List of top Quantitative Aptitude Questions asked in CAT

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 \( 2x + 3y = 12 \) and \( x - y = 1 \), what is the value of \( x \)?
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 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?
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 shopkeeper sells an item at a 20% profit. If the cost price is increased by 10% and the selling price by Rs. 10, the profit percentage becomes 15%. What is the original cost price?

If the area of a square is 64 cm², what is the length of its diagonal? 
 

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?

A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less. What is the speed of the train? 
 

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?
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?
If \( \sin \theta + \cos \theta = \sqrt{2} \), what is \( \sin \theta \cos \theta \)?
What is the sum of the first 20 terms of the arithmetic sequence 3, 7, 11, …?
A pipe can fill a tank in 6 hours, and another pipe can empty it in 8 hours. If both pipes are opened together, how long will it take to fill the tank?

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

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

The number of ways to arrange 5 distinct books on a shelf is: 
 

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