List of top Quantitative Aptitude Questions asked in CAT

If ABCD is a square and BCE is an equilateral triangle, what is the measure of \( \angle DEC \)?
Instead of a metre scale, a cloth merchant uses a 120 cm scale while buying, but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20% on cash payment, what is his overall profit percentage?
If the roots of the equation \( x^2 - 2px + p^2 - 1 = 0 \) are real and distinct, what is the range of \( p \)?
In how many ways can 5 different books be arranged on a shelf if two particular books must be together?
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 \( a, b, c \) are in geometric progression, and \( a, b, 2c \) are in arithmetic progression, then what is the common ratio of the geometric progression?
A and B run a 1 km race. If A gives B a start of 50 m and still beats him by 15 seconds, and if A gives B a start of 70 m and beats him by 10 seconds, find the time taken by A to run 1 km.
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 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 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 sum of money doubles in 4 years at a certain rate of compound interest. In how many years will it become 8 times? 
 

If \( \sin \theta + \cos \theta = \sqrt{2} \), what is \( \sin \theta \cos \theta \)?
A car travels from A to B at 60 km/h and returns at 40 km/h. If the total time taken is 5 hours, what is the distance between A and B?

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? 
 

A sum of Rs. 1000 is divided among A, B, and C in the ratio 2:3:5. How much does C get? 
 

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?
The ratio of two numbers is 3:4. If their sum is 70, what is the larger number?
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 sum of Rs. 10,000 is invested at 5% per annum compound interest for 2 years. What is the total amount?

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 $2^x = 3^y = 6^z$, what is the value of $xy$ in terms of $z$?

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

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?

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?