List of top Quantitative Aptitude Questions asked in CAT

Sujith says: - Multiplying first two digits by 3 gives all ones.
- Multiplying next two digits by 6 gives all twos.
- Multiplying last two digits by 9 gives all threes.
What is the sum of digits in the number?
What is the number of positive integers less than or equal to 1000 that are divisible by neither 2 nor 5?
Rs. 6000 is invested at 7 simple interest per annum for 4 years. Find the total amount.
A bag has 5 red and 7 blue balls. Two balls are drawn without replacement. What is the probability both are red?
The sum of an infinite geometric series is 12, and the first term is 8. Find the common ratio.
Consider the curves: \[ y = 2x^3 + 3x^2 + 4, y = 3x^2 - 2x + 8 \] How many times do they intersect for \( -3 \leq x \leq 2 \)?
If $\log_2 x + \log_4 x = 3$, find $x$.
Find the number of ways to arrange 6 distinct books on a shelf if 2 specific books must be adjacent.
Some persons are standing in a circle, all facing the center. Each pair not adjacent sings a 3-minute song, one after another. Total time = 1 hour. How many persons are there?
A mixture has milk and water in the ratio 4:1. If 5 liters of water is added, the ratio becomes 2:1. Find the original milk quantity.
In a seating arrangement, 5 people (A, B, C, D, E) sit in a row. A and B must sit together, and C cannot sit at the ends. How many arrangements are possible?
The HCF of two numbers is 12, and their LCM is 144. If one number is 48, find the other.
A number when divided by 4, 5 and 6 leaves remainders 2, 3 and 4 respectively. What is the smallest such number?
Find the distance between points (2, 3) and (5, 7).
Let P, Q, S, R, T, U and V represent the seven distinct digits from 0 to 6, not necessarily in that order. If PQ and RS are both two-digit numbers adding up to the three-digit number TUV, find the value of V.
In how many ways can 5 distinct letters be arranged in a circle?
A rectangle has a perimeter of 50 cm and an area of 150 cm². Find its length.
Find the roots of $x^2 - 8x + 15 = 0$.
If each X-Ray occupies 30MB and a new technology reduces space by 60%, what is the total magnetic media memory required to store all the X-Rays in the year 2000? (1MB = \(10^6\) Bytes)
The average of 5 numbers is 20. If a number 10 is removed, what is the new average?
In a bag there are a total of 150 coins in three denominations – Re.1, ₹2 and ₹5 – with at least one coin of each denomination. The total value of Re.1 coins is at least 50% of the total value of the coins. There are 23 ₹5 coins and the total value of ₹2 coins is at least 3% of the total value of coins. Find the number of ₹2 coins in the bag.
The 4th term of a geometric progression is 8, and the 7th term is 64. Find the 10th term.
If $x^2 - 7x + 12 = 0$, what is the value of $x^3 - 4x^2 + 3x$?
If \( g = 9 \), then what is the minimum possible number of times for which the weighing machine is to be used?
There are five cards in a row with numbers from 1 to 100. Each adjacent pair must not differ by a multiple of 4. The remainder when each number is divided by 4 is written on a sixth card, in that order. How many different sequences can be written on the sixth card?