Number Series, Coding, Odd Man OutMTP June 2023 Series IQuestion 2071 of 217
All Questions

Identify the sequence of letters and find out the missing number. AGM, DJP, HNT, ______.

Options

AMSY
BNTZ
CLRX
DKOW
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Correct Answer

✅ Option a — MSY

All Options:

  • AMSY
  • BNTZ
  • CLRX
  • DKOW

Detailed Solution & Explanation

To find the missing term of the letter series AGM,DJP,HNT,…\displaystyle AGM, DJP, HNT, \dots, let us convert each letter to its numerical position in the alphabet (where A=1,B=2,…,Z=26\displaystyle A = 1, B = 2, \dots, Z = 26):

Let us analyze the progression for each letter position separately:

1. **First Letter Progression:**
- Letters: A→D→H→?\displaystyle A \to D \to H \to ?
- Alphabetical positions: 1→4→8→?\displaystyle 1 \to 4 \to 8 \to ?
- Let us check the differences between successive positions: 4−1=+3\displaystyle 4 - 1 = +3 and 8−4=+4\displaystyle 8 - 4 = +4.
- The difference is increasing by 1\displaystyle 1 at each step (+3,+4\displaystyle +3, +4). Thus, the next difference must be +5\displaystyle +5:
8+5=13  ⟹  M8 + 5 = 13 \implies \mathbf{M}
2. **Second Letter Progression:**
- Letters: G→J→N→?\displaystyle G \to J \to N \to ?
- Alphabetical positions: 7→10→14→?\displaystyle 7 \to 10 \to 14 \to ?
- Let us check the differences between successive positions: 10−7=+3\displaystyle 10 - 7 = +3 and 14−10=+4\displaystyle 14 - 10 = +4.
- Following the +3,+4,+5\displaystyle +3, +4, +5 difference pattern, the next position is:
14+5=19  ⟹  S14 + 5 = 19 \implies \mathbf{S}
3. **Third Letter Progression:**
- Letters: M→P→T→?\displaystyle M \to P \to T \to ?
- Alphabetical positions: 13→16→20→?\displaystyle 13 \to 16 \to 20 \to ?
- Let us check the differences between successive positions: 16−13=+3\displaystyle 16 - 13 = +3 and 20−16=+4\displaystyle 20 - 16 = +4.
- Following the +3,+4,+5\displaystyle +3, +4, +5 difference pattern, the next position is:
20+5=25  ⟹  Y20 + 5 = 25 \implies \mathbf{Y}

Combining the three letters, the correct next term in the sequence is **MSY**, which corresponds to **Option A**.

*Note on Answer Key Discrepancy:* The textbook/exam answer key lists **Option C** (LRX\displaystyle LRX) as correct. However, LRX\displaystyle LRX does not satisfy the clear, consistent arithmetic progression +3,+4,+5\displaystyle +3, +4, +5 observed in each letter of the series. MSY is mathematically and logically the unique correct answer. This represents a typographical error in the official answer key, and the correct option is **Option A**.

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

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