Number Series, Coding and DecodingMCQMTP June 24 Series IQuestion 2075 of 217
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Find out the next number in the following series 7,11,13,17,19,23,25,29,?\displaystyle 7, 11, 13, 17, 19, 23, 25, 29, ?

Options

A30\displaystyle 30
B31\displaystyle 31
C32\displaystyle 32
D33\displaystyle 33
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Correct Answer

✅ Option b — 31\displaystyle 31

All Options:

  • A30\displaystyle 30
  • B31\displaystyle 31
  • C32\displaystyle 32
  • D33\displaystyle 33

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Detailed Solution & Explanation

To find the next number in the series 7,11,13,17,19,23,25,29,?\displaystyle 7, 11, 13, 17, 19, 23, 25, 29, ?, we can analyze the logical progression using two standard methods:

**Method 1: Alternating Differences (+4\displaystyle +4 and +2\displaystyle +2)**
Let us examine the difference between successive terms of the series:
- 11−7=+4\displaystyle 11 - 7 = +4
- 13−11=+2\displaystyle 13 - 11 = +2
- 17−13=+4\displaystyle 17 - 13 = +4
- 19−17=+2\displaystyle 19 - 17 = +2
- 23−19=+4\displaystyle 23 - 19 = +4
- 25−23=+2\displaystyle 25 - 23 = +2
- 29−25=+4\displaystyle 29 - 25 = +4
We observe a clear, repeating, alternating pattern of adding 4\displaystyle 4 and then adding 2\displaystyle 2 (+4,+2,+4,+2,…\displaystyle +4, +2, +4, +2, \dots).
Following this pattern, the next difference must be +2\displaystyle +2. We add 2\displaystyle 2 to the last term (29\displaystyle 29):
29+2=3129 + 2 = 31
**Method 2: Split Alternating Subseries**
We can divide the series into two independent subseries based on odd and even positions:

1. **Odd-position Subseries (1st, 3rd, 5th, 7th, 9th terms):**
- Terms: 7,13,19,25,?\displaystyle 7, 13, 19, 25, ?
- We observe a constant difference of +6\displaystyle +6 between consecutive terms (7+6=13\displaystyle 7+6=13, 13+6=19\displaystyle 13+6=19, 19+6=25\displaystyle 19+6=25).
- Following this constant +6\displaystyle +6 progression, the 9th term (the missing term) must be:
25+6=3125 + 6 = 31
2. **Even-position Subseries (2nd, 4th, 6th, 8th terms):**
- Terms: 11,17,23,29\displaystyle 11, 17, 23, 29
- We also observe a constant difference of +6\displaystyle +6 (11+6=17\displaystyle 11+6=17, 17+6=23\displaystyle 17+6=23, 23+6=29\displaystyle 23+6=29).

Both independent methods mathematically prove that the next term in the sequence is **31\displaystyle 31**, which corresponds to **Option B**.

*Note on Answer Key Discrepancy:* The textbook answer key lists **Option D** (33\displaystyle 33) as the correct option. However, 33\displaystyle 33 violates both the alternating difference pattern and the split-series progression, whereas 31\displaystyle 31 is logically and mathematically perfect. This is a clear typographical error in the official answer key, and the correct option is **Option B**.

Hence, **Option B** 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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