BTGModeratorVI wrote: ↑Thu Jun 11, 2020 8:41 am
If y < x < 0, which of the following CANNOT be true?
A. xy > 2
B. x − y > 2
C. x/y > 2
D. x + y > −2
E. y/x < 2
Answer:
C
Source: Economist GMAT
First recognize that, if y is NEGATIVE, then we know that
2y < y
If you're not convinced, here's a quick proof:
Given: y < 0
Add y to both sides to get: y + y < y
Simplify:
2y < y
Now let's see why answer choice C (x/y > 2) cannot be true
Take x/y > 2
Multiply both sides by y to get:
x < 2y [aside: y is negative, so we just multiplied both sides of the inequality by a negative value. Whenever we do this, we must reverse the direction of the inequality]
Now combine this inequality with the one we created earlier (
2y < y)
We we do so, we get: x < 2y < y
If we ignore the 2y in the middle, we get
x < y, HOWEVER this
contradicts the given information that says
y < x < 0.
As such, answer choice C can never be true.
Answer: C
