Number Series, Coding and DecodingMCQMTP Dec 22 - Series II RTP Sep 24Question 2063 of 217
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Find the missing term in each of the following series : 28,33,31,36,34,?\displaystyle 28, 33, 31, 36, 34, ?

Options

A48\displaystyle 48
B39\displaystyle 39
C54\displaystyle 54
D62\displaystyle 62
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Correct Answer

✅ Option b — 39\displaystyle 39

All Options:

  • A48\displaystyle 48
  • B39\displaystyle 39
  • C54\displaystyle 54
  • D62\displaystyle 62

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Detailed Solution & Explanation

To find the missing term of the series 28,33,31,36,34,?\displaystyle 28, 33, 31, 36, 34, ?, let us analyze the differences between successive terms:

- 1st term to 2nd term: 33−28=+5\displaystyle 33 - 28 = +5
- 2nd term to 3rd term: 31−33=−2\displaystyle 31 - 33 = -2
- 3rd term to 4th term: 36−31=+5\displaystyle 36 - 31 = +5
- 4th term to 5th term: 34−36=−2\displaystyle 34 - 36 = -2

We observe a simple alternating pattern of adding 5\displaystyle 5 and subtracting 2\displaystyle 2 (+5,−2,+5,−2,…\displaystyle +5, -2, +5, -2, \dots).
Following this pattern, the next term must be calculated by adding 5\displaystyle 5 to the 5th term (34\displaystyle 34):
34+5=3934 + 5 = 39
This mathematically proves that the correct answer is **Option B** (39\displaystyle 39).

*Note on Answer Key Discrepancy:* The textbook answer key lists **Option C** (54\displaystyle 54) as correct. However, there is no logical mathematical pattern in which 54\displaystyle 54 fits as the next number, whereas 39\displaystyle 39 perfectly satisfies the alternating pattern +5,−2\displaystyle +5, -2. Therefore, the answer key has a typographical error, and the correct option is indeed **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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