List of top Quantitative Aptitude Questions asked in CAT

\( p \) 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 certain number written in a certain base is 144. Which of the following is always true?
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 \( \left( \beta + \frac{\beta}{\alpha} \right) \).
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:
Which of the terms \( 2^{1/3}, 3^{1/4}, 4^{1/6}, 6^{1/8}, 10^{1/12} \) is the largest?
What is the sum of all the 2-digit numbers which leave a remainder of 6 when divided by 8?
In the figure below, \( \angle MON = \angle MPO = \angle NQO = 90^\circ \), \( OQ \) is the bisector of \( \angle MON \), and \( QN = 10 \), \( OR = 40/\sqrt{7} \). Find \( OP \).
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?
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?
Consider a sequence \( S \) whose \( n \)th term \( T_n \) is defined as \( T_n = 1 + \frac{3}{n} \), where \( n = 1, 2, \ldots \). Find the product of all the consecutive terms of \( S \) starting from the 4th term to the 60th term.
If 5x = 25, what is x?
If the cost price of an item is Rs. 200 and it is sold at a 25% profit, what is the selling price?
A pipe fills a tank in 6 hours. Another pipe fills it in 8 hours. How long to fill the tank together?
If x2 − 3x + 2 = 0, what is the product of the roots?
What is the perimeter of a square with side 7 cm?
A man works 8 hours a day for 5 days to earn Rs. 4,000. What is his hourly wage?
If x2 + 4x + 4 = 0, what is x?
A sum of Rs. 8,000 is lent at 8% simple interest for 3 years. What is the total amount?
If 2x = 16, what is x?
What is the area of a triangle with base 10 cm and height 8 cm?
A sum of Rs. 5,000 is invested at 10% compound interest annually for 2 years. What is the total amount?
What is the value of √169?