CAT 2023

Slot 2

QA

All Questions

Let both the series $a_{1},a_{2},a_{3}$... and $b_{1},b_{2},b_{3}$... be in arithmetic progression such that the common differences of both the series are prime numbers. If $a_{5}=b_{9},a_{19}=b_{19}$ and $b_{2}=0$, then $a_{11}$ equals

For any natural numbers m, n, and k, such that k divides both $m+2n$ and $3m+4n$, k must be a common divisor of

Let $a_{n}$ and $b_{n}$ be two sequences such that $a_{n}=13+6(n-1)$ and $b_{n}=15+7(n-1)$ for all natural numbers n. Then, the largest three digit integer that is common to both these sequences, is

The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000. Then, the price of the original precious stone is

Let a, b, m and n be natural numbers such that $a>1$ and $b>1$. If $a^{m}b^{n}=144^{145}$, then the largest possible value of $n-m$ is

The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is

A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, is

Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. He repays Rs 10320 at the end of the first year and closes the loan by paying the outstanding amount at the end of the third year. Then, the total interest, in rupees, paid over the three years is nearest to

Ravi is driving at a speed of 40 km/h on a road. Vijay is 54 meters behind Ravi and driving in the same direction as Ravi. Ashok is driving along the same road from the opposite direction at a speed of 50 km/h and is 225 meters away from Ravi. The speed, in km/h, at which Vijay should drive so that all the three cross each other at the same time, is

Pipes A and C are fill pipes while Pipe B is a drain pipe of a tank. Pipe B empties the full tank in one hour less than the time taken by Pipe A to fill the empty tank. When pipes A, B and C are turned on together, the empty tank is filled in two hours. If pipes B and C are turned on together when the tank is empty and Pipe B is turned off after one hour, then Pipe C takes another one hour and 15 minutes to fill the remaining tank. If Pipe A can fill the empty tank in less than five hours, th...

If a certain amount of money is divided equally among n persons, each one receives Rs 352. However, if two persons receive Rs 506 each and the remaining amount is divided equally among the other persons, each of them receive less than or equal to Rs 330. Then, the maximum possible value of n is

If $p^{2}+q^{2}-29=2pq-20=52-2pq$, then the difference between the maximum and minimum possible value of $(p^{3}-q^{3})$