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CAT 2025 Number System — Previous Year Question

Year

CAT 2025

Section

Quantitative

Topic

Number System

Difficulty

Medium

Question

Slot-1

If a, b, and c are all positive integers, with 4a > b, then which of the following conditions is BOTH NECESSARY AND SUFFICIENT for the expression 3a213ab492b+c3\sqrt[3]{3^a \cdot 21^{3a-b} \cdot 49^{2b+c}} to be a positive integer?

a − b = c

a − b + 2c is divisible by 3

a, b, and c are divisible by 3

a − b and c are divisible by 3

None of the other conditions is both necessary and sufficient

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