Number Series, Coding, Odd Man OutPYQ Dec 22Question 2100 of 217
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If 'FROZEN' is decoded as 'OFAPSG'. Tick the right option that depicts 'MOLTEN' written in this way?

Options

AOFPOMN
BOFSMPN
COFUMPN
DOFUNPN
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Correct Answer

✅ Option c — OFUMPN

All Options:

  • AOFPOMN
  • BOFSMPN
  • COFUMPN
  • DOFUNPN

Detailed Solution & Explanation

To find the right option that depicts how **MOLTEN** is coded based on the coding of **FROZEN** as **OFAPSG**:

Let us first analyze the two-step coding rule of the sequence **FROZEN** →\displaystyle \to **OFAPSG**:
- **Step 1 (Reverse the Word):** We write the letters in reverse order:
FROZEN→N E Z O R F\text{FROZEN} \to \text{N E Z O R F}
- **Step 2 (Shift +1\displaystyle +1):** We shift each letter forward by +1\displaystyle +1 position in the alphabet:
- N+1→O\displaystyle N + 1 \to \mathbf{O}
- E+1→F\displaystyle E + 1 \to \mathbf{F}
- Z+1→A\displaystyle Z + 1 \to \mathbf{A} (wraps around to the start of the alphabet)
- O+1→P\displaystyle O + 1 \to \mathbf{P}
- R+1→S\displaystyle R + 1 \to \mathbf{S}
- F+1→G\displaystyle F + 1 \to \mathbf{G}
This gives the code exactly as **OFAPSG**.

Now we apply this exact same two-step rule to the word **MOLTEN**:
- **Step 1 (Reverse the Word):** We write the letters in reverse order:
MOLTEN→N E T L O M\text{MOLTEN} \to \text{N E T L O M}
- **Step 2 (Shift +1\displaystyle +1):** We shift each letter forward by +1\displaystyle +1 position:
- N+1→O\displaystyle N + 1 \to \mathbf{O}
- E+1→F\displaystyle E + 1 \to \mathbf{F}
- T+1→U\displaystyle T + 1 \to \mathbf{U}
- L+1→M\displaystyle L + 1 \to \mathbf{M}
- O+1→P\displaystyle O + 1 \to \mathbf{P}
- M+1→N\displaystyle M + 1 \to \mathbf{N}

Putting the shifted letters in sequence, the correct code for **MOLTEN** is **OFUMPN**.

*Note on Answer Key Discrepancy:* The textbook answer key lists **Option A** (OFPOMN\displaystyle OFPOMN) as correct. However, OFPOMN\displaystyle OFPOMN completely violates the logical progression and alphabetical shifts (e.g., coding T\displaystyle T as P\displaystyle P and L\displaystyle L as O\displaystyle O), whereas OFUMPN\displaystyle OFUMPN is the unique, mathematically proven result under the established rule. This represents a typographical error in the official answer key, and the correct option is **Option C**.

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

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