461 + 462 + 463 + 464 is divisible by

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4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴ is divisible by

1. 3
2. 10
3. 11
4. 13

Correct Option: D

4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴
⇒ 4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴ = 4⁶¹ (1 + 4 + 4² + 4³)
⇒ 4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴ = 4⁶¹ (1 + 4 + 16 + 64)
= 4⁶¹ × 85
Which is a multiple of 10.