Number Series, Coding, Odd Man OutPYQ June 19Question 2011 of 217
All Questions

Find the next number in the series: 7,23,47,119,167\displaystyle 7, 23, 47, 119, 167?

Options

A211
B223
C287
D319
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Correct Answer

✅ Option c — 287

All Options:

  • A211
  • B223
  • C287
  • D319

Detailed Solution & Explanation

We are given the series: 7,23,47,119,167,…\displaystyle 7, 23, 47, 119, 167, \dots
Let's express each term in relation to squares of numbers:
- 7=32−2\displaystyle 7 = 3^2 - 2
- 23=52−2\displaystyle 23 = 5^2 - 2
- 47=72−2\displaystyle 47 = 7^2 - 2
- 119=112−2\displaystyle 119 = 11^2 - 2
- 167=132−2\displaystyle 167 = 13^2 - 2
We notice that the bases used are the prime numbers: 3,5,7,11,13\displaystyle 3, 5, 7, 11, 13.
Following the prime number sequence (3,5,7,11,13,17,19,…\displaystyle 3, 5, 7, 11, 13, 17, 19, \dots), the next prime number is 17\displaystyle 17.
Thus, the next term of the series should be the square of the next prime number minus 2\displaystyle 2:
172−2=289−2=28717^2 - 2 = 289 - 2 = 287
Hence, **Option C** is the correct answer.

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