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CDS 2024 · PYQ · Number System / Divisibility · medium

The expression 555⁷⁷⁷ + 777⁵⁵⁵ is divisible by which of the following ? 1. 2 2. 3 3. 37 Select the correct answer using the code given below :

  1. A.1 and 2 only
  2. B.2 and 3 only
  3. C.1 and 3 only
  4. D.1, 2 and 3✓ Correct

Explanation

555 = 3 × 5 × 37 and 777 = 3 × 7 × 37. Both are divisible by 3 and 37. 555⁷⁷⁷ is odd (5 raised to odd power times odd) and 777⁵⁵⁵ is odd. Odd + odd = even, so divisible by 2. Both terms are divisible by 3, so sum divisible by 3. Both divisible by 37, so sum divisible by 37. Hence divisible by 2, 3, and 37.
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