CAT 2025 Number System Question (Hard)

Question

Suppose a , b , c are three distinct natural numbers, such that 3 a c 8 a b . Then, the smallest possible value of 3 a 2 b c is

Accepted Answer

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 corr

CAT 2025

Quantitative

Number System

Hard

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

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