Number Series, Coding and DecodingMCQPYQ Dec 22Question 2029 of 217
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Find the missing number in the following series? $3, 5, 5, 19, 7, 41, 9, ?, 11, 109$

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option a — 71

All Options:

  • A71
  • B61
  • C69
  • D79

Detailed Solution & Explanation

We are given the series: $3, 5, 5, 19, 7, 41, 9, ?, 11, 109\displaystyle <br>Let's split this series into two alternating sequences:<br>1. **Odd-positioned terms (1st, 3rd, 5th, 7th, 9th):**<br>- &#36;3, 5, 7, 9, 11
- Pattern: consecutive odd numbers starting from 3\displaystyle 3 (common difference +2\displaystyle +2).
2. **Even-positioned terms (2nd, 4th, 6th, 8th, 10th):**
- $5, 19, 41, ?, 109\displaystyle <br>- Let's compute the differences between these consecutive terms:<br>- &#36;19 - 5 = 14
- $41 - 19 = 22<br>−Noticethatthedifferencesincreaseby\displaystyle <br>- Notice that the differences increase by8\displaystyle each time (&#36;14 + 8 = 22).
- The next difference should be $22 + 8 = 30\displaystyle .<br>- The missing term (at the 8th position) is:<br><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mn>41</mn><mo>+</mo><mn>30</mn><mo>=</mo><mn>71</mn></mrow><annotation encoding="application/x-tex">41 + 30 = 71</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">41</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">30</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">71</span></span></span></span></span><br>- Let's check the next term in the sequence using a difference of &#36;30 + 8 = 38:
71+38=10971 + 38 = 109
This matches the 10th term perfectly!
Hence, **Option A** 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 Syllabus

Exam Strategy Tip

This topic carries 5 Marks weightage. Focus on understanding core concepts rather than memorizing.

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