From the letters of the word HANDSOME, which one of the following words cannot be formed if each letter is used at most as many times as it appears in HANDSOME?

Introduction / Context:
This question belongs to the alphabet test and word formation category in verbal reasoning. The task is to look at a given parent word, here HANDSOME, and decide which one of the option words cannot be formed by using its letters. The important hidden condition is that no letter may be used more times than it appears in the original word. This is a very common style of question in many aptitude and government examinations, and it tests careful observation and counting of individual letters rather than vocabulary knowledge alone.

Given Data / Assumptions:

• Parent word: HANDSOME • Letters in HANDSOME: H, A, N, D, S, O, M, E • Each of these letters appears exactly once in the word HANDSOME. • Option words: HATS, HOME, NAME, SAND • Assumption: For forming an option word, we may only use letters from HANDSOME, and no letter may be repeated more than its frequency in HANDSOME.

Concept / Approach:
The correct technique is to break each option word into its letters and check two things. First, every letter in the option must appear in the parent word HANDSOME. Second, the frequency of each letter in the option must not exceed the number of times that letter appears in HANDSOME. Since every letter in HANDSOME appears only once, no option is allowed to use any letter twice. If a word demands a letter that is completely absent in HANDSOME, or demands a repeated letter, that word cannot be formed.

Step-by-Step Solution:
Step 1: Write the multiset of letters in HANDSOME as {H, A, N, D, S, O, M, E} with each letter available once. Step 2: Check option HATS. It needs H, A, T, S. Letters H, A, and S are present in HANDSOME, but the letter T does not appear anywhere in HANDSOME. Therefore, HATS cannot be formed. Step 3: Check option HOME. It needs H, O, M, E. All four letters H, O, M, and E are present once each in HANDSOME, so HOME can be formed. Step 4: Check option NAME. It needs N, A, M, E. All these letters N, A, M, and E are present in HANDSOME, so NAME can be formed. Step 5: Check option SAND. It needs S, A, N, D. All four letters S, A, N, and D are present in HANDSOME, so SAND can be formed. Step 6: The only option that breaks the rule is the one containing letter T, which is not available in the parent word.

Verification / Alternative check:
A quick verification method is to highlight or mark each letter of HANDSOME as it is used while trying to build each option word. For HOME, NAME, and SAND, you will be able to match every required letter. For HATS, you will eventually look for T and fail to locate it. Since there are exactly eight letters and no duplicates in HANDSOME, any option with even one new letter is automatically invalid. This confirms that HATS is the only impossible word among the given options.

Why Other Options Are Wrong:
HOME is wrong as the answer because all its letters appear in HANDSOME exactly once, so HOME can indeed be formed. NAME is wrong as the answer because N, A, M, and E all occur in HANDSOME, so NAME is a valid formation. SAND is wrong as the answer because S, A, N, and D are also available in HANDSOME and can form the word SAND.

Common Pitfalls:
Many learners forget to check for missing letters and focus only on word familiarity. Sometimes students mentally rearrange letters too quickly and overlook a missing character such as T. Another error is silently allowing repetition of a letter even when the parent word contains it only once. In this question, however, each letter in HANDSOME appears exactly once, so any option that needs a repeated letter or a new letter is automatically invalid. Working methodically and checking each letter avoids these mistakes.

Final Answer:
The only word that cannot be formed from the letters of HANDSOME is HATS, so the correct option is HATS.