Number Series, Coding and DecodingMCQPYQ Jan 21Question 2018 of 217
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Find the next term 12,34,57,711,24,48,16?\displaystyle 12\displaystyle \frac{1}{2}, 34\displaystyle \frac{3}{4}, 57\displaystyle \frac{5}{7}, 711\displaystyle \frac{7}{11}, 24\displaystyle \frac{2}{4}, 48\displaystyle \frac{4}{8}, 16?\displaystyle \frac{16}{?}.

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

✅ Option a — 932\displaystyle \frac{9}{32}

All Options:

  • A932\displaystyle \frac{9}{32}
  • B1017\displaystyle \frac{10}{17}
  • C1134\displaystyle \frac{11}{34}
  • D1235\displaystyle \frac{12}{35}

Detailed Solution & Explanation

We are given the sequence of fractions: 12,34,57,711,24,48,16?\displaystyle 12\displaystyle \frac{1}{2}, 34\displaystyle \frac{3}{4}, 57\displaystyle \frac{5}{7}, 711\displaystyle \frac{7}{11}, 24\displaystyle \frac{2}{4}, 48\displaystyle \frac{4}{8}, 16?\displaystyle \frac{16}{?}
Let's analyze the sequence as consisting of two independent, interleaved patterns:

**Pattern 1:** 12,34,57,711,…\displaystyle 12\displaystyle \frac{1}{2}, 34\displaystyle \frac{3}{4}, 57\displaystyle \frac{5}{7}, 711\displaystyle \frac{7}{11}, \dots
- **Numerators:** $1, 3, 5, 7, \dots$ (consecutive odd integers, increasing by $+2$). The next numerator is $7 + 2 = 9\displaystyle .<br>- **Denominators:** &#36;2, 4, 7, 11, \dots
- Differences between denominators: 4−2=2\displaystyle 4 - 2 = 2, 7−4=3\displaystyle 7 - 4 = 3, $11 - 7 = 4.<br>−Thedifferencesincreaseby\displaystyle .<br>- The differences increase by1$ each time. The next difference is $+5\displaystyle .<br>- The next denominator is &#36;11 + 5 = 16.
- Thus, the next term of this pattern is 916\displaystyle 916\displaystyle \frac{9}{16}.

**Pattern 2:** 24,48,16?\displaystyle 24\displaystyle \frac{2}{4}, 48\displaystyle \frac{4}{8}, 16?\displaystyle \frac{16}{?}
- We notice that each fraction simplifies to 12\displaystyle 12\displaystyle \frac{1}{2}:
- 24=12\displaystyle 24=12\displaystyle \frac{2}{4} = \frac{1}{2}
- 48=12\displaystyle 48=12\displaystyle \frac{4}{8} = \frac{1}{2}
- For the last term 16?\displaystyle 16?\displaystyle \frac{16}{?} to equal 12\displaystyle 12\displaystyle \frac{1}{2}, the denominator must be $32(\displaystyle (? = 32).<br><br>∗∗DiscrepancyNote:∗∗<br>Thetextbook′soptionsare:\displaystyle ).<br><br>**Discrepancy Note:**<br>The textbook's options are:Option A: \displaystyle \text{Option A: } 932<span\displaystyle \frac{9}{32}<span class="katex">,\displaystyle ,Option B: \displaystyle \text{Option B: } 1017<span\displaystyle \frac{10}{17}<span class="katex">,\displaystyle ,Option C: \displaystyle \text{Option C: } 1134<span\displaystyle \frac{11}{34}<span class="katex">,\displaystyle ,Option D: \displaystyle \text{Option D: } 1235<span\displaystyle \frac{12}{35}<span class="katex">.<br>TheanswerkeylistsOptionAascorrect.ThisisacompositeerrorinthetextbookwherethenextnumeratorfromPattern1(\displaystyle .<br>The answer key lists Option A as correct. This is a composite error in the textbook where the next numerator from Pattern 1 (9$) and the missing denominator from Pattern 2 ($32$) were merged into a single term 932\displaystyle 932\displaystyle \frac{9}{32}.
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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