List of top Quantitative Aptitude Questions asked in CAT

If \( x^2 - 5x + 6 = 0 \), what is the sum of the roots?
What is the sum of the first 20 terms of the arithmetic sequence 3, 7, 11, …?

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 $ab + bc + ca$?
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?
The HCF of two numbers is 12, and their LCM is 144. If one number is 36, what is the other number?
What is the remainder when \(3^{100}\) is divided by 7?

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 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.)
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?
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?
If \(3x + 4y = 12\) and \(x - y = 1\), what is the value of \(x + y\)?

If $\log_2 x + \log_4 x = 5$, what is the value of $x$? 
 

A boat travels 36 km downstream in 3 hours and 24 km upstream in 3 hours. What is the speed of the boat in still water? 
 

If $x^2 - 5x + 6 = 0$, what is the value of $x^3 - 3x^2 + 2x$? 
 

The cost price of an article is Rs. 200. It is sold at a 10% discount on the marked price, yielding a 25% profit. What is the marked price?