CAT Quant Questions

What is the number of all possible positive integer values of n for which n^2 + 96 is a perfect square

Numbers

What is the number of all possible positive integer values of n for which n² + 96 is a perfect square?

2
4
5
Infinite

How many times will the digit 5 come in counting from 1 to 99

Numbers

How many times will the digit 5 come in counting from 1 to 99 excluding those which are divisible by 3?

It takes the pendulum of a clock 7 seconds to strike 4 o'clock

Clocks

It takes the pendulum of a clock 7 seconds to strike 4 o'clock. How much time will it take to strike 11 o'clock?

18 seconds
19.25 seconds
20 seconds
23.33 seconds

When they work alone, B needs 25% more time to finish a job than A does

Time Work

When they work alone, B needs 25% more time to finish a job than A does. They two finish the job in 13 days in the following manner: A works alone till half the job is done, then A and B work together for four days, and finally B works alone to complete the remaining 5% of the job. In how many days can B alone finish the entire job?

Humans and robots can both perform a job but at different efficiencies

Time Work

Humans and robots can both perform a job but at different efficiencies. Fifteen humans and five robots working together take thirty days to finish the job, whereas five humans and fifteen robots working together take sixty days to finish it. How many days will fifteen humans working together (without any robot) take to finish it?

The distance from A to B is 60 km. Partha and Narayan start from A

Time Distance

The distance from A to B is 60 km. Partha and Narayan start from A at the same time and move towards B. Partha takes four hours more than Narayan to reach B. Moreover, Partha reaches the mid-point of A and B two hours before Narayan reaches B. The speed of Partha, in km per hour, is

Let f(x) = min{2x^2, 52 − 5x}, where x is any positive real number

Relations Functions

Let f(x) = min{2x², 52 − 5x}, where x is any positive real number. Then the maximum possible value of f(x) is

John borrowed Rs. 2,10,000 from a bank at an interest rate of 10% per annum

Interests

John borrowed Rs. 2,10,000 from a bank at an interest rate of 10% per annum, compounded annually. The loan was repaid in two equal instalments, the first after one year and the second after another year. The first instalment was interest of one year plus part of the principal amount, while the second was the rest of the principal amount plus due interest thereon. Then each instalment, in Rs., is

Two types of tea, A and B, are mixed and then sold at Rs. 40 per kg

Ratio Proportion

Two types of tea, A and B, are mixed and then sold at Rs. 40 per kg. The profit is 10% if A and B are mixed in the ratio 3 : 2, and 5% if this ratio is 2 : 3. The cost prices, per kg, of A and B are in the ratio

18 : 25
19 : 24
21 : 25
17 : 25

In an examination, the maximum possible score is N

Percentages

In an examination, the maximum possible score is N while the pass mark is 45% of N. A candidate obtains 36 marks, but falls short of the pass mark by 68%. Which one of the following is then correct?

N ≤ 200
243 ≤ N ≤ 252
N ≥ 253
201 ≤ N ≤ 242

If f(x + 2) = f(x) + f(x + 1) for all positive integers x

Relations Functions

If f(x + 2) = f(x) + f(x + 1) for all positive integers x, and f(11) = 91, f(15) = 617, then f(10) equals

The number of integers x such that 0.25 2^x 200, and 2^x + 2

Numbers

The number of integers x such that 0.25 < 2^x < 200, and 2^x + 2 is perfectly divisible by either 3 or 4, is

How many numbers with two or more digits can be formed

Quant PnC

How many numbers with two or more digits can be formed with the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, so that in every such number, each digit is used at most once and the digits appear in the ascending order?

