Multiple choice

$In each of the following questions, two equations I and II are given. You have to solve them and-(I) \ p^{3} – 2695 = 11129 (II) \ q^{3} – 6329 – 5838 = 0$ Give answer-

  1. If p > q

  2. If p ≥ q

  3. If p < q

  4. If p ≤ q

  5. If p = q or relationship can not be established.

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Equation I: p³ - 2695 = 11129, so p³ = 11129 + 2695 = 13824. Since 18³ = 18 × 18 × 18 = 5832 (that's not it), let me calculate: 20³ = 8000, 24³ = 13824 (since 24 × 24 = 576, 576 × 24 = 13824). So p = 24. Equation II: q³ - 6329 - 5838 = 0, so q³ = 6329 + 5838 = 12167. Since 23³ = 12167 (23 × 23 = 529, 529 × 23 = 12167), so q = 23. Comparing: p = 24 and q = 23, therefore p > q. The answer is A.