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y=1, x can be 0, 1, 2 etc ie. can be greater or less than y y=-1, x can be 2,3,4 etc

insuff

Taking 1) and 2) together x and y has to be positive.

I don't understand why x and y have to be positive? (frankly I don't totally understand how to 'investigate' #2 either, but I kinda see where you're going with your explanation there...)

y=1, x can be 0, 1, 2 etc ie. can be greater or less than y y=-1, x can be 2,3,4 etc

insuff

Taking 1) and 2) together x and y has to be positive.

I don't understand why x and y have to be positive? (frankly I don't totally understand how to 'investigate' #2 either, but I kinda see where you're going with your explanation there...)

From 1 and 2 we know that x = 4y/9 and x>-y

if y is negative, ie. y = -1, x should be -4/9. But that doesnt satisfy eq 2 which says that x should be greater than -y as -4/9 is not greater than -(-1)
So y has to be positive, ie. y = 1, x = 4/9, and x is always > -y

Re: Inequality Challenge [#permalink]
31 Oct 2009, 14:01

(1) 9x=4y Restating statement, we receive x=4/9y, 4/9y<y, while y>0, and 4/9y>y, while y<0. While we cannot determine sign of x or y, (1) alone is NOT SUFFICIENT.

(2) x=-y x>y for all x>0, and x<y for all x<0. But again sign of x or y is not known. So, (2) alone is NOT SUFFICIENT.

Both statements together could be true only if x=y=0.

Re: Is x > y? 1. 9x = 4y 2. x = -y [#permalink]
16 Jan 2013, 23:29

slingfox wrote:

Is x > y?

1. 9x = 4y 2. x = -y

Thank you for this question. here is my solution.

1. \(9x=4y\) also means: (a) \(\frac{x}{y}=\frac{4}{9}\) which means y > x NO! (b) \(\frac{x}{y}=\frac{{-4}}{{-9}}\) which means x > y YES! INSUFFICIENT!

2. \(\frac{x}{y}=-1\) this means: (a) they have the same number but of different sign, one is negative the other is positive BUT we don't know which one is positive or negative (b) x = y = 0 INSUFFICIENT!

in 1 we can reformulate and get x/y= 4/9 this give us 2 case x>0, y>0 in this case x<Y so answer is no x<0, y<0 in this case x>y so answer is yes insuf.....

in 2. we have x>-y this equivalent to x+y>0 so x>y or y>x works here insuff

both statement together we can eliminate the second case were x and y are negative then we will be left with x>0 and y>0 which give us the answer no.

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