If the word "MOMENTUM" is coded as "EMOMNTUM" by rearranging its letters according to a fixed rule, then how will the word "MAGNETIC" be written in the same code language?

Introduction / Context:
This coding and decoding problem involves rearranging the letters of a word according to a positional pattern. The example "MOMENTUM" to "EMOMNTUM" indicates that some subset of letters is reversed or shifted, while others remain in the same order. We must detect that pattern and then apply it to the word "MAGNETIC".

Given Data / Assumptions:

• MOMENTUM is coded as EMOMNTUM.
• We must code MAGNETIC under the same rule.
• Both words have eight letters, so the pattern of rearranging positions is likely the same in both cases.
• No letter substitutions are performed, only reordering of existing letters.

Concept / Approach:
To find the pattern, compare MOMENTUM and EMOMNTUM position by position. Observe which positions in the original word correspond to each position in the coded word. Once we know this mapping of positions, we can apply it directly to the letters of MAGNETIC. In this case, the first four letters of the word are rearranged, while the last four letters remain unchanged.

Step-by-Step Solution:
Step 1: Write MOMENTUM with its positions: 1 M, 2 O, 3 M, 4 E, 5 N, 6 T, 7 U, 8 M. Step 2: Write the code EMOMNTUM and match letters: positions in the code are 1 E, 2 M, 3 O, 4 M, 5 N, 6 T, 7 U, 8 M. Step 3: Note that the last four letters N, T, U and M appear in the same relative order as positions 5, 6, 7 and 8 in the original word. Step 4: Focus on the first four letters. MOMENTUM has M, O, M, E at positions 1 to 4. The code EMOMNTUM starts with E, M, O, M. Step 5: This shows that the first four letters of the code are the original first four letters reversed: positions [4, 3, 2, 1]. So the mapping is 4th, 3rd, 2nd, 1st, followed by 5th, 6th, 7th, 8th. Step 6: Now apply the same positional mapping to MAGNETIC, whose letters and positions are: 1 M, 2 A, 3 G, 4 N, 5 E, 6 T, 7 I, 8 C. Step 7: Rearrange the first four letters in the order 4, 3, 2, 1: N, G, A, M. Step 8: Append the last four letters unchanged: E, T, I and C. Step 9: This gives N G A M E T I C, written as NGAMETIC.

Verification / Alternative check:
We can verify by reconstructing MOMENTUM using the same rule in reverse. For EMOMNTUM, taking the first four letters and reversing them gives MOME. Concatenating the unchanged last four letters NTUM yields MOMENTUM again. Applying this check confirms that our understanding of the pattern is correct, justifying its use for MAGNETIC.

Why Other Options Are Wrong:
Options NGMAEITC, NGAMECTI and NGMAETIC use the same letters but place them in different orders that do not correspond to reversing the first four letters and keeping the last four in their original sequence. They might arise from reversing too many positions or from a random rearrangement, but they do not follow the positional rule demonstrated by the example.

Common Pitfalls:
Some candidates mistakenly reverse the entire word instead of only the first four letters, or they reverse the wrong block of letters. Others may suspect that letters are being substituted rather than simply moved. Closely aligning original and coded positions is essential to avoid such errors and to see the exact pattern clearly.

Final Answer:
Using the same positional rearrangement that converts MOMENTUM to EMOMNTUM, the word "MAGNETIC" is coded as NGAMETIC.