle = 1 / 2 ( â ˆ  ) ( 30 ) = 1 / 2 ( 22 / 7 ) ( 30 ) = 660 / 14 = 47.14 cm to two decimal places answer : a"
Answer: a
Python program:
a = square_edge_by_perimeter / (
b = circumface / (
Problem: two trains 200 m and 300 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 18 , b ) 10.9 , c ) 10.4 , d ) 10.8 , e ) 10.1
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 200 + 300 = 500 m . required time = 500 * 9 / 250 = 18 secs answer : a"
Answer: a
Python program:
a = 200 + 300 
b = 60 + 40 
c = b * const_0_2778
d = a / c
Problem: the manager at a health foods store mixes a unique superfruit juice cocktail that costs $ 1399.45 per litre to make . the cocktail includes mixed fruit juice and a ç ai berry juice , which cost $ 262.85 per litre and $ 3104.35 per litre , respectively . the manager has already opened 35 litres of the mixed fruit juice . how many litres of the a ç ai berry juice does he need to add ?
Options: a ) 17 litres , b ) 23.3 litres , c ) 11 litres , d ) 07 litres , e ) 38 litres
Rationale: "262.85 ( 35 ) + 3 , 104.35 x = 1 , 399.45 ( 35 + x ) solve the equation . 262.85 ( 35 ) + 3 , 104.35 x = 1 , 399.45 ( 35 + x ) 9 , 199.75 + 3 , 104.35 x = 48980.75 + 1 , 399.45 x 9 , 199.75 + 1 , 704.9 x = 48980.75 1 , 704.9 x = 39,781 x ≈ 23.3 answer is b ."
Answer: b
Python program:
a = 35 * 1399
b = 35 * 262
c = a - b
d = 3104 - 35
e = c / d
Problem: when n is divided by 15 , the remainder is 8 . what is the remainder when 5 n is divided by 6 ?
Options: a ) 2 , b ) 6 , c ) 3 , d ) 4 , e ) 1
Rationale: "let n = 8 ( leaves a remainder of 8 when divided by 48 ) 5 n = 5 ( 8 ) = 40 , which leaves a remainder of 4 when divided by 6 . answer d"
Answer: d
Python program:
a = 8 - reminder
Problem: a number x is 18 times another number y . the percentage that y is less than x is
Options: a ) 12.5 % , b ) 87.5 % , c ) 80 % , d ) 94.4 % , e ) 1 %
Rationale: "say y = 1 and x = 18 . then y = 1 is less than x = 18 by ( 18 - 1 ) / 18 * 100 = 17 / 18 * 100 = 94.4 % . answer : d ."
Answer: d
Python program:
a = 18 - 1
b = a / 18
c = b * 100
Problem: a dozen eggs and 5 pounds of oranges are currently at the same price . if the price of a dozen eggs rises by 3 percent and the price of oranges rises by 6 % . how much more will it cost to buy a dozen eggs and 10 pounds of oranges .
Options: a ) 8 % , b ) 9 % , c ) 10 % , d ) 11 % , e ) 5 %
Rationale: say currently both a dozen eggs and 5 pounds of oranges cost $ 100 ( they are at the same price ) . so , to buy a dozen eggs and 5 pounds of oranges we need $ 100 . after the increase , the price of a dozen eggs will be $ 103 and the price of 5 pounds of oranges will be $ 106 . so after the increase , to buy a dozen eggs and 5 pounds of oranges we ' ll need $ 209 . increase = 9 % . answer : b .
Answer: b
Python program:
a = 3 / 100
b = a * 10
c = 10 + b 
d = 6 / 100
e = d * 10
f = 10 + e 
g = c + f 
h = 10 + 10 
i = g - h
j = i * 100
k = 10 + 10 
l = j / k
m = l * 2
Problem: a number is said to be prime saturated if the product of all the different positive prime factors of a is less than the square root of a . what is the greatest two digit prime saturated integer ?
Options: a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95
Rationale: "clearly d a number is said to be prime saturated if the product of all the different positive prime factors of a is less than the square root of a . 96 has more number of smaller prime factor thats the clue ! ! = d"
Answer: d
Python program:
a = 2 * 3
b = 100 - 10
c = a + b
Problem: the area of a circular field is 13.86 hectares . find the cost of fencing it at the rate of rs . 4.60 per metre .
