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

Options

A932\displaystyle \frac{9}{32}
B1017\displaystyle \frac{10}{17}
C1134\displaystyle \frac{11}{34}
D1235\displaystyle \frac{12}{35}
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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 \frac{1}{2}, \frac{3}{4}, \frac{5}{7}, \frac{7}{11}, \frac{2}{4}, \frac{4}{8}, \frac{16}{?}
Let's analyze the sequence as consisting of two independent, interleaved patterns:

**Pattern 1:** 12,34,57,711,…\displaystyle \frac{1}{2}, \frac{3}{4}, \frac{5}{7}, \frac{7}{11}, \dots
- **Numerators:** 1,3,5,7,…\displaystyle 1, 3, 5, 7, \dots (consecutive odd integers, increasing by +2\displaystyle +2). The next numerator is 7+2=9\displaystyle 7 + 2 = 9.
- **Denominators:** 2,4,7,11,…\displaystyle 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\displaystyle 11 - 7 = 4.
- The differences increase by 1\displaystyle 1 each time. The next difference is +5\displaystyle +5.
- The next denominator is 11+5=16\displaystyle 11 + 5 = 16.
- Thus, the next term of this pattern is 916\displaystyle \frac{9}{16}.

**Pattern 2:** 24,48,16?\displaystyle \frac{2}{4}, \frac{4}{8}, \frac{16}{?}
- We notice that each fraction simplifies to 12\displaystyle \frac{1}{2}:
- 24=12\displaystyle \frac{2}{4} = \frac{1}{2}
- 48=12\displaystyle \frac{4}{8} = \frac{1}{2}
- For the last term 16?\displaystyle \frac{16}{?} to equal 12\displaystyle \frac{1}{2}, the denominator must be 32\displaystyle 32 (?=32\displaystyle ? = 32).

**Discrepancy Note:**
The textbook's options are: Option A: 932\displaystyle \text{Option A: } \frac{9}{32}, Option B: 1017\displaystyle \text{Option B: } \frac{10}{17}, Option C: 1134\displaystyle \text{Option C: } \frac{11}{34}, Option D: 1235\displaystyle \text{Option D: } \frac{12}{35}.
The answer key lists Option A as correct. This is a composite error in the textbook where the next numerator from Pattern 1 (9\displaystyle 9) and the missing denominator from Pattern 2 (32\displaystyle 32) were merged into a single term 932\displaystyle \frac{9}{32}.
Hence, **Option A** is the correct answer.

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