Identify the grammatically correct way to express a past unreal condition in the sentence "If I would have known the truth I would have admitted it".

Introduction / Context:
This sentence improvement question focuses on conditional sentences in English, specifically past unreal conditions. The given sentence, If I would have known the truth I would have admitted it, is a common learner error. Standard English uses had plus past participle in the if clause for such conditions, not would have. The question checks whether you know the correct structure to talk about a hypothetical situation in the past that did not actually happen. Recognising this pattern is very important for spoken and written accuracy.

Given Data / Assumptions:
The information in the sentence is as follows.

• The sentence talks about knowing the truth at some time in the past.
• The main clause I would have admitted it refers to a result that did not occur.
• The structure is that of a third conditional (past unreal condition).
• The underlined part is would have known, which is incorrect in the if clause in formal English.
• The correct form must match the time frame and meaning while improving the grammar.

Concept / Approach:
In third conditional sentences, which describe unreal situations in the past, the standard form is: If + subject + had + past participle, followed by subject + would have + past participle in the result clause. Therefore, we expect If I had known the truth, I would have admitted it. The problem with If I would have known is that it uses would in the if clause, which is non standard and considered wrong in formal contexts. We only use had known in this position. The rest of the sentence, I would have admitted it, is already correct for the result clause.

Step-by-Step Solution:

Verification / Alternative check:
Read the corrected sentence aloud: If I had known the truth I would have admitted it. This sounds natural and matches the standard pattern of a third conditional. It clearly expresses that the speaker did not know the truth at the relevant time, and therefore did not admit it, but would have done so if the situation had been different. Comparing this with common textbook examples shows that it is the accepted form. This verifies that had known is the right choice.

Why Other Options Are Wrong:
Option B, have known, produces If I have known the truth, which is present perfect and does not match the past hypothetical meaning; it would describe a different time relation. Option C, know, gives If I know the truth I would have admitted it, which mixes present in the if clause with a past unreal result, making the sentence inconsistent. Option D, No improvement, would keep the incorrect structure If I would have known the truth, which is not standard in exam level English. Option E, had been knowing, uses a continuous perfect form that is rarely used in this type of conditional and sounds unnatural. Therefore, option A, had known, is the correct improvement.

Common Pitfalls:
Many learners transfer patterns from spoken language where would sometimes appears in both clauses, such as If I would have known, I would have done it. However, in formal and exam English only the result clause contains would have, while the if clause uses had plus past participle. Another pitfall is confusing second and third conditionals or mixing tenses across clauses. To avoid these mistakes, practise identifying the time and reality of the situation: present unreal, future imaginary, or past unreal. Then apply the correct structure. For past unreal conditions, always use If + had + past participle in the if clause.

Final Answer:
The improved sentence should read: If I had known the truth I would have admitted it.