Find next number of the series $7, 23, 47, 119, 167$
Select Your Answer (Keyboard: A, B, C, D)
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Number Series, Coding and DecodingMCQMTP Dec 2023 Series IQuestion 2073 of 217
All Questions Correct Answer
✅ Option c — $287$
All Options:
- A$211$
- B$223$
- C$287$
- D$319$
Detailed Solution & Explanation
To find the next number in the series $7, 23, 47, 119, 167, ?T_nnp_n$ represents the sequence of consecutive prime numbers starting from $3\displaystyle ($3, 5, 7, 11, 13, \dots). Note that is omitted because it is a composite number, not a prime number.
Let us compute the terms to verify this pattern:
- 1st term ():
- 2nd term ():
- 3rd term ():
- 4th term (): $11^2 - 2 = 121 - 2 = 119p_5 = 13\displaystyle ): $13^2 - 2 = 169 - 2 = 167
Following this logical progression, the next prime number after $13\displaystyle is $17. Therefore, the 6th term must be:
- 6th term (): $17^2 - 2 = 289 - 2 = 287\displaystyle <br><br>This mathematical proof uniquely demonstrates that the next term in the series is **$287**, which corresponds to **Option C**.
*Note on Answer Key Discrepancy:* The textbook/exam answer key lists **Option A** ($211$) as the correct answer. However, $211$ does not correspond to any logical progression or prime square pattern, whereas $287$ fits the consecutive prime-squared minus two formula perfectly. This is a clear typographical error in the official answer key, and the correct option is **Option C**.
Hence, **Option C** is the correct answer.
Let us compute the terms to verify this pattern:
- 1st term ():
- 2nd term ():
- 3rd term ():
- 4th term (): $11^2 - 2 = 121 - 2 = 119p_5 = 13\displaystyle ): $13^2 - 2 = 169 - 2 = 167
Following this logical progression, the next prime number after $13\displaystyle is $17. Therefore, the 6th term must be:
- 6th term (): $17^2 - 2 = 289 - 2 = 287\displaystyle <br><br>This mathematical proof uniquely demonstrates that the next term in the series is **$287**, which corresponds to **Option C**.
*Note on Answer Key Discrepancy:* The textbook/exam answer key lists **Option A** ($211$) as the correct answer. However, $211$ does not correspond to any logical progression or prime square pattern, whereas $287$ fits the consecutive prime-squared minus two formula perfectly. This is a clear typographical error in the official answer key, and the correct option is **Option C**.
Hence, **Option C** is the correct answer.
About This Chapter: Number Series, Coding and Decoding
Paper
Paper 3: Quantitative Aptitude
Weightage
5 Marks
Key Topics
Number series, Coding & Decoding, Odd man out
This chapter covers Number series, Coding & Decoding, Odd man out and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.
View Official ICAI SyllabusExam Strategy Tip
This topic carries 5 Marks weightage. Focus on understanding core concepts rather than memorizing.
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