Question

In a game, a "word" is any combination of at least five letters of the English alphabet (the word does not have to have a meaning). A "sentence" in this game consists of exactly six such words, and it must satisfy all of the following rules:
1. The six words are written from left to right on a single line, in strictly increasing alphabetical order.
2. The sentence may start with any word. Each successive word is obtained from the word right before it by applying exactly ONE of three operations: deleting one letter, adding one letter, or replacing one letter with another letter.
3. At most three of the six words can begin with the same letter.
4. Apart from the first word, every word must be formed using an operation different from the one used to form the word immediately before it (so the same operation can never be used twice in a row).

If the first word in a sentence is "illicit" and the fourth word is "licit", then the third word can be

• A. Implicit
• B. Explicit
• C. Enlist
• D. Elicit

Hint:

Since each step is exactly one add, delete, or replace move, ask which candidate word turns into "licit" by changing just a single letter.

Answer 1

The Correct Option is D

Step 1: Set up what we know.
The first word is "illicit" (7 letters: i-l-l-i-c-i-t). The fourth word must be "licit" (5 letters: l-i-c-i-t). Since the fourth word comes right after the third word, and each step is exactly one add, delete, or replace move, the third word must turn into "licit" using exactly ONE such move. So the real test for each option is simple: can this candidate word become "licit" using only one delete, add, or replace?

Step 2: Test "Implicit".
"Implicit" has 8 letters (i-m-p-l-i-c-i-t). To reach "licit" (5 letters), we would have to remove three letters at once, "i", "m", and "p", from the front. One operation removes only one letter, so this cannot be done in a single move. "Implicit" is ruled out.

Step 3: Test "Explicit".
"Explicit" has 8 letters (e-x-p-l-i-c-i-t). Turning it into "licit" needs the removal of three letters, "e", "x", and "p", from the front, again three deletions bundled into one step. A single operation cannot do this. "Explicit" is ruled out.

Step 4: Test "Enlist".
"Enlist" has 6 letters (e-n-l-i-s-t). To become "licit" (l-i-c-i-t), we would need to drop "e" and "n" from the front (two deletions) and also swap the "s" for a "c" (a replacement). That is well more than one operation, so "Enlist" cannot become "licit" in a single step either.

Step 5: Test "Elicit".
"Elicit" has 6 letters (e-l-i-c-i-t). Comparing it letter by letter with "licit" (5 letters, l-i-c-i-t), simply deleting the very first letter "e" from "Elicit" gives exactly "licit". That is a single delete operation, nothing more. "Elicit" works.

Step 6: Note the fifth option for completeness.
"Inlist" (6 letters: i-n-l-i-s-t) has the same problem as "Enlist": two extra letters up front ("i", "n") plus an "s" that must become "c", which is again more than one move. It cannot be the answer either.

Final Answer:
Only "Elicit" can become "licit" using exactly one operation, so it is the word that fits as the third word in the sentence. \[ \boxed{\text{Elicit}} \]