ktrout2020 wrote:Is xy > 0?
(1) x - y > -5
(2) x - 2y < -7
Source: Veritas
Target question: Is xy > 0
Statement 1: x - y > -5
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 1 and y = 1, in which case
xy = (1)(1) = 1. So, xy > 0
Case b: x = 1 and y = -1, in which case
xy = (1)(-1) = -1. So, xy < 0
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Statement 2: x - 2y < -7
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = -10 and y = -1, in which case
xy = (-10)(-1) = 10. So, xy > 0
Case b: x = -10 and y = 1, in which case
xy = (-10)(1) = -10. So, xy < 0
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that x - y > -5, which we can rewrite as -5 < x - y
Statement 2 tells us that x - 2y < -7
Since -7 < -5, we can COMBINE the inequalities to get: x - 2y < -7 < -5 < x - y
Focus on x - 2y < x - y
Subtract x from both sides: -2y < -y
Add 2y to both sides: 0 < y
So, y is POSITIVE, but there's no info about x.
Consider these two conflicting scenarios:
Case a: x = 2 and y = 5, in which case
xy = (2)(5) = 10. So, xy > 0
Case b: x = -1 and y = 3.5, in which case
xy = (-1)(3.5) = -3.5. So, xy < 0
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
