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Math Expert V
Joined: 02 Sep 2009
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Difficulty:   25% (medium)

Question Stats: 65% (00:54) correct 35% (00:49) wrong based on 313 sessions

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Is $$x \gt y$$?

(1) $$|x| \gt |y|$$

(2) $$\frac{x}{y} \gt 0$$

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Math Expert V
Joined: 02 Sep 2009
Posts: 58443

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Official Solution:

(1) $$|x| \gt |y|$$. This statement just tells us that $$x$$ is further from zero than $$y$$, which is not sufficient to say whether $$x \gt y$$. Consider: $$x=2$$, $$y=1$$ and $$x=-2$$, $$y=1$$. Not sufficient.

(2) $$\frac{x}{y} \gt 0$$. This statement tells us that $$x$$ and $$y$$ have the same sign, either both are negative or both are positive. Not sufficient.

(1)+(2) If from (2) $$x$$ and $$y$$ are both negative then from (1) we would have $$-x \gt -y$$ which is the same as $$x \lt y$$ (answer NO). But if from (2) $$x$$ and $$y$$ are both positive then from (1) we would have $$x \gt y$$ (answer YES). Not sufficient.

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Quick question:

From (1)+(2) If from (2) x and y are both negative then from (1) shouldn't we have |-x|> |-y| which will give us x>y. So won't it be sufficient with both statements?
Math Expert V
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IntheHunt wrote:
Quick question:

From (1)+(2) If from (2) x and y are both negative then from (1) shouldn't we have |-x|> |-y| which will give us x>y. So won't it be sufficient with both statements?

Absolute value properties:

When $$x \le 0$$ then $$|x|=-x$$, or more generally when $$\text{some expression} \le 0$$ then $$|\text{some expression}| = -(\text{some expression})$$. For example: $$|-5|=5=-(-5)$$;

When $$x \ge 0$$ then $$|x|=x$$, or more generally when $$\text{some expression} \ge 0$$ then $$|\text{some expression}| = \text{some expression}$$. For example: $$|5|=5$$.

So, if both x and y are negative, then |x| = -x and |y| = - y.

Theory on Abolute Values: math-absolute-value-modulus-86462.html
Absolute value tips: absolute-value-tips-and-hints-175002.html

DS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=37
PS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=58

Hard set on Abolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html

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GMAT 1: 710 Q41 V46 Show Tags

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IntheHunt wrote:
Quick question:

From (1)+(2) If from (2) x and y are both negative then from (1) shouldn't we have |-x|> |-y| which will give us x>y. So won't it be sufficient with both statements?

I thought the same at first.

Another way to look at it:

If |x| > |y|, test values for x and y both being positive, as well as x and y both being negative.

If negative:

|-2| > |-1|

This would mean that y (which is -1) is greater than x (which is -2).

If positive:

|2| > |1|

This would mean that x (which is 2) is greater than y (which is 1).

Therefore, the answer is E.
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Joined: 12 Jan 2013
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Bunuel wrote:
Official Solution:

(1) $$|x| \gt |y|$$. This statement just tells us that $$x$$ is further from zero than $$y$$, which is not sufficient to say whether $$x \gt y$$. Consider: $$x=2$$, $$y=1$$ and $$x=-2$$, $$y=1$$. Not sufficient.

(2) $$\frac{x}{y} \gt 0$$. This statement tells us that $$x$$ and $$y$$ have the same sign, either both are negative or both are positive. Not sufficient.

(1)+(2) If from (2) $$x$$ and $$y$$ are both negative then from (1) we would have $$-x \gt -y$$ which is the same as $$x \lt y$$ (answer NO). But if from (2) $$x$$ and $$y$$ are both positive then from (1) we would have $$x \gt y$$ (answer YES). Not sufficient.

Hi Bunuel,

I am slightly confused. In 1 we say X is further than Y from zero (which is highlighted in the attached PNG file - hopefully that is the correct representation).
In 2 we say that X and Y are the same sign.

So together, wouldn't it be that -X < -Y (i.e. further to the left of the number line and further than Y from zero) and X > Y (i.e. further than Y from zero to the right)?

Thanks
>> !!!

You do not have the required permissions to view the files attached to this post.

Math Expert V
Joined: 02 Sep 2009
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zizzi wrote:
Bunuel wrote:
Official Solution:

(1) $$|x| \gt |y|$$. This statement just tells us that $$x$$ is further from zero than $$y$$, which is not sufficient to say whether $$x \gt y$$. Consider: $$x=2$$, $$y=1$$ and $$x=-2$$, $$y=1$$. Not sufficient.

(2) $$\frac{x}{y} \gt 0$$. This statement tells us that $$x$$ and $$y$$ have the same sign, either both are negative or both are positive. Not sufficient.

(1)+(2) If from (2) $$x$$ and $$y$$ are both negative then from (1) we would have $$-x \gt -y$$ which is the same as $$x \lt y$$ (answer NO). But if from (2) $$x$$ and $$y$$ are both positive then from (1) we would have $$x \gt y$$ (answer YES). Not sufficient.

Hi Bunuel,

I am slightly confused. In 1 we say X is further than Y from zero (which is highlighted in the attached PNG file - hopefully that is the correct representation).
In 2 we say that X and Y are the same sign.

So together, wouldn't it be that -X < -Y (i.e. further to the left of the number line and further than Y from zero) and X > Y (i.e. further than Y from zero to the right)?

Thanks

|x| > |y| means that x is further from zero than y: x from y NOT -x from -y.
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Hi Bunuel

Ok let me try again (edited this question)
Here is my question -
From Statement 2, can i not say x>0 ?

Thanks
Rahul

Originally posted by itsrahulmohan on 31 Aug 2018, 17:41.
Last edited by itsrahulmohan on 01 Sep 2018, 20:10, edited 1 time in total.
Retired Moderator G
Joined: 11 Aug 2016
Posts: 370

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My 2 cents.

Statement 2 tells us that both x & Y are of the same sign. they could both be +ve or both be -ve.
Statement 1 tells us that the magnitude of X is greater than Y.

on combining Statement 1 and Statement 2

Case 1:Both x & y are +ve.(this is the one you took as example)
We open the modulus.
X>Y. the answer to our question is Yes.

Case 2: Both x & y are -ve.

ON opening the modulus, we get
-X>-Y
multiplying by -1 on both sides
X<Y. The answer to our question is No

Here, we get two different answers to our questions. Hence E is correct.

itsrahulmohan wrote:
Hi Bunuel

From Statement 2, can i not say x>0 and tie this with statement no.1 to confirm x and y are both positive, therefore answer C?
cos positive 3 is greater than positive 2 as per statement 1

Thanks
Rahul

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