This question is a letter analogy puzzle. We need to identify the relationship between the first pair of terms (VEGT and SHJQ) and apply the same relationship to the third term (FGCM) to find the missing fourth term.

Analyzing the Letter Relationship

Let's look at the correspondence between the letters in VEGT and SHJQ:

The pattern observed is that the letters in the second term are derived from the corresponding letters in the first term by applying a shift in their alphabetical position: -3, +3, +3, -3.

Applying the Pattern to FGCM

Now, let's apply this pattern to the third term, FGCM, to find the fourth term.

• First letter: F. Apply -3 shift. F is the 6th letter. $6 - 3 = 3$. The 3rd letter is C.
• Second letter: G. Apply +3 shift. G is the 7th letter. $7 + 3 = 10$. The 10th letter is J.
• Third letter: C. Apply +3 shift. C is the 3rd letter. $3 + 3 = 6$. The 6th letter is F.
• Fourth letter: M. Apply -3 shift. M is the 13th letter. $13 - 3 = 10$. The 10th letter is J.

Following this pattern, FGCM transforms into CJFJ.

Comparing with Options

Let's compare our result with the given options:

1. BJFJ
2. CJPJ
3. CJFJ
4. DJPJ

Our calculated term, CJFJ, matches option 3.

Conclusion on Letter Analogy

The analogy holds with the pattern of letter shifts: VEGT related to SHJQ by (-3, +3, +3, -3) shift, and FGCM related to CJFJ by the same (-3, +3, +3, -3) shift.

Revision Table: Letter Position Shifts

Additional Information: Solving Analogy Questions

Analogy questions test your ability to find relationships between pairs of words, letters, numbers, or symbols. For letter analogies, common patterns include:

• Letter shifts (adding or subtracting a constant number from letter positions).
• Skipping letters (e.g., alternating shifts like +1, -2, +3, -4).
• Reversing the order of letters.
• Vowel/consonant patterns.
• Mirror images or symmetry (less common in simple letter sequences).

To solve these, it's helpful to know the alphabetical position of each letter. Writing down the alphabet or using a table can assist in quickly identifying the pattern. Always test your hypothesized pattern on the first pair before applying it to the second pair.