Target question: Is xy > 0?abhasjha wrote:Is xy > 0?
(1) x - y > -2
(2) x - 2y > -6
Statement 1: x - y > -2
Let's multiply both sides of the inequality by -1 to get: y - x < 2
This tells us that y is less than 2 greater than x.
Does this provide enough information to answer the target question? No.
Consider these two possible cases x and y that satisfy the given inequality:
Case a: x = 1, y = 1, in which case xy > 0
Case b: x = -1, y = 0.5, in which case xy < 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x - 2y > -6
Let's multiply both sides of the inequality by -1 to get: 2y - x < 6
This tells us that 2y is less than 6 greater than x.
Does this provide enough information to answer the target question? No.
Consider these two possible cases x and y that satisfy the given inequality:
Case a: x = 1, y = 1, in which case xy > 0
Case b: x = -1, y = 0.5, in which case xy < 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 says that y is less than 2 greater than x
Statement 2 says that 2y is less than 6 greater than x
Since both conclusions are very similar, and since each statement alone was INSUFFICIENT, I suspect that the combined statements are not sufficient, so I'll start looking for some values that prove insufficiency.
Here are two sets of values:
Case a: x = 1, y = 1, in which case xy > 0
Case b: x = -1, y = 0.5, in which case xy < 0
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer = E
Cheers,
Brent
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