In a circle with center O and radius 1 cm

Geometry

In a circle with center O and radius 1 cm, an arc AB makes an angle 60 degrees at O. Let R be the region bounded by the radii OA, OB and the arc AB. If C and D are two points
on OA and OB, respectively, such that OC = OD and the area of triangle OCD is half that of R, then the length of OC, in cm, is

(π/3√3)^1/2
(π/4)^1/2
(π/6)^1/2
(π/4√3)^1/2

In a parallelogram ABCD of area 72 sq cm, the sides CD and AD have lengths 9 cm and 16 cm

Geometry

In a parallelogram ABCD of area 72 sq cm, the sides CD and AD have lengths 9 cm and 16 cm, respectively. Let P be a point on CD such that AP is perpendicular to CD. Then the area, in sq cm, of triangle APD is

18√3
24√3
32√3
12√3

Let ABCD be a rectangle inscribed in a circle of radius 13 cm

Geometry

Let ABCD be a rectangle inscribed in a circle of radius 13 cm. Which one of the following pairs can represent, in cm, the possible length and breadth of ABCD?

24, 10
25, 9
24, 12
25, 10

Raju and Lalitha originally had marbles in the ratio 4:9

Ratio Proportion

Raju and Lalitha originally had marbles in the ratio 4:9. Then Lalitha gave some of her marbles to Raju. As a result, the ratio of the number of marbles with Raju to that with Lalitha became 5:6. What fraction of her original number of marbles was given by Lalitha to Raju?

1/4
7/33
1/5
6/19

A CAT aspirant appears for a certain number of tests

Averages

A CAT aspirant appears for a certain number of tests. His average score increases by 1 if the first 10 tests are not considered, and decreases by 1 if the last 10 tests are not considered. If his average scores for the first 10 and the last 10 tests are 20 and 30, respectively, then the total number of tests taken by him is

A wholesaler bought walnuts and peanuts, the price of walnut per kg being thrice

Profit Loss

A wholesaler bought walnuts and peanuts, the price of walnut per kg being thrice that of peanut per kg. He then sold 8 kg of peanuts at a profit of 10% and 16 kg of walnuts at a profit of 20% to a shopkeeper. However, the shopkeeper lost 5 kg of walnuts and 3 kg of peanuts in transit. He then mixed the remaining nuts and sold the mixture at Rs. 166 per kg, thus making an overall profit of 25%. At what price, in Rs. per kg, did the wholesaler buy the walnuts?

Each of 74 students in a class studies at least one of the three subjects

Quant Sets

Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, then the number of students studying H is

Train T leaves station X for station Y at 3 pm

Time Distance

Train T leaves station X for station Y at 3 pm. Train S, traveling at three quarters of the speed of T, leaves Y for X at 4 pm. The two trains pass each other at a station Z, where the distance between X and Z is three-fifths of that between X and Y. How many hours does train T take for its journey from X to Y?

log12 81 = p, then 3[(4-p)/(4+p)] is equal to

Logarithms

log₁₂ 81 = p, then 3[(4-p)/(4+p)] is equal to

log₄ 16
log₆ 8
log₆ 16
log₂ 8

A right circular cone, of height 12 ft, stands on its base

Mensuration

A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With π = 22/7, the volume, in cubic ft, of the remaining part of the cone is

Points E, F, G, H lie on the sides AB, BC, CD, and DA

Geometry

Points E, F, G, H lie on the sides AB, BC, CD, and DA, respectively, of a square ABCD. If EFGH is also a square whose area is 62.5% of that of ABCD and CG is longer than EB, then the ratio of length of EB to that of CG is

2 : 5
4 : 9
3 : 8
1 : 3

While multiplying three real numbers, Ashok took one of the numbers

Numbers

While multiplying three real numbers, Ashok took one of the numbers as 73 instead of 37. As a result, the product went up by 720. Then the minimum possible value of the sum of squares of the other two numbers is

If x is a positive quantity such that 2x = 3^log5 2, then x is equal to

Logarithms

If x is a positive quantity such that 2^x = 3^{log₅ 2}, then x is equal to

1 + log₃ 5/3
log₅ 8
1 + log₅ 3/5
log₅ 9

If u^2 + (u − 2v − 1)^2 = −4v(u + v), then what is the value of u + 3v

Polynomials

If u² + (u − 2v − 1)² = −4v(u + v), then what is the value of u + 3v?

