Problem Solving

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