Find odd man out of the following series 3, 4, 10, 32, 136, 685, 4116

Option b: 32. Solution: Let's establish the mathematical pattern linking consecutive terms starting with T1 = 3 : - T2 = T1 × 1 + 1 = 3 × 1 + 1 = 4 - T3 = T2 × 2 + 2 = 4 × 2 + 2 = 10 - T4 = T3 × 3 + 3 = 10 × 3 + 3 = 33 (the series lists 32 , which is incorrect) - Let's verify if 33 is correct by computing the next term: T5 = 33 × 4 + 4 = 132 + 4 = 136 (matches perfectly!) T6 = 136 × 5 + 5 = 680 + 5 = 685 (matches perfectly!) T7 = 685 × 6 + 6 = 4110 + 6 = 4116 (matches perfectly!) This pattern ( Tn = Tn-1 × (n-1) + (n-1) ) is perfectly consistent for all terms except 32 , which should be 33 . Therefore, 32 is the odd man out. Hence, Option B is the correct answer.

Number Series, Coding and DecodingMCQMTP Dec 22 Series IIQuestion 2191 of 217

All Questions

Find odd man out of the following series $\displaystyle 3, 4, 10, 32, 136, 685, 4116$

Options

\displaystyle 10

\displaystyle 32

\displaystyle 136

\displaystyle 4116

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Correct Answer

✅ Option b — $\displaystyle 32$

All Options:

A $\displaystyle 10$
B $\displaystyle 32$
C $\displaystyle 136$
D $\displaystyle 4116$

Detailed Solution & Explanation

Let's establish the mathematical pattern linking consecutive terms starting with

\displaystyle T_1 = 3

:
-

\displaystyle T_2 = T_1 \times 1 + 1 = 3 \times 1 + 1 = 4

\displaystyle T_3 = T_2 \times 2 + 2 = 4 \times 2 + 2 = 10

\displaystyle T_4 = T_3 \times 3 + 3 = 10 \times 3 + 3 = 33

(the series lists

\displaystyle 32

, which is incorrect)
- Let's verify if

\displaystyle 33

is correct by computing the next term:

T_5 = 33 \times 4 + 4 = 132 + 4 = 136

(matches perfectly!)

T_6 = 136 \times 5 + 5 = 680 + 5 = 685

(matches perfectly!)

T_7 = 685 \times 6 + 6 = 4110 + 6 = 4116

(matches perfectly!)

This pattern (

\displaystyle T_n = T_{n-1} \times (n-1) + (n-1)

) is perfectly consistent for all terms except

\displaystyle 32

, which should be

\displaystyle 33

. Therefore,

\displaystyle 32

is the odd man out.

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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Find odd man out of the following series 3,4,10,32,136,685,4116\displaystyle 3, 4, 10, 32, 136, 685, 41163,4,10,32,136,685,4116