RELATIONSHIP Word Analysis: Finding the Extra Letter

The question asks to identify which word from the options contains an "extra letter" compared to the main word "RELATIONSHIP". This typically means either a letter not present in the main word or a letter used more times than it appears in the main word.

Analyzing the Main Word

First, let's list the unique letters and their frequencies in the word RELATIONSHIP:

• Letters: R, E, L, A, T, I, O, N, S, H, P
• Frequency Count:
  • R: $1$
  • E: $1$
  • L: $1$
  • A: $1$
  • T: $1$
  • I: $2$
  • O: $1$
  • N: $1$
  • S: $1$
  • H: $1$
  • P: $1$

The set of unique letters available is {R, E, L, A, T, I, O, N, S, H, P}.

Evaluating Option Words

Now, let's examine each option word against the letters and frequencies in RELATIONSHIP:

Option 1: RETAIN

• Letters: R, E, T, A, I, N
• Analysis: All letters (R, E, T, A, I, N) are present in RELATIONSHIP. Their frequencies in RETAIN (all are $1$) do not exceed their frequencies in RELATIONSHIP (I is $2$, others are $1$).
• Result: No extra letters found.

Option 2: POSHER

• Letters: P, O, S, H, E, R
• Analysis: All letters (P, O, S, H, E, R) are present in RELATIONSHIP. Their frequencies in POSHER (all are $1$) do not exceed their frequencies in RELATIONSHIP (all are $1$).
• Result: No extra letters found.

Option 3: EARTH

• Letters: E, A, R, T, H
• Analysis: All letters (E, A, R, T, H) are present in RELATIONSHIP. Their frequencies in EARTH (all are $1$) do not exceed their frequencies in RELATIONSHIP (all are $1$).
• Result: No extra letters found.

Option 4: THRILLS

• Letters: T, H, R, I, L, L, S
• Analysis: All unique letters (T, H, R, I, L, S) are present in RELATIONSHIP. However, let's check frequencies:
  • T: $1$ (in THRILLS) vs $1$ (in RELATIONSHIP) - OK
  • H: $1$ vs $1$ - OK
  • R: $1$ vs $1$ - OK
  • I: $1$ vs $2$ - OK
  • L: $2$ (in THRILLS) vs $1$ (in RELATIONSHIP) - NOT OK
  • S: $1$ vs $1$ - OK
• Result: The letter 'L' appears twice in THRILLS but only once in RELATIONSHIP. This constitutes an "extra letter".

Conclusion

Based on the frequency analysis, the word THRILLS uses the letter 'L' ($2$ times) more frequently than it appears in the word RELATIONSHIP ($1$ time). Therefore, THRILLS contains an extra instance of the letter 'L'.