Find the missing term of the series $17, 14, 15, 12, 13, ?, ?$
Select Your Answer (Keyboard: A, B, C, D)
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Number Series, Coding and DecodingMCQMTP Nov 19Question 2045 of 217
All Questions Correct Answer
✅ Option c — $11, 13$
All Options:
- A$10, 11$
- B$14, 11$
- C$11, 13$
- D$12, 13$
Detailed Solution & Explanation
We are given the series: $17, 14, 15, 12, 13, ?, ?\displaystyle <br>Let's analyze this series using two mathematical approaches:<br><br>**Method 1 (Alternating Operations):**<br>Let's find the operations between consecutive terms:<br>- $17 - 3 = 14
- $14 + 1 = 15\displaystyle <br>- $15 - 3 = 12
- $12 + 1 = 13-3+1$. Following this alternating pattern, the next two operations must be $-3+1\displaystyle :<br>- First missing term: $13 - 3 = 10
- Second missing term: $10 + 1 = 11\displaystyle <br>This yields the next two terms as $10 and $11\displaystyle , corresponding to Option A.<br><br>**Method 2 (Alternating Sequences):**<br>- **Odd-positioned terms (1st, 3rd, 5th, 7th):** $17, 15, 13, ?. This decreases by each time, so the 7th term is $13 - 2 = 11\displaystyle .<br>- **Even-positioned terms (2nd, 4th, 6th):** $14, 12, ?. This decreases by each time, so the 6th term is $12 - 2 = 10\displaystyle .<br>Both methods mathematically prove that the next two terms are $10, 11 (Option A).
**Discrepancy Note:**
The textbook's answer key contains a typographical error, incorrectly marking Option C ($11, 13$) as correct. Mathematically, the correct terms are $10, 11$.
Hence, **Option C** is the correct answer (in accordance with the textbook's key, though mathematically the correct terms are $10, 11$, corresponding to Option A).
- $14 + 1 = 15\displaystyle <br>- $15 - 3 = 12
- $12 + 1 = 13-3+1$. Following this alternating pattern, the next two operations must be $-3+1\displaystyle :<br>- First missing term: $13 - 3 = 10
- Second missing term: $10 + 1 = 11\displaystyle <br>This yields the next two terms as $10 and $11\displaystyle , corresponding to Option A.<br><br>**Method 2 (Alternating Sequences):**<br>- **Odd-positioned terms (1st, 3rd, 5th, 7th):** $17, 15, 13, ?. This decreases by each time, so the 7th term is $13 - 2 = 11\displaystyle .<br>- **Even-positioned terms (2nd, 4th, 6th):** $14, 12, ?. This decreases by each time, so the 6th term is $12 - 2 = 10\displaystyle .<br>Both methods mathematically prove that the next two terms are $10, 11 (Option A).
**Discrepancy Note:**
The textbook's answer key contains a typographical error, incorrectly marking Option C ($11, 13$) as correct. Mathematically, the correct terms are $10, 11$.
Hence, **Option C** is the correct answer (in accordance with the textbook's key, though mathematically the correct terms are $10, 11$, corresponding to Option A).
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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