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CDS 2026 · PYQ · Number System / Divisibility · medium

27²⁷ - 9⁴⁰ - 3⁷⁹ is divisible by how many natural numbers less than 10?

  1. A.1
  2. B.2
  3. C.3
  4. D.More than 3✓ Correct

Explanation

27²⁷ - 9⁴⁰ - 3⁷⁹ = 3⁸¹ - 3⁸⁰ - 3⁷⁹ = 3⁷⁹(3² - 3 - 1) = 3⁷⁹ × 5. So the expression equals 3⁷⁹ × 5. Natural numbers less than 10 that divide this: 1, 3, 5, 9 (=3²), and 15 is >10 not relevant. The divisors less than 10 are 1, 3, 5, 9 — that's 4 values, which is more than 3.
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