Applyo - College Application Platform

CAT 2025 Slot 2 QA Question & Solution

Number SystemsHard

Question

Suppose a,b,c are three distinct natural numbers, such that $3ac=8(a+b)$. Then, the smallest possible value of $3a+2b+c$ is

Solution

Our task is to minimise $$3a+2b+c$$.

Here, the coefficient for $$c$$ is the minimum. 

$$3ac=8(a+b)$$

We know that a, b, and c are natural numbers. So, the product $$ac$$ should definately be a multiple of 8.

Case 1: a = 1, c = 8 and b = 2 $$\Rightarrow$$ 3a+2b+c = 15

Case 2: a = 2, c = 4 and b = 1 $$\Rightarrow$$ 3a+2b+c = 12

So, 12 is the correct answer.