Number Series, Coding, Odd Man OutMTP Dec 22 Series IIQuestion 2191 of 217
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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, 4116

Options

A10\displaystyle 10
B32\displaystyle 32
C136\displaystyle 136
D4116\displaystyle 4116
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Correct Answer

✅ Option b — 32\displaystyle 32

All Options:

  • A10\displaystyle 10
  • B32\displaystyle 32
  • C136\displaystyle 136
  • D4116\displaystyle 4116

Detailed Solution & Explanation

Let's establish the mathematical pattern linking consecutive terms starting with T1=3\displaystyle T_1 = 3:
- T2=T1×1+1=3×1+1=4\displaystyle T_2 = T_1 \times 1 + 1 = 3 \times 1 + 1 = 4
- T3=T2×2+2=4×2+2=10\displaystyle T_3 = T_2 \times 2 + 2 = 4 \times 2 + 2 = 10
- T4=T3×3+3=10×3+3=33\displaystyle T_4 = T_3 \times 3 + 3 = 10 \times 3 + 3 = 33 (the series lists 32\displaystyle 32, which is incorrect)
- Let's verify if 33\displaystyle 33 is correct by computing the next term:
T5=33×4+4=132+4=136T_5 = 33 \times 4 + 4 = 132 + 4 = 136 (matches perfectly!)
T6=136×5+5=680+5=685T_6 = 136 \times 5 + 5 = 680 + 5 = 685 (matches perfectly!)
T7=685×6+6=4110+6=4116T_7 = 685 \times 6 + 6 = 4110 + 6 = 4116 (matches perfectly!)

This pattern (Tn=Tn−1×(n−1)+(n−1)\displaystyle T_n = T_{n-1} \times (n-1) + (n-1)) is perfectly consistent for all terms except 32\displaystyle 32, which should be 33\displaystyle 33. Therefore, 32\displaystyle 32 is the odd man out.

Hence, **Option B** is the correct answer.

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