Number Series, Coding, Odd Man OutPYQ Jun 23Question 2032 of 217
All Questions

Find the next number in the series: Q1F, S2E, U6D, W21C, \_\_\_\_\_\_?

Options

AY66B
BY44B
CY88B
DZ66B
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Correct Answer

✅ Option c — Y88B

All Options:

  • AY66B
  • BY44B
  • CY88B
  • DZ66B

Detailed Solution & Explanation

We are given the alphanumeric series: Q1F, S2E, U6D, W21C, ______?
Let's analyze each component of the terms separately:
1. **First Letter:** Q, S, U, W
- Alphabetic positions: Q (17), S (19), U (21), W (23).
- Pattern: +2\displaystyle +2 position shift each time. The next letter position is 23+2=25\displaystyle 23 + 2 = 25, which is **Y**.
2. **Middle Number:** 1, 2, 6, 21
- Let's analyze the recurrence relation:
- 1×1+1=2\displaystyle 1 \times 1 + 1 = 2
- 2×2+2=6\displaystyle 2 \times 2 + 2 = 6
- 6×3+3=21\displaystyle 6 \times 3 + 3 = 21
- The next number is 21×4+4=88\displaystyle 21 \times 4 + 4 = 88.
- The pattern is xn=n⋅xn−1+n\displaystyle x_n = n \cdot x_{n-1} + n for n≥1\displaystyle n \ge 1.
3. **Last Letter:** F, E, D, C
- Alphabetic positions: F (6), E (5), D (4), C (3).
- Pattern: −1\displaystyle -1 position shift (moving backward in the alphabet). The next letter is **B**.
Combining the components: Y + 88 + B = **Y88B**.
Hence, **Option C** is the correct answer.

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