Analyzing the Word Analogy

The question presents a word analogy: MATE:NATE :: FATE:?. We need to find the relationship between the first pair (MATE:NATE) and apply it to the third term (FATE) to find the fourth term.

Identifying the Pattern

• Observe the first pair: MATE and NATE. The last three letters 'ATE' are constant. The first letter changes from 'M' to 'N'.
• Observe the second pair: FATE and ?. The last three letters 'ATE' are expected to remain constant. The first letter needs to be determined.
• Let's find the relationship between the first letters M and N.
• Find their positions in the English alphabet: M is the 13th letter ($Pos(M) = 13$) and N is the 14th letter ($Pos(N) = 14$).
• Consider the sum of these positions: $13 + 14 = 27$.
• Now, let's apply this logic to the second pair (FATE: ?).
• The first letter is F. Its alphabetical position is 6 ($Pos(F) = 6$). Let the alphabetical position of the unknown first letter be $x$.
• Assuming the sum of the alphabetical positions of the first letters must be the same for both pairs (as per the analogy structure): $Pos(F) + x = 27$.

Calculating the Missing Letter

• Substitute the known value: $6 + x = 27$.
• Solve for $x$: $x = 27 - 6$.
• $x = 21$.
• The 21st letter in the alphabet is U.

Determining the Final Term

Replace the first letter 'F' in 'FATE' with the determined letter 'U'. The resulting word is UATE.

Therefore, the analogy is MATE:NATE :: FATE:UATE.