Question

If 4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴ is divisible by x, then find the value of x.
1. 3
2. 10
3. 11
4. 13

Answer 1

Correct Answer - Option 2 : 10

Given:
Number = 461 + 462 + 463 + 464

Concept used:
ax × ay = ax + y
ax/ay = ax – y

Calculation:
461 + 462 + 463 + 464
⇒ 4⁶¹ + 4⁶¹ × 4 + 4⁶¹ × 4² + 4⁶¹ × 4³
⇒ 4⁶¹(1 + 4 + 16 + 64)
⇒ 4⁶¹ × 85
⇒ 4⁶⁰ × 4 × 85
⇒ 4⁶⁰ × 340, which is clearly divisible by 10 (Option 2).
∴ The correct answer is 10.