Positives and Negatives

[MichelleK617]

Are x and y both positive?

(1) 2x - 2y = 1

(2) x/y > 1

I couldn't really figure out a solid way of doing this problem and chose E. Correct Answer is C.

for (1), I started out by simplifying to x - y = 1/2 and then to x = 1/2 + y. From this, I decided that when x is positive, y had to be greater than 1/2. If x is negative, y has to be negative. NS.

for (2), I simplified - not sure if it was making it more complicated - the statement to x > y for when x > 0 and then x < -y for when x <0 . When x > 0, y can be either positive or negative. When x < 0, y has to be positive. NS.

I know I'm totally off the track here and there is no way I will be able to put these two statements together without confusing myself even further. Can someone show me how to do this easily? Thanks.

[Chelsey Cooley]

This problem just cries out for case testing. If you work through a DS problem abstractly, you run the risk of making a mistake in your thinking - specifically, making a wrong assumption about what can and can't happen. Now, you can possibly avoid that by getting really good at making abstract leaps of reasoning. Easier said than done. But if you do good case testing, you actually become immune to that type of mistake. That's huge.

Here's what it looks like (and try it yourself before reading further!)

1.
Case 1: x = 10, y = 9.5 - yes
Case 2: x = -10, y = -10.5 - no
NS

2.
Case 1: x = 10, y = 9.5 (reusing cases can speed you up, but it can also be confusing. If you find it confuses you, it isn't worth it.) - yes
Case 2: x = -10, y = -2 (but, you might notice that our original Case 2 no longer works... hmm.) - no
NS

1 + 2.
Case 1: x = 10, y = 9.5 (this is why it's good to reuse cases sometimes...) - yes
At this point, your specific goal is to find a case that would give us a 'no' answer to the question. That will definitely involve some logical reasoning. Your thinking might go like this: 'the only possibility that might work is one where both x and y are negative. Can I find a case that fits both statements, where x and y are both negative? To fit statement 2, x would have to be more negative than y, like -2 and -1. But if x is more negative than y, then 2x - 2y will be negative! It can't come out to positive 1. So, it's actually impossible to construct an (x,y) pair that fits both statements, where x and y are negative. I'm stuck with just the positive case. That means that together, the statements are sufficient.'

I hadn't solved this problem before seeing your question, and the first time I tried it, I got overconfident and worked through it logically. I got the same answer as you (E) and started wondering if the official answer was wrong! I only worked it out when I tried testing cases. I have a 51 on the math section of the GMAT - so if that happens to me, it can happen to anyone. If that doesn't sell you on case testing, nothing will.

[sahilk47]

Hi Chelsey

Can we solve the question the following way (essentially note the boldface part):

Stat 1: 2x - 2y = 1
=> x - y = 1/2
=> x = y + 1/2
y can take any value and accordingly x can be positive or negative. For example y = -1/4 but x = 1/4 Thus Insufficient.

Stat 2: x/y > 1
=> x and y can be both positive in which case x > y and x and y can be both negative in which case x < y Thus Insufficient.

Taking both statements together:

If both x and y are positive then of course life is great.

If both x and y are negative then for x/y >1 to hold true we must have x < y < 0
x < y < 0 gives us:

x - y < 0

But we know x - y = 1/2 Since we are getting contradictory result, so we can ignore this case and thus sufficient. Answer (C)

Thank you.

[RonPurewal]

yes.