If y<x<0, which of the following CANNOT be true?

[BTGModeratorVI]

If y < x < 0, which of the following CANNOT be true?

A. x·y > 2
B. x−y > 2
C. x/y > 2
D. x+y > −2
E. y/x < 2

Answer: C
Source: Economist GMAT

[Brent@GMATPrepNow]

If y < x < 0, which of the following CANNOT be true?

A. x·y > 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

Cheers,
Brent

[Scott@TargetTestPrep]

If y < x < 0, which of the following CANNOT be true?

A. x·y > 2
B. x−y > 2
C. x/y > 2
D. x+y > −2
E. y/x < 2

Answer: C
Source: Economist GMAT

We can let x = -1 and y = -4. So we have:

A. xy = (-1)(-4) = 4 > 2 ? → Yes

B. x - y = (-1) - (-4) = 3 > 2 ? → Yes

C. x/y = (-1)/(-4) = 1/4 > 2 ? → No

Since we are using actual numbers, let’s make sure the last two choices are also true before we can determine whether C is the correct answer.

D. x + y = (-1) + (-4) = -5 > -2 ? → No

E. y/x = (-4)/(-1) = 4 > 2 ? → Yes

Since both C and D give a “No” answer, we need to analyze them further. One way we can do that is to use another pair of numbers for x and y. So let’s let x = -0.5 and y = -1 and test them on choices C and D:

C. x/y = (-0.5)/(-1) = 0.5 > 2 ? → No

D. x + y = (-0.5) + (-1) = -1.5 > -2 ? → Yes

We can now see that the correct answer must be C.

Answer: C