Options: a ) 2399 , b ) 3888 , c ) 2999 , d ) 5808 , e ) 6072
Rationale: "explanation : area = ( 13.86 x 10000 ) sq . m = 138600 sq . m circumference = cost of fencing = rs . ( 1320 x 4.60 ) = rs . 6072 . answer : e ) 6072"
Answer: e
Python program:
a = 13 / 86
b = math.sqrt(a)
c = b * 100
d = circumface * (
Problem: 3 years ago the average age of a class of 6 members was 19 years . a boy have been added , the average age of the class is the same today . what is the age of the boy ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: 6 * 22 = 132 7 * 19 = 133 ` 1 a
Answer: a
Python program:
a = 6 + 1 
b = a * 19
c = 6 * 19
d = 6 * 3
e = c + d 
f = b - e
Problem: find the number of shares that can be bought for rs . 8200 if the market value is rs . 28 each with brokerage being 2.5 % .
Options: a ) 237 , b ) 270 , c ) 177 , d ) 285.7 , e ) 111
Rationale: "explanation : cost of each share = ( 28 + 2.5 % of 28 ) = rs . 28.7 therefore , number of shares = 8200 / 28.7 = 285.7 answer : d"
Answer: d
Python program:
a = 2 / 5
b = 28 + a 
c = 8200 / b
d = math.floor(c)
Problem: if ( x + 3 ) ^ 2 / ( 3 x + 29 ) = 2 , then the difference between the two possible values of x is :
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "( x + 3 ) ^ 2 / ( 3 x + 29 ) = 2 ( x + 3 ) ^ 2 = 2 ( 3 x + 29 ) x ^ 2 + 6 x + 9 = 6 x + 58 x ^ 2 - 49 = 0 ( x - 7 ) ( x + 7 ) = 0 x = 7 or x = - 7 the answer is d ."
Answer: d
Python program:
a = 29 * 3
b = 3 * 3
c = a - b
d = math.sqrt(c)
e = d * 2
Problem: a train 710 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 2898 , b ) 277 , c ) 500 , d ) 297 , e ) 590
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 710 + x ) / 60 = 65 / 3 x = 590 m . answer : e"
Answer: e
Python program:
a = 78 - 1
b = a * const_0_2778
c = 710 / b
Problem: in a certain corporation , there are 300 male employees and 100 female employees . it is known that 20 % of the male employees have advanced degrees and 40 % of the females have advanced degrees . if one of the 400 employees is chosen at random , what is the probability this employee has an advanced degree or is female ?
Options: a ) 1 / 20 , b ) 1 / 10 , c ) 1 / 5 , d ) 2 / 5 , e ) 3 / 4
Rationale: "in this corporation , there are 400 total employees . there are 100 women . of the 300 men , 20 % have advanced degrees — - 10 % of 300 must be 30 , so 20 % of 300 must be 60 . add the women and the men with advanced degrees : 100 + 60 = 160 . this is the or region , full set of individuals that satisfy the condition “ has an advanced degree or is female . ” of the 400 employees , what ’ s the probability of picking one of the 160 in this particular group ? p = 160 / 400 = 16 / 40 = 4 / 10 = 2 / 5 answer = d"
Answer: d
Python program:
a = 20 * 20
b = 40 / a
c = 1 - b
d = c * 100
e = d / 400
f = 20 * 20
g = 20 / f
h = g * 300
i = 20 * 20
j = 40 / i
k = j * 100
l = h + k 
m = l / 400
n = e + m
Problem: the price of 24 apples is equal to that of 28 oranges . the price of 45 apples and 60 oranges together is rs . 1350 . the total price of 30 apples and 40 oranges is
Options: a ) 850 , b ) 900 , c ) 750 , d ) 950 , e ) 800
Rationale: let the price of one apple = a and price of one orange = b price of 24 apples is equal to that of 28 oranges 24 a = 28 b = > 6 a = 7 b ⇒ b = 6 a / 7 - - - - - ( equation 1 ) price of 45 apples and 60 oranges together is rs . 1350 = > 45 a + 60 b = 1350 = > 3 a + 4 b = 90 ⇒ 3 a + 4 ( 6 a ) / 7 = 90 ( ∵ substituted the value of b from equation 1 ) ⇒ a + 4 ( 2 a ) / 7 = 30 = > 7 a + 8 a = 30 × 7 = 210 = > 15 a = 210 ⇒ a = 21015 = 423 = 14 b = 6 a 7 = ( 6 × 14 ) / 7 = 6 × 2 = 12 total price of 30 apples and 40 oranges = 30 a + 45 b = ( 30 × 14 ) + ( 40 × 12 ) = 420 + 480 = 900 answer is b .
