List of top Quantitative Aptitude Questions asked in CAT

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?
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 \( B \).
If \( ax^2 + bx + c = 0 \) and \( 2a, b, 2c \) are in arithmetic progression, then which of the following are the roots of the equation?
A certain number written in a certain base is 144. Which of the following is always true?
\( p \) is a prime and \( m \) is a positive integer. How many solutions exist for the equation \[ p^5 - p = (m^2 + m + 6)(p - 1)? \]
A rectangle is drawn such that none of its sides has length greater than ‘\( a \)’. All lengths less than ‘\( a \)’ are equally likely. The chance that the rectangle has its diagonal greater than ‘\( a \)’ (in terms of %) is:
If \( (a^2 + b^2), (b^2 + c^2) \) and \( (a^2 + c^2) \) are in geometric progression, which of the following holds true?
If \( x \) is a real number and \( \lfloor x \rfloor \) is the greatest integer \( \leq x \), then \[ 3\lfloor x \rfloor + 2 - \lfloor x \rfloor = 0 \] Will the above equation have any real root?
If \( \alpha \) and \( \beta \) are the roots of the quadratic equation \[ x^2 - 10x + 15 = 0, \] then find the quadratic equation whose roots are \( \left( \alpha + \frac{\alpha}{\beta} \right) \) and \( \left( \beta + \frac{\beta}{\alpha} \right) \).
Find the remainder when \( 2^{1040} \) is divided by 131.
Let \( P = \{2, 3, 4, \ldots, 100\} \) and \( Q = \{101, 102, 103, \ldots, 200\} \). How many elements of \( Q \) are there such that they do not have any element of \( P \) as a factor?
What is the sum of all the 2-digit numbers which leave a remainder of 6 when divided by 8?
If the roots of the equation \[ (a^2 + b^2)x^2 + 2(b^2 + c^2)x + (b^2 + c^2) = 0 \] are real, which of the following must hold true?
A train travels 240 km in 4 hours. What is its speed in km/h?
The values of the numbers \(2^{2004}\) and \(5^{2004}\) are written one after another. How many digits are there in all?
If a = 2b and b = 3c, what is the ratio a:b:c?
A man works 8 hours a day for 5 days to earn Rs. 4,000. What is his hourly wage?
Vaibhav wrote a certain number of positive prime numbers on a piece of paper. Vikram wrote down the product of all the possible triplets among those numbers. For every pair of numbers written by Vikram, Vishal wrote down the corresponding GCD. If 90 of the numbers written by Vishal were prime, how many numbers did Vaibhav write?
If the concentration of petrol in the second tank is 75% and the cost price of kerosene is half that of petrol, then what is Govind Lal's net profit percentage on selling the contents of the second tank given that he claims to sell the petrol at a profit of 25%?
If the sum of three consecutive integers is 24, what is the middle integer?
A sum of Rs. 12,000 is lent at 6% simple interest for 4 years. What is the interest?
A car travels 300 km at an average speed of 60 km/h. How long does it take?
A sum of Rs. 5,000 is invested at 10% compound interest annually for 2 years. What is the total amount?
A man invests Rs. 10,000 at 5% simple interest per annum. What is the interest earned after 2 years?