Gmat prep - x and y positive

[g.shankaran]

Are x and y both positive?

1) 2x- 2y = 1
2) x/y > 1

The ans is C.

But I thought it was E. I went wrong somewhere, can you please correct.

This was my explanation.

from 1 . x-y = 1/2
from 2. we have x > y

so taking values x = 1/4 y= -1/4 which satisfies both the statements, then x and y are not positive.

if we take x = 3/2 and y = 1, then both x and y are positive.

So, I thought the answer would be E. Please help..

[vineeshp]

Ya even i got this one wrong.

The important point you missed from statement 2 is x/y > 1 means that x/y is positive. which means either both x and y are positive or both x and y are negative. and also that x > y.

This extra information helps us eliminate the additional cases you mentioned from statement 1. Both have to be of the same sign.

[Geva@EconomistGMAT]

Inequalities have an issue with multiplying by a negative value - when multiplying an inequality by a negative value, you must flip the sign. but when multiplying an inequality by a positive value, you must leave the sign in the same direction.

Many GMAT inequalities questions (esp. DS) will play on this:

When moving from x/y>1 to x>y, you are basically multiplying both sides of the inequality by 'x'. The problem is that you do not know whether x is positive or negative, and thus do not know what to do with the sign:
If x is positive, then the sign maintains the same direction, and x>y.
If x is negative, then the sign is flipped, and x<y. (this to denote the situation where x and y are negative, but x is a smaller, "more negative" valu than y, e.g. x=-6, y=-2).

Thus, you cannot decide that stat. (2) is sufficient because you cannot multiply the inequality by x until you know x's sign, and know what to do with the sign. The main takeaway from this question is this: Beware of multiplying inequalities by an unknown variable - there are two scenarios, unless the question somehow tells you that x is positive or x is negative.

the combination is sufficient because 2x=2y+1, or x=y+1/2. x and y need to be positive or negative together from stat. (2), bu if they are both negative, it follows that x must be smaller than y - which does not coincide with x=y+1/2.

[kevincanspain]

You could also say that since x = y + 1/2 and x/y > 1, (y + 1/2)/y > 1 i.e. 1/(2y) > 0
Thus y > 0