1/4
0
1/2
-1/4

Given an equilateral triangle T1 with side 24 cm

Progressions

Given an equilateral triangle T1 with side 24 cm, a second triangle T2 is formed by joining the midpoints of the sides of T1. Then a third triangle T3 is formed by joining the midpoints of the sides of T2. If this process of forming triangles is continued, the sum of the areas, in sq cm, of infinitely many such triangles T1, T2, T3, ... will be

164√3
188√3
248√3
192√3

In an apartment complex, the number of people aged 51 years

Averages

In an apartment complex, the number of people aged 51 years and above is 30 and there are at most 39 people whose ages are below 51 years. The average age of all the people in the apartment complex is 38 years. What is the largest possible average age, in years, of the people whose ages are below 51 years?

If among 200 students, 105 like pizza and 134 like burger

Quant Sets

If among 200 students, 105 like pizza and 134 like burger, then the number of students who like only burger can possibly be

In a circle, two parallel chords on the same side of a diameter

Geometry

In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is

√12
√14
√13
√11

A trader sells 10 litres of a mixture of paints A and B

Mixtures Alligation

A trader sells 10 litres of a mixture of paints A and B, where the amount of B in the mixture does not exceed that of A. The cost of paint A per litre is Rs. 8 more than that of paint B. If the trader sells the entire mixture for Rs. 264 and makes a profit of 10%, then the highest possible cost of paint B, in Rs. per litre, is

If log log2 (5 + log3 a) = 3 and log5 (4a + 12 + log2 b) = 3

Logarithms

If log log₂ (5 + log₃ a) = 3 and log₅ (4a + 12 + log₂ b) = 3, then a + b is equal to

Point P lies between points A and B such that the length of BP

Time Distance

Point P lies between points A and B such that the length of BP is thrice that of AP. Car 1 starts from A and moves towards B. Simultaneously, car 2 starts from B and moves towards A. Car 2 reaches P one hour after car 1 reaches P. If the speed of car 2 is half that of car 1, then the time, in minutes, taken by car 1 in reaching P from A is

Given that x^2018 y^2017 = 1/2 and x^2016 y^2019 = 8

Numbers

Given that x²⁰¹⁸y²⁰¹⁷ = 1/2 and x²⁰¹⁶y²⁰¹⁹ = 8, the value of x² + y³ is

35/4
37/4
31/4
33/4

A tank is fitted with pipes, some filling it and the rest draining it

Time Work

A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at the same rate, and all draining pipes drain at the same rate. The empty tank gets completely filled in 6 hours when 6 filling and 5 draining pipes are on, but this time becomes 60 hours when 5 filling and 6 draining pipes are on. In how many hours will the empty tank get completely filled when one draining and two filling pipes are on?

Let x, y, z be three positive real numbers in a geometric progression

Progressions

Let x, y, z be three positive real numbers in a geometric progression such that x < y < z. If 5x, 16y, and 12z are in an arithmetic progression then the common ratio of the geometric progression is:

5^6 - 1 is divisible by

Divisibility

5⁶ - 1 is divisible by

5
13
31
None of these

If n is any odd number greater than 1, then n(n^2 - 1) is

Divisibility

If n is any odd number greater than 1, then n(n² - 1) is

divisible by 24 always
divisible by 96 always
divisible by 48 always
None of these

Let N = 55^3 + 17^3 - 72^3. N is divisible by

Divisibility

Let N = 55³ + 17³ - 72³. N is divisible by

both 3 and 17
both 7 and 13
both 3 and 13
both 17 and 7

After the division of a number successively by 3, 4 and 7, the remainders

Remainders

After the division of a number successively by 3, 4 and 7, the remainders obtained are 2, 1 and 4 respectively. What will be the remainder if 84 divides the same number?