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If y-x > x + y, where x and y are integers, which of the following mus
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If y-x > x + y, where x and y are integers, which of the following mus [#permalink] New post  19 Jan 2022, 06:21
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If \(y-x > x + y\), where x and y are integers, which of the following must be true?

I. \(x < 0\)
II. \(y > 0 \)
III. \(xy > 0 \)

A. I only
B. II only
C. I and II only
D. I and III only
E. II and III only.
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If y-x > x + y, where x and y are integers, which of the following mus [#permalink] New post  19 Jan 2022, 06:35
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carcass wrote:
If \(y-x > x + y\), where x and y are integers, which of the following must be true?

I. \(x < 0\)
II. \(y > 0 \)
III. \(xy > 0 \)

A. I only
B. II only
C. I and II only
D. I and III only
E. II and III only.


Take: y - x > x + y
Add x to both sides: y > 2x + y
Subtract y from both sides: 0 > 2x
Divide both sides by 2 to get: 0 > x

So, statement I must be true, but statements II and III are not necessarily true.

Answer: A

Aside: We can show that statement II is not necessarily true with the following counterexample...
If y - x > x + y, it could be the case that x = -1 and y = -2
In this case, y < 0, which means statement II is not necessarily true

Aside: We can show that statement III is not necessarily true with the following counterexample...
If y - x > x + y, it could be the case that x = -1 and y = 1
In this case, xy < 0, which means statement III is not necessarily true
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Re: If y-x > x + y, where x and y are integers, which of the following mus [#permalink] New post  22 Jan 2022, 15:15
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A is the answer
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Re: If y-x > x + y, where x and y are integers, which of the following mus [#permalink]
22 Jan 2022, 15:15
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