If |x|=|2y| what is the value of... from Advanced GMAT Quant

[atharshiraz]

So I am trying to figure out this question on page 105 of Advanced GMAT Quant (Strategy guide supplement).

It says :
If |x|=|2y| , what is the value of x-2y?
(1) x+2y = 6
(2) xy >0


Now from my studies of absolutes we know that if :
|x|=2
then there are two scenarios :
x=2 or -x=2

But what if there are absolute signs on both sides (LHS and RHS) then should it not be :
x=2y (regular case given in the problem)
-x=2y (negate the LHS)
in other words this is the same as
x=-2y (given in the problem)?

Now when x is +ve and y is -ve.
then x-2y = +x - (-2y) ;
now since x=-2y :
= +x - (x) = 0
And also since x=2y:
= +x -(-x) = 2x which is the only version listed in the table (that says : "2x (which is +)")

Why are we picking 2x and not zero as a possible answer for x-2y ? The table given only assumes that x =2y and does not consider x=-2y apparently.

The same goes for when both x and 2y are +ve:
=x-2y=+x-(2y)= +x-(x)=0
and
+x -(2y)= +x - (-x)= 2x?
but the table on page 105 lists only zero as a value. May I ask why ?

The answer given is that both (1) and (2) are sufficient on their own (or D).

[RonPurewal]

i'm having a hard time following everything in your post. basically, there are too many abbreviations and not enough words, so i really can't tell what is going on.

but, i can tell you that you're considering a bunch of cases that are actually impossible. also, there are algebraic errors.

for instance, here:

Now when x is +ve and y is -ve.
then x-2y = +x - (-2y) ;

^^^ this is wrong; the left-hand side is x - 2y, but the right-hand side is x + 2y. (when you subtract a negative, that's addition.)

now since x=-2y :
= +x - (x) = 0
And also since x=2y:
= +x -(-x) = 2x which is the only version listed in the table (that says : "2x (which is +)")

^^^ here's where the real problem is.
you just got done saying that x is positive and y is negative.
... if that's true, then you can't have x = 2y, because x would be positive while 2y would be negative. so, only x = -2y would remain.

for each possible pair of signs, the same thing is going to happen: only one of the two versions will actually be possible. to determine which one, just think about signs; you don't need any "rules" to figure this out.
i.e.,
if x and y have the same sign (both positive or both negative), then x = 2y works, but x = -2y is impossible.
if x and y have opposite signs, then x = -2y works, but x = 2y is impossible.

give it a shot again.