Answer: b
Python program:
a = 24 / 28
b = 60 * a
c = 45 + b 
d = 1350 / c
e = d * 30
f = 24 / 28
g = 60 * f
h = 45 + g 
i = 1350 / h
j = 24 / 28
k = i * j
l = k * 40
m = e + l
Problem: rhoda tosses a coin 5 times . find the probability of getting exactly 4 heads .
Options: a ) 5 / 32 , b ) 6 / 32 , c ) 5 / 16 , d ) 4 / 32 , e ) 8 / 32
Rationale: exactly 4 heads out of 5 would be : hhhht , hhthh , or many other combinations . therefore , no . of possible combinations are 5 ! / 4 ! * 1 ! = 5 probability = 5 / 2 ^ 5 = 5 / 32 answer : a
Answer: a
Python program:
a = math.comb(5, 4)
b = 2 ** 5
c = a / b
Problem: if two of the 4 expressions x + y , x + 5 y , x - y , and 5 x - y are chosen at random , what is the probability r that their product will be of the form of x ^ 2 - ( by ) ^ 2 , where b is an integer ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) r = 1 / 6
Rationale: only ( x + y ) ( x - y ) pair will give the form x ^ 2 - ( by ) ^ 2 the probability of selecting these two pairs are 1 / 4 * 1 / 3 = 1 / 12 , assuming x + y is picked first , then x - y , but x - y can be picked first followed by x + y . so the probability r = 1 / 12 * 2 = 1 / 6 ans e
Answer: e
Python program:
a = 1 / 2
b = 1 / 3
c = a * b
Problem: 25 binders can bind 1400 books in 21 days . how many binders will be required to bind 1600 books in 20 days ?
Options: a ) 87 , b ) 18 , c ) 17 , d ) 16 , e ) 30
Rationale: "binders books days 25 1400 21 x 1600 20 x / 25 = ( 1600 / 1400 ) * ( 21 / 20 ) = > x = 30 answer : e"
Answer: e
Python program:
a = 1600 / 20
b = 25 * 21
c = 1400 / b
d = a / c
Problem: the amount of principal rs . 8000 at compound interest at the ratio of 5 % p . a . for 3 years is
Options: a ) rs . 9621 , b ) rs . 6921 , c ) rs . 9261 , d ) rs . 6261 , e ) rs . 6361
Rationale: "c . i = p ( 1 + r / 100 ) ^ n = 8000 ( 1 + 5 / 100 ) ^ 3 = 8000 ( 21 / 20 * 21 / 20 * 21 / 20 ) = rs 9261 answer : c"
Answer: c
Python program:
a = 5 / 100
b = 1 + a 
c = b ** 3
d = 8000 * c
Problem: the ratio of the capacity to do work of a and b is 3 : 2 . if they together can complete a work in 18 days , then how long does a take to complete the work alone ?
Options: a ) 45 , b ) 30 , c ) 24 , d ) 40 , e ) none of these
Rationale: llet a and b take 3 x and 2 x days to complete the work 1 / 3 x + 1 / 2 x = 1 / 18 ⇒ x = 15 so a will take 45 days . answer : a
Answer: a
Python program:
a = 18 * 3
b = 18 * 2
c = a + b 
d = c / 3
e = d * 3
f = e / 2
Problem: in a can , there is a mixture of milk and water in the ratio 4 : 5 . if it is filled with an additional 14 litres of milk the can would be full and ratio of milk and water would become 6 : 5 . find the capacity of the can ?
Options: a ) 40 , b ) 77 , c ) 48 , d ) 52 , e ) none of these
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 4 / 9 ( t - 14 ) after adding milk , quantity of milk in the mixture = 6 / 11 t . 6 t / 11 - 14 = 4 / 9 ( t - 14 ) 10 t = 1386 - 616 = > t = 77 . answer : b"
Answer: b
Python program:
a = 6 / 5
b = a * 5
c = b - 4
d = 14 / c
e = 5 * d
f = 6 / 5
g = f * 5
h = g - 4
i = 14 / h
j = e + i 
k = j + 14