Directions: In the following question, relationships between various terms are expressed in the given statements. These statements are followed by two conclusions. Evaluate the conclusions using the provided statements and choose the correct option.
Statements: P > Q = R ≤ S ≥ T; U ≤ S = V; W < X = V
Conclusions:
I. Q < U
II. X ≥ R
Correct Answer :
Only conclusion II is true
Solution :
The correct option is Only conclusion II is true.
Step-by-step Explanation:
Given Statements:
1. P > Q = R ≤ S ≥ T
2. U ≤ S = V
3. W < X = V
Analyzing Conclusion I: Q < U
From Statement 1, we have: Q = R ≤ S ⇒ Q ≤ S.
From Statement 2, we have: U ≤ S.
Since both Q and U are less than or equal to S (Q ≤ S and U ≤ S), a definitive relation between Q and U cannot be established. Therefore, conclusion I does not follow.
Analyzing Conclusion II: X ≥ R
From Statement 1, we have: R ≤ S.
From Statement 2, we have: S = V.
From Statement 3, we have: V = X.
Combining these relations together:
R ≤ S = V = X ⇒ R ≤ X, which means X ≥ R.
Therefore, conclusion II definitely follows.
Thus, only conclusion II is true.
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