Given: P = Q R, R <= S < T, P T Which statement is always true?

Question

Given: P = Q R, R <= S < T, P T

Which statement is always true?

1. A. P = S
2. B. S < Q
3. C. Q T
4. D. T R (Correct answer)

Correct Answer

Option D — D

Detailed Solution & Explanation

The correct answer is Option D.

Key Points

• Given: P ≥ Q > R and R ≤ S < T and P > T.
• Check T > R: from R ≤ S < T we have R ≤ S and S < T, so R < T, i.e. T > R is always true.
• Why the others fail: P = S is not forced; S < Q is not guaranteed (S could exceed Q); Q > T is not guaranteed (we only know P > T, and Q ≤ P).
• Only T > R must always hold.

Exam Tip

• to test 'always true' in inequality chains, try to build a counter-example; if you cannot, the statement is necessarily true — as with T > R here.

Additional Information

• Chain the inequalities carefully: P ≥ Q > R and R ≤ S < T and P > T. A conclusion is "always true" only if it follows in every arrangement the constraints permit.
• Mixing ≥ with > matters: P ≥ Q allows equality, so P > Q cannot be concluded.
• Where two chains share a term, combine them through that term and check each candidate conclusion against the merged chain.