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# Is x > y?

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Is x > y? [#permalink]  31 Oct 2009, 12:41
00:00

Difficulty:

45% (medium)

Question Stats:

43% (02:09) correct 56% (01:16) wrong based on 39 sessions
Is x > y?

(1) 9x = 4y
(2) x = -y
[Reveal] Spoiler: OA

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Last edited by Bunuel on 17 Jan 2013, 03:39, edited 1 time in total.
Renamed the topic and added OA.
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Re: Inequality Challenge [#permalink]  31 Oct 2009, 14:01
(1) 9x=4y
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.

KUDOS if you find it helpful
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Re: Inequality Challenge [#permalink]  31 Oct 2009, 14:04
1
KUDOS
Statement 1: 9x = 4y

x = (4/9)y

Therefore,

If y < 0: x > y
If y > 0: x < y
If y = 0: x = y

Insufficient.

Statement 2: x = -y

If y < 0: x > y
If y > 0: x < y
If y = 0: x = y

Insufficient.

Both Statements Together

(1) 9x = 4y
(2) x = -y

It should be apparent that this is only true iff x = y = 0. Therefore, sufficient!

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Re: Inequality Challenge [#permalink]  31 Oct 2009, 18:26
Thanks for the very clear explanations guys.
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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!

Combine both:
9(-y) = 4y
13y = 0
y=0 and x=0

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Re: Is x > y? 1. 9x = 4y 2. x = -y [#permalink]  17 Jan 2013, 00:35
Expert's post
slingfox wrote:
Is x > y?

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

Another simpler approach could be...

Statement 1-

Say x= 4, & y=9 => x<y => NO.
But if x= -4, & y=-9 => x>y => Yes.

Insufficient

Statement 2-

Say x= 1, & y=-1 => x>y => Yes.
But if x= -1, & y=1 => x<y => No.

Insufficient

Statement 1, & 2 together-

Only one case is possible => x=y=0. Answer C.

-Shalabh Jain
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Re: Is x > y? 1. 9x = 4y 2. x = -y   [#permalink] 17 Jan 2013, 00:35
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