How many meaningful English words can be formed using all the letters L, G, E and U exactly once in each word?

Introduction / Context:
This question belongs to the category of meaningful word formation and tests basic combinational reasoning together with vocabulary knowledge. You must identify how many distinct meaningful English words can be created by rearranging the four letters L, G, E and U using each letter exactly once. The answer is not asking for the total number of possible permutations, but specifically for the count of those permutations that are valid words in standard English usage.

Given Data / Assumptions:
1) The set of letters is L, G, E and U.2) Each letter must be used exactly once in each word.3) Only meaningful English words are to be counted, not arbitrary sequences of letters.4) Standard vocabulary as used in competitive exams should be assumed, including common nouns and verbs.

Concept / Approach:
The approach is to think of familiar words that can be built from these letters, paying attention to likely positions of vowels and consonants. Often, English words with one vowel will place the vowel in the middle or near the start. Systematically test possible patterns by fixing the vowel position and rearranging consonants around it. After you identify candidate words, verify that each candidate is a valid dictionary word, not a misspelling or obscure abbreviation, and then count how many such words you have found.

Step-by-Step Solution:
1) List all letters: L, G, E, U. The vowel is E or U depending on the arrangement, and the consonants are L and G.2) Try obvious arrangements: GLUE is an immediate candidate since it is a very common English word meaning an adhesive substance.3) Check GLUE: G, L, U and E are all used exactly once, and GLUE is accepted vocabulary.4) Consider other permutations: LUGE is another candidate, where LUGE is a term for a small one or two person sled used in winter sports and also the sport itself.5) Check LUGE: L, U, G and E are all present exactly once, and LUGE is a recognised English word, especially in sports contexts.6) Examine whether any other arrangement forms a standard word. Combinations such as GULE or ULEG are not commonly accepted English words in exam contexts.7) Since GLUE and LUGE are both valid and no other common words arise, the total number of meaningful words is two.

Verification / Alternative check:
A confirmation approach is to list all 4 factorial, that is 24 permutations, and quickly scan them for familiar patterns. Among these, GLUE and LUGE stand out as widely used English words. Others like GLEU, EGUL or ELGU do not correspond to everyday vocabulary. Additionally, many reasoning and aptitude books provide this very example and explicitly state that two words, GLUE and LUGE, can be formed. This external knowledge reinforces your analytical conclusion that the correct count is two.

Why Other Options Are Wrong:
Zero is wrong because at least GLUE is a very common and obvious word.One is wrong because it ignores LUGE, which is also a legitimate word in standard English.Four is wrong because there are not that many different meaningful words using precisely these four letters once each.None of these is incorrect because the correct count, two, is already available among the options.

Common Pitfalls:
Many candidates spot only GLUE and stop, quickly marking “One” without considering that LUGE is also an English word. Others may be unfamiliar with LUGE and wrongly assume it is not acceptable. It is important in verbal reasoning to remember that exam vocabularies include common sports, science and general knowledge terms. When in doubt, quickly review common permutations rather than immediately settling on the first word you notice. Developing a broad reading habit helps you recognise less frequent words such as LUGE in test situations.

Final Answer:
The letters L, G, E and U can form exactly two meaningful English words, GLUE and LUGE, so the correct answer is Two.