If y-x x + y, where x and y are integers, which of the following mus

Question

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.

BrentGMATPrepNow · Answer

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

Carcass · Answer

screenshot.276.jpg A is the answer

KarishmaB · Answer

Solving this question comes down to just understanding the basics of algebra. Given: y-x > x + y We can cancel off y from both sides to get: 2x < 0 which is same as x < 0 What does it mean when we say "we can cancel off y from both sides?" It means that it has no impact on the inequality whatsoever. Say if we are given x < 0, if I add y to both sides, I get y + x < y (the inequality doesn't change) If I add 2z on both sides, I get 2z + y + x < 2z + y (the inequality still doesn't change) Hence y can be anything, it doesn't matter. So the only thing y-x > x + y tells us is that x < 0 Answer (A)

If y-x > x + y, where x and y are integers, which of the following mus

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