List of top Quantitative Aptitude Questions asked in CAT

If \( \log_3 2, \log_3 (2^x - 5), \log_3 (2^x - 7/2) \) are in arithmetic progression, then what is the value of \( x \)?
A person buys 12 articles for Rs. 12 and sells them at Rs. 12 for 10 articles. What is the profit percentage?
The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 124. What are their current ages?
A shopkeeper sells a product at a 20% profit. If he buys it at 20% less cost and sells it for Rs. 10 less, he earns a 25% profit. What is the original cost price?
In a triangle ABC, the lengths of the sides AB and AC are 17.5 cm and 9 cm respectively. Let D be a point on AB such that AD = 7 cm. What is the length of CD?
A cube of side 4 cm is painted on all its faces. If it is sliced into 1 cm cubes, how many 1 cm cubes will have exactly one face painted?
The average price of 10 books is Rs. 12 while the average price of 8 of these books is Rs. 11.75. Of the remaining two books, if the price of one book is 60% more than the price of the other, what is the price of each of these two books?

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

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?
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?
If \( \sin \theta + \cos \theta = \sqrt{2} \), what is \( \sin \theta \cos \theta \)?
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.)
What is the sum of the first 20 terms of the arithmetic sequence 3, 7, 11, …?
If \( 2x + 3y = 12 \) and \( x - y = 1 \), what is the value of \( x \)?
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?
The ratio of two numbers is 3:4. If their sum is 70, what is the larger number?
The area of a circle is 154 cm². What is its radius? (Use \( \pi = \frac{22}{7} \))
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?
A train travels 360 km in 4 hours. What is its speed in km/h?
A man can row at 6 km/h in still water. If the river flows at 2 km/h and it takes him 1 hour to row to a place and return, what is the distance to the place?
If \( x^2 - 5x + 6 = 0 \), what is the sum of the roots?
If \( \log_2 x + \log_2 (x - 2) = 3 \), what is \( x \)?
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 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?
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?