If 1³ + 2³ + 3³ + ......... + x³ = 441, Find the value of x:

Question

If 1³ + 2³ + 3³ + ......... + x³ = 441,

Find the value of x:

1. A. 21
2. B. 6 (Correct answer)
3. C. 20
4. D. 7

Correct Answer

Option B — 6

Detailed Solution & Explanation

The correct answer is 6.

Key Points

• Use the identity 1³ + 2³ + … + x³ = [x(x + 1)/2]².
• So [x(x + 1)/2]² = 441, giving x(x + 1)/2 = √441 = 21.
• Then x(x + 1) = 42, and since 6 × 7 = 42, we get x = 6.

Additional Information

• Check directly: 1 + 8 + 27 + 64 + 125 + 216 = 441 ✓
• The distractor 21 is the value of the *sum* 1 + 2 + … + x, not of x itself — a step short of the answer.

*Ministry of Papers worked solution. The Commission has not yet published the official key for this paper; this answer will be reconciled with it on release.*