From the given alternatives, select the word which cannot be formed using the letters of the word Apparent, assuming that no letter is used more times than it appears in the original word.

Introduction / Context:
This word formation question revolves around the base word Apparent. You need to decide which option cannot be formed from its letters when no letter can be reused more times than it appears in Apparent. The task reinforces careful checking of which letters are available and helps you spot extra letters that would make a candidate word impossible to construct.

Given Data / Assumptions:

• Base word: Apparent.
• Letters available: A, P, P, A, R, E, N, T (two As, two Ps and one each of R, E, N, T).
• Options: Pear, Pent, Rent, Relevent.
• No new letters may be added and letter frequency must not exceed that of the base word.

Concept / Approach:
We identify the pool of letters from Apparent and compare each option with this pool. Any option containing a letter that is absent from the base word is impossible. Similarly, if an option requires more occurrences of any letter than available, it cannot be formed. Because the base word does not contain L or V, these letters in an option are immediate warning signs that the word is invalid for this question.

Step-by-Step Solution:
Step 1: List distinct letters of Apparent: {A, P, R, E, N, T} with counts A(2), P(2), R(1), E(1), N(1), T(1). Step 2: Check Pear: P, E, A, R all appear in the pool and within allowed frequencies, so Pear can be formed. Step 3: Check Pent: P, E, N, T all exist in the base word, so Pent can also be formed. Step 4: Check Rent: R, E, N, T all occur in Apparent, so Rent can be formed. Step 5: Check Relevent: R, E, L, E, V, E, N, T require L and V. These letters do not appear anywhere in Apparent, which means Relevent cannot be formed from the letters of Apparent.

Verification / Alternative check:
To verify quickly, make a mental or written note that Apparent has no L and no V. Among the options, only Relevent uses L and V, immediately signalling that it cannot be constructed. Pear, Pent and Rent, on the other hand, draw solely from the available letters. This quick recognition of absent letters ensures that you reach the correct answer efficiently.

Why Other Options Are Wrong:
Pear uses P, E, A and R, all of which exist in Apparent. Pent uses P, E, N and T, again all available. Rent uses R, E, N and T, also present in the base word. Since each of these words can be formed using the letter pool from Apparent, they do not satisfy the requirement of being impossible and must therefore be rejected as final answers.

Common Pitfalls:
A common error is to pay attention only to the shape or sound of words and overlook the introduction of new letters like L and V. Another pitfall is forgetting to consider letter frequency, particularly for repeated letters like A and P, even though this issue does not cause a conflict in this specific problem. The safest strategy is to clearly write out the allowed letters and quickly scan each option for any that fall outside this set.

Final Answer:
The word that cannot be formed from Apparent is Relevent, so Relevent is the correct answer.