Decoding the Letter Logic

The question presents a word pair analogy: FOAM is related to HQCO in a specific way, and we need to find the word related to VOTE using the same logic.

Let's analyze the relationship between FOAM and HQCO by looking at the positions of the letters in the alphabet:

• F is the 6th letter, H is the 8th letter. Difference: $8 - 6 = 2$.
• O is the 15th letter, Q is the 17th letter. Difference: $17 - 15 = 2$.
• A is the 1st letter, C is the 3rd letter. Difference: $3 - 1 = 2$.
• M is the 13th letter, O is the 15th letter. Difference: $15 - 13 = 2$.

The logic applied is shifting each letter of the original word two positions forward in the alphabet.

Applying the Logic to VOTE

Now, we apply the same "+2" logic to the word VOTE:

• V (22nd letter) + 2 positions = 24th letter, which is X.
• O (15th letter) + 2 positions = 17th letter, which is Q.
• T (20th letter) + 2 positions = 22nd letter, which is V.
• E (5th letter) + 2 positions = 7th letter, which is G.

Therefore, VOTE transforms into XQVG.

Identifying the Correct Option

Comparing our result with the given options:

• Option 1: XPVG
• Option 2: XQUG
• Option 3: XQVG
• Option 4: XVPG

The derived word XQVG matches Option 3.