Question
Download Solution PDFRead the following question and decide which of the given statements is/are sufficient.
Question:
Is Y > 0?
Statements:
1. X + Y > 0
2. X - Y > 0
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is indeed option 3) Neither 1 nor 2 is sufficient to answer the question. Here's the explanation:
Statement 1: X + Y > 0
This statement only tells us that the sum of X and Y is greater than 0. However, it doesn't give us any information about the value of Y alone, so we can't determine whether Y is greater than 0. For example, if X = -5 and Y = 6, then X + Y = 1, which is greater than 0, but Y alone is greater than 0.
Statement 2: X - Y > 0
This statement tells us that the difference between X and Y is greater than 0. However, it still doesn't give us any information about the value of Y alone. For example, if X = 10 and Y = 5, then X - Y = 5, which is greater than 0, but Y alone is greater than 0.
Combining both statements, we have:
X + Y > 0 and X - Y > 0
Adding these inequalities, we get:
2X > 0
Therefore, X > 0.
However, we still cannot determine whether Y is greater than 0 or not, since we don't have enough information about the value of Y.
Hence, neither statement alone nor both together are sufficient to answer the question "Is Y > 0?".
The correct answer is option 3) Neither 1 nor 2 is sufficient to answer the question.
Last updated on Jul 19, 2025
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