Question 67

Logical Reasoning Odd One Out Medium

Find the odd number in the series : $$2,9,28,65,126,216,344, \ldots $$

(A) 28
(B) 65
(C) 126
(D) 216
✓ Correct Answer: Option D Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

The odd number in the series is 216.


Uncovering the Pattern

The pattern for this series is n3 + 1, where 'n' is the term's position in the sequence, starting with n=1.

Let's check each number against the rule:

  • 13 + 1 = 1 + 1 = 2 (Correct)
  • 23 + 1 = 8 + 1 = 9 (Correct)
  • 33 + 1 = 27 + 1 = 28 (Correct)
  • 43 + 1 = 64 + 1 = 65 (Correct)
  • 53 + 1 = 125 + 1 = 126 (Correct)
  • 73 + 1 = 343 + 1 = 344 (Correct)

The sixth number in the series is the one that breaks the pattern:

  • The correct number should be: 63 + 1 = 216 + 1 = 217.
  • The number given in the series is 216.

Therefore, 216 is the odd number in the series.

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