CAT 2024 Slot 3 Breakup G Strategy

Indices + Logs

If 3^a = 4, 4^b = 5, 5^c = 6, 6^d = 7, 7^e = 8, and 8^f = 9, then what is the value of abcdef?

Functions + Quadratic

For any non-zero real x, let f(x) + 2 f(1/x) = 3x. Find the sum of all possible values of x for which f(x) = 3.

Average Problem

The average of three distinct real numbers is 28. If the smallest number is increased by 7 and the largest number is reduced by 10, the order of the numbers remains unchanged, and the new arithmetic mean becomes 2 more than the middle number, while the difference between the largest and the smallest numbers becomes 64. Then, the largest number in the original set of three numbers is _____

Gopi and Ravi Profit

Gopi marks a price on a product in order to make 20% profit. Ravi gets 10% discount on this marked price, and thus saves Rs 15. Then, the profit, in rupees, made by Gopi by selling the product to Ravi is:

System of Equations

For some constant real numbers p, k and a, consider the system of linear equations: px − 4y = 2 and 3x + ky = a. A necessary condition for the system to have no solution for (x,y) is:

Milk and Water

A 300 litre container. Water x litres, rest milk. Remove 2x litres solution, refill water. Final solution 72% milk. Find x.

Rajesh & Vimal Land

Rajesh owns 20 hectares, Vimal owns 30 hectares with wheat and mustard in 5:3 ratio. Total wheat:mustard is 11:9. Find Rajesh's ratio.

Aman Bank Investment

Aman invests Rs 4000 in a bank at a certain rate of interest, compounded annually. If the ratio of the value of the investment after 3 years to the value after 5 years is 25:36, then the minimum number of years required for the value to exceed Rs 20000 is _____