Difficulty: Easy
Correct Answer: 2
Explanation:
Introduction / Context:
This is a short word formation question from basic vocabulary and reasoning. You are given a small set of letters and must determine how many distinct meaningful English words can be made using all the letters exactly once. Such questions help evaluate both your vocabulary and your ability to mentally permute letters. They are simple in structure but can be tricky if you do not quickly recognise familiar word patterns.
Given Data / Assumptions:
The letters provided are A, L and W. Each letter must be used exactly once in forming each word. We have to count how many different meaningful English words can be formed using these three letters. We assume standard everyday English and ignore very obscure or highly technical words. The answer should match one of the counts 1, 2, 3, 4 or more than four.
Concept / Approach:
With three distinct letters, the total number of possible three letter permutations is 3 factorial, that is six. These permutations are A L W, A W L, L A W, L W A, W A L and W L A. We must now check which of these sequences correspond to real English words. The most promising patterns usually start with a consonant and have vowels placed centrally, forming familiar structures like consonant vowel consonant. By scanning the set of permutations with this in mind, the meaningful words become clear.
Step-by-Step Solution:
List all permutations: ALW, AWL, LAW, LWA, WAL and WLA.
Check ALW: this does not correspond to any standard English word.
Check AWL: this spells AWL, which is a real word meaning a small pointed tool used for making holes, especially in leather or wood.
Check LAW: this spells LAW, a common English word referring to rules or systems of rules enforced by authorities.
Check LWA, WAL and WLA: none of these are standard English words in general usage.
Therefore the only meaningful words obtainable are AWL and LAW.
Verification / Alternative check:
To verify, you can mentally try to use each candidate in a sentence. Sentences such as the cobbler used an awl and he studied law clearly sound natural and show that AWL and LAW are valid words. Attempts to use ALW, LWA, WAL or WLA in similar sentences will fail because they are not recognised English words. You might also recall that AWL and LAW both appear in basic vocabulary lists, while the other arrangements do not. This usage based check supports the conclusion that exactly two meaningful words can be formed.
Why Other Options Are Wrong:
Option 1 is incorrect because we have clearly found at least two valid words, AWL and LAW. Options 3, 4 and More than four are wrong because no additional everyday English words can be formed from A, L and W apart from these two. Counting any more would require accepting non standard abbreviations or names, which aptitude exams typically do not do in such questions. Therefore, any count other than two does not match the real number of meaningful words.
Common Pitfalls:
Some students stop after identifying LAW and assume that it is the only word, forgetting to test other permutations equally. Others might treat partial forms or non English sounding combinations as valid words simply because they resemble initials or codes. To avoid these errors, always list all permutations explicitly and test each one for meaning. If a sequence does not appear in normal reading or conversation, it likely should not be counted. Developing a wide reading habit will naturally increase your ability to quickly recognise valid words in such problems.
Final Answer:
Exactly 2 meaningful English words, AWL and LAW, can be formed using the letters A, L and W.
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