List of top Quantitative Aptitude Questions asked in CAT

There are 12 towns grouped into four zones with three towns per zone. It is intended to connect the towns with telephone lines such that every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required?
In how many ways can 5 different books be arranged on a shelf if two particular books must be together?
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?
The figure shows a circle of diameter AB and radius 6.5 cm. If chord CA is 5 cm long, find the area of triangle ∆ABC.
circle
A bag contains 3 red, 4 white, and 5 blue balls. Two balls are drawn at random. What is the probability that both are of the same color?
A man can row at 5 km/h in still water. If the river flows at 1 km/h and it takes him 1 hour to row to a place and return, what is the distance he rows to the place?
Two liquids A and B are in the ratio 5 : 1 in container 1 and 1 : 3 in container 2. In what ratio should the contents of the two containers be mixed so as to obtain a mixture of A and B in the ratio 1 : 1?
A car travels from A to B at 60 km/h and returns at 40 km/h. What is the average speed for the entire journey?
If \( \sin \theta + \cos \theta = \sqrt{2} \), then what is the value of \( \theta \) (in degrees)?
The HCF of two numbers is 12, and their LCM is 144. If one number is 36, what is the other number?
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?
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 probability of getting a sum of 7 when two dice are rolled? 
 

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 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? 
 

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

A train travels 360 km in 4 hours. What is its speed in km/h?

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

The sum of the first $n$ terms of an arithmetic progression is $S_n = 3n^2 + 2n$. What is the 5th term?
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 \( 2x + 3y = 12 \) and \( x - y = 1 \), what is the value of \( x \)?

A sum of money doubles in 4 years at a certain rate of compound interest. In how many years will it become 8 times? 
 

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

The area of a circle is $154$ cm². What is the circumference of the circle? 
 

A man invests Rs. 5000 at 5% simple interest per annum. How much interest will he earn after 3 years?