Which of the following numbers will completely divide 412 + 413 + 414 + 415 ?

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SSC Selection Post 2024 (Higher Secondary Level) Official Paper (Held On: 25 Jun, 2024 Shift 4)
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  1. 17
  2. 11
  3. 3
  4. 7

Answer (Detailed Solution Below)

Option 1 : 17
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Detailed Solution

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Given:

 412 + 413 + 414 + 415

Formula used:

Factor out the common term 412 from the expression.

Calculation:

412 + 413 + 414 + 415

⇒ 412 (1 + 4 + 42 + 43)

⇒ 412 (1 + 4 + 16 + 64)

⇒ 412 (85)

Now, we need to check which of the given options divides 85 completely.

85 = 5 × 17

Therefore, the number that completely divides 85 is 17.

∴ The correct answer is option (1).

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