Number Series, Coding, Odd Man OutMTP May 18Question 2040 of 217
All Questions

5,7,11,?,35,67\displaystyle 5, 7, 11, ?, 35, 67

Options

A23
B28
C30
D19
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Correct Answer

✅ Option c — 30

All Options:

  • A23
  • B28
  • C30
  • D19

Detailed Solution & Explanation

We are given the series: 5,7,11,?,35,67\displaystyle 5, 7, 11, ?, 35, 67
Let's compute the differences between consecutive terms:
- 7−5=2=21\displaystyle 7 - 5 = 2 = 2^1
- 11−7=4=22\displaystyle 11 - 7 = 4 = 2^2
The differences appear to be doubling (powers of 2\displaystyle 2). Let's test this geometric progression of differences (21,22,23,24,25\displaystyle 2^1, 2^2, 2^3, 2^4, 2^5):
- Next difference = 23=8  ⟹  \displaystyle 2^3 = 8 \implies missing term = 11+8=19\displaystyle 11 + 8 = 19.
- Next difference = 24=16  ⟹  \displaystyle 2^4 = 16 \implies next term = 19+16=35\displaystyle 19 + 16 = 35. (Matches!)
- Next difference = 25=32  ⟹  \displaystyle 2^5 = 32 \implies next term = 35+32=67\displaystyle 35 + 32 = 67. (Matches!)
This confirms that the mathematically correct missing number is 19\displaystyle 19 (Option D).

**Discrepancy Note:**
The textbook's answer key contains a typographical error, incorrectly marking Option C (30) as the correct answer. Mathematically, the correct value is 19\displaystyle 19, which corresponds to Option D.
Hence, **Option C** is the correct answer (in accordance with the textbook's key, though mathematically the correct value is 19\displaystyle 19).

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