List of top Quantitative Aptitude Questions asked in CAT

What is the value of $\sin 30^\circ + \cos 60^\circ$? 
 

A number when divided by 7 leaves a remainder of 4. What is the remainder when its square is divided by 7? 
 

The HCF of two numbers is 12, and their LCM is 144. If one number is 36, what is the other? 
 

A car travels at 60 km/h for half the distance and 80 km/h for the other half. What is the average speed for the entire journey? 
 

What is the number of solutions to $|x - 2| = |x - 4|$? 
 

A pipe can fill a tank in 6 hours, and another pipe can empty it in 8 hours. If both are open, how long will it take to fill the tank? 
 

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

A man invests Rs. 5000 at 6% simple interest per annum. How much interest will he earn in 3 years? 
 

What is the value of $\sqrt{50 + \sqrt{50 + \sqrt{50 + \ldots}}}$? 
 

A number is divisible by 3 and 5. What is the smallest such number greater than 100? 
 

What is the sum of digits of $2^{10}$? 
 

A boat travels 24 km upstream in 6 hours and 30 km downstream in 5 hours. What is the speed of the boat in still water? 
 

What is the value of x if:

2x · 3x+1 = 3888

In how many ways can 6 people be seated around a circular table? 
 

What is the probability that a leap year has 53 Sundays? 
 

If \[ x = \frac{x}{y+z}, \quad y = \frac{y}{z+x}, \quad z = \frac{z}{x+y} \] then which of the following statements is/are true?
If \( \log_x(a - b) - \log_x(a + b) = \log_x\left(\frac{b}{a}\right) \), find \( \frac{a^2 + b^2}{b^2 + a^2} \)
The side of an equilateral triangle is 10 cm long. By drawing parallels to all its sides, the distance between any two parallel lines being the same, the triangle is divided into smaller equilateral triangles, each of which has sides of length 1 cm. How many such small triangles are formed?
Letters of the word “ATTRACT” are written on cards and kept on a table. Manish lifts three cards at a time, writes all possible combinations of the three letters on a piece of paper, and then replaces the cards. He is to strike out all the words which look the same when seen in a mirror. How many words is he left with?
A student is asked to form numbers between 3000 and 9000 with digits 2, 3, 5, 7 and 9. If no digit is to be repeated, in how many ways can the student do so?
A solid sphere of radius 12 inches is melted and cast into a right circular cone whose base diameter is \( \sqrt{2} \) times its slant height. If the radius of the sphere and the cone are the same, how many such cones can be made and how much material is left out?
A car \( A \) starts from a point \( P \) towards another point \( Q \). Another car \( B \) starts (also from \( P \)) 1 hour after the first car \( A \), and overtakes it after covering 30% of the distance \( PQ \). After that, the cars continue. On reaching \( Q \), car \( B \) reverses and meets car \( A \), after covering \( 2\frac{1}{3} \) of the distance \( QP \). Find the time taken by car \( B \) to cover the distance \( PQ \) (in hours).
A vessel has a milk solution in which milk and water are in the ratio 4:1. By addition of water to it, milk solution with milk and water in the ratio 4:3 was formed. On replacing 14 L of this solution with pure milk, the ratio of milk and water changed to 5:3. What is the volume of the water added?
In the figure, \( OABC \) is a parallelogram. The area of the parallelogram is 21. Coordinates are: \( O = (0,0) \), \( A = (7,0) \), and point \( C \) lies on line \( x = 3 \). Find coordinates of \( B \).
Find the complete set of values that satisfy the relations \[ |x - 3|<2 \quad \text{and} \quad |x| - 2|<3 \]