List of top Questions asked in CAT- 2015

If the roots of the equation $x^2 - kx + 16 = 0$ are integers, what is the sum of the roots? 
 

If \( \log_2 x + \log_2 (x - 2) = 3 \), what is \( x \)?
A bag contains 4 red, 3 white, and 2 blue balls. Two balls are drawn at random. What is the probability that both are red?
The area of a circle is 154 cm². What is its radius? (Use \( \pi = \frac{22}{7} \))
If \( 2x + 3y = 12 \) and \( x - y = 1 \), what is the value of \( x \)?
A car travels from A to B at 60 km/h and returns at 40 km/h. What is the average speed for the round trip?
If $a + b + c = 12$ and $a^2 + b^2 + c^2 = 50$, what is the value of $ab + bc + ca$?

Find the main idea of the passage? 
 

A key reason why Latin American rejected the Inter-American development Bank was that 
 

A rectangular garden has a perimeter of 100 meters and an area of 600 m². What is the length of the garden?
A and B can complete a task in 12 days, B and C in 15 days, A and C in 20 days. How many days will A alone take?
What is the remainder when \(3^{100}\) is divided by 7?
The HCF of two numbers is 12, and their LCM is 144. If one number is 36, what is the other number?
Four people A, B, C, D form two teams of two. A and B cannot be together, C and D cannot be together. Who is in the same team as A?

What is the probability of getting a sum of 7 when two dice are rolled? 
 

A number when divided by 7 leaves a remainder of 4. What is the remainder when the square of the number is divided by 7?
A and B start a business with investments of Rs. 4000 and Rs. 6000. If the profit after 1 year is Rs. 5000, what is A’s share?
A pipe can fill a tank in 6 hours, and another pipe can empty it in 8 hours. If both are opened together, how many hours will it take to fill the tank? (Enter the answer as a fraction or decimal.)
In a class, 60% of students are boys, and 40% are girls. If 30% of boys and 20% of girls passed an exam, what percentage of the class passed?
The sum of the ages of a father and son is 50 years. Five years ago, the father’s age was four times the son’s age. What is the father’s current age?
A rectangle has an area of 60 cm² and a perimeter of 32 cm. What is the length if it is greater than the width?
Course Enrollment
In a college, 120 students are enrolled in three courses: Math (M), Physics (P), and Chemistry (C).

- 70 take Math
- 60 take Physics
- 50 take Chemistry
- 30 take both Math and Physics
- 20 take both Physics and Chemistry
- 15 take both Math and Chemistry
- 10 take all three courses
Team Selection Puzzle
A manager must select a team of 3 employees from 5 (E1, E2, E3, E4, E5) with the following conditions:

1. If E1 is selected, E2 is not selected
2. E3 and E4 cannot both be selected
3. E5 is always selected
Expenditure Distribution
A company’s expenditure in 2015 (total Rs. 200 crores) is distributed as follows:

- Salaries: 40%
- Rent: 20%
- Utilities: 15%
- Marketing: 10%
- Miscellaneous: 15%
Book Arrangement
Five books (A, B, C, D, E) are arranged in a row on a shelf. The following conditions apply:

1. Book A is not at either end
2. Book B is to the immediate left of Book C
3. Book D is not adjacent to Book E
4. Book E is in the third position