CAT 2025 Surds and Indices Question (Hard)

Question

If , where and are natural numbers, then equals

Accepted Answer

12 12x times 4 24x 12 times 5 2y 8 4z times 20 12x times 243 3x-6 On rewriting after prime factorisation, we get, times 3 12x times 2 48x 24 times 5 2y 2 12z times times 5 12x times 3 15x-30 Since LHS RHS, the corresponding powers must be equal. We have, Powers of 3 12x 15x-30 or x 10, and Powers of

CAT 2025

Quantitative

Surds and Indices

Hard

If $12^{12x} \times 4^{24x+12} \times 5^{2y} = 8^{4z} \times 20^{12x} \times 243^{3x-6}$ , where $x, y$ and $z$ are natural numbers, then $x+y+z$ equals

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