List of top Quantitative Aptitude Questions asked in CAT

If $a, b, c$ are in geometric progression and $a + b + c = 21$, $abc = 216$, what is the value of $b$? 
 

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? 
 

A sum of Rs. 10,000 is invested at 5% per annum compound interest for 2 years. What is the total amount?

If $x^2 + y^2 = 25$ and $xy = 12$, what is the value of $x + y$? 
 

The sum of the squares of three consecutive integers is 110. What is the smallest integer?
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 shop sells two types of pens at Rs. 10 and Rs. 15 each. If 50 pens are sold for Rs. 650, how many pens of Rs. 10 were sold? 
 

A man travels 300 km, partly at 60 km/h and partly at 80 km/h. If the total time taken is 4.5 hours, how many kilometers did he travel at 60 km/h?
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 shopkeeper marks up an article by 25% and then offers a 20% discount. What is the net profit percentage? 
 

The ratio of two numbers is 3:4. If their sum is 70, what is the larger number?
If \( \log_2 x + \log_2 (x - 2) = 3 \), what is \( x \)?
If the sum of two numbers is 15 and their product is 56, what is the sum of their reciprocals?
If $a + b + c = 12$ and $a^2 + b^2 + c^2 = 50$, what is the value of $ab + bc + ca$?
If \( x^2 - 5x + 6 = 0 \), what is the sum of the roots?
If $2^x = 3^y = 6^z$, what is the value of $xy$ in terms of $z$?
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 and B can complete a work in 12 days, B and C in 15 days, and A and C in 20 days. How long will A alone take to complete the work?
A shopkeeper sells an item at a 20% discount on the marked price and still makes a 25% profit on the cost price. If the cost price is Rs. 400, what is the marked price?
A rectangular garden has a perimeter of 100 meters and an area of 600 m². What is the length of the garden?
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 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?
The ratio of the speeds of two trains is 3:4. If the second train covers 400 km in 5 hours, what is the speed of the first train?
What is the remainder when \(3^{100}\) is divided by 7?
If \( \sin \theta + \cos \theta = \sqrt{2} \), what is \( \sin \theta \cos \theta \)?