Number Series, Coding, Odd Man OutPYQ Sep 24Question 2174 of 217
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Find the odd man out from the following series : 7,23,47,119,171,287\displaystyle 7, 23, 47, 119, 171, 287.

Options

A171
B119
C287
D7
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Correct Answer

✅ Option a — 171

All Options:

  • A171
  • B119
  • C287
  • D7

Detailed Solution & Explanation

Let's examine the mathematical pattern of the terms in the series: 7,23,47,119,171,287\displaystyle 7, 23, 47, 119, 171, 287.
Each correct term follows the pattern p2−2\displaystyle p^2 - 2, where p\displaystyle p is a consecutive prime number starting from 3\displaystyle 3:
- For p=3\displaystyle p = 3: 32−2=7\displaystyle 3^2 - 2 = 7
- For p=5\displaystyle p = 5: 52−2=23\displaystyle 5^2 - 2 = 23
- For p=7\displaystyle p = 7: 72−2=47\displaystyle 7^2 - 2 = 47
- For p=11\displaystyle p = 11: 112−2=119\displaystyle 11^2 - 2 = 119
- For p=13\displaystyle p = 13: 132−2=167\displaystyle 13^2 - 2 = 167 (the series lists 171\displaystyle 171, which is incorrect)
- For p=17\displaystyle p = 17: 172−2=287\displaystyle 17^2 - 2 = 287

The pattern of p2−2\displaystyle p^2 - 2 using consecutive prime numbers holds perfectly for all terms except 171\displaystyle 171, which should be 167\displaystyle 167. Therefore, 171\displaystyle 171 is the odd man out.

Hence, **Option A** is the correct answer.

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