BTGModeratorVI wrote: ↑Fri Apr 03, 2020 9:39 am
Is xy > 0?
(1) x - y > -2
(2) x - 2y < -6
Answer:
C
Source: GMATPrep test
Target question: Is xy > 0?
Statement 1: x - y > -2
Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 5 and y = 1. In this case, xy = (5)(1) = 5. So, the answer to the target question is
YES, xy IS greater than 0
Case b: x = 5 and y = -1. In this case, xy = (5)(-1) = -5. So, the answer to the target question is
NO, xy is NOT greater than 0
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x - 2y < -6
Let's TEST some values again.
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 1 and y = 10. In this case, xy = (1)(10) = 10. So, the answer to the target question is
YES, xy IS greater than 0
Case b: x = -1 and y = 10. In this case, xy = (-1)(10) = -10. So, the answer to the target question is
NO, xy is NOT greater than 0
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
IMPORTANT: There’s a useful inequality property that says
If two inequalities have their inequality symbols facing the SAME DIRECTION, we can ADD the inequalities.
We have:
x - y > -2
x - 2y < -6
Take the BOTTOM equation and multiply both sides by -1 to get:
x - y > -2
-x + 2y > 6 [since we multiplied both sides by a NEGATIVE value, we REVERSED the direction of the inequality symbol]
Now ADD the equations to get: y > 4
In other words,
y is POSITIVE
Now take:
x - y > -2
-x + 2y > 6
Take the TOP equation and multiply both sides by 2 to get:
2x - 2y > -4
-x + 2y > 6
Now ADD the equations to get: x > 2
In other words,
x is POSITIVE
Since x and y are both POSITIVE, we know that
xy IS positive
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
