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# If x = 5 y, is x > 0?

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Manager
Joined: 10 Feb 2011
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If x = 5 y, is x > 0?  [#permalink]

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14 Mar 2011, 15:34
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63% (01:29) correct 37% (01:34) wrong based on 91 sessions

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If x = 5 – y, is x > 0?

(1) x > 5 + y.
(2) y < 0.
Intern
Joined: 27 Sep 2010
Posts: 9
Re: 286. If x = 5 – y, is x > 0? (1) x > 5 + y. (2) y < 0.  [#permalink]

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14 Mar 2011, 16:33
given: x=5-y. Is x>0
st(1) 5-y>5+y, y<0. Since we don't know how much y is less than 0 - we cannot deduce about x +ve Or -ve from x>5+y. Not Sufficient.
st(2) y<0 and y=5-x ---> 5-x<0 OR x>5 Hence x>0 Sufficient

IOM
banksy wrote:
286. If x = 5 – y, is x > 0?
(1) x > 5 + y.
(2) y < 0.
Math Expert
Joined: 02 Sep 2009
Posts: 61544
Re: 286. If x = 5 – y, is x > 0? (1) x > 5 + y. (2) y < 0.  [#permalink]

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14 Mar 2011, 16:36
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banksy wrote:
286. If x = 5 – y, is x > 0?
(1) x > 5 + y.
(2) y < 0.

If x = 5 – y, is x > 0?

Given: y = 5 - x.

(1) x > 5 + y --> x > 5 + (5 - x) --> x > 5. Sufficient.

(2) y < 0 --> 5 - x < 0 --> x > 5. Sufficient.

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Re: 286. If x = 5 – y, is x > 0? (1) x > 5 + y. (2) y < 0.  [#permalink]

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14 Mar 2011, 16:40
x= 5-Y and x>5+y this implies.. y= -ve and x= +ve

x=5-y and y = -ve implies that x=+ve

ans d
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Re: 286. If x = 5 – y, is x > 0? (1) x > 5 + y. (2) y < 0.  [#permalink]

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14 Mar 2011, 16:51
per condition given it's also y<0 and y can be -100 for example;
by plugging x=5-y into x>5+y, we get 5-y>5+y and y<0. So if y=-100, x can be -90 as -90>5+(-100). How it comes this is Sufficient?
Bunuel wrote:
banksy wrote:
286. If x = 5 – y, is x > 0?
(1) x > 5 + y.
(2) y < 0.

If x = 5 – y, is x > 0?

Given: y=5-x.

(1) x > 5 + y --> x>5+(5-x) --> x>5. Sufficient.

(2) y < 0 --> 5-x<0 --> x>5. Sufficient.

Math Expert
Joined: 02 Sep 2009
Posts: 61544
Re: 286. If x = 5 – y, is x > 0? (1) x > 5 + y. (2) y < 0.  [#permalink]

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14 Mar 2011, 17:00
zaur2010 wrote:
per condition given it's also y<0 and y can be -100 for example;
by plugging x=5-y into x>5+y, we get 5-y>5+y and y<0. So if y=-100, x can be -90 as -90>5+(-100). How it comes this is Sufficient?
Bunuel wrote:
banksy wrote:
286. If x = 5 – y, is x > 0?
(1) x > 5 + y.
(2) y < 0.

If x = 5 – y, is x > 0?

Given: y=5-x.

(1) x > 5 + y --> x>5+(5-x) --> x>5. Sufficient.

(2) y < 0 --> 5-x<0 --> x>5. Sufficient.

Yes, you can substitute $$x$$ in $$x>5+y$$ to get: $$5-y>5+y$$ --> $$y<0$$ (though it's better to substitute $$y$$, not $$x$$, because it gives the answer right away as shown in the solution). Now, as $$y<0$$ we have that $$x=5-negative=5+positive=positive$$, for example: $$x=5-(-100)=5+100=105$$.

Hope it's clear.
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Re: 286. If x = 5 – y, is x > 0? (1) x > 5 + y. (2) y < 0.  [#permalink]

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14 Mar 2011, 17:04
fair enough x>0, thanks
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Re: 286. If x = 5 – y, is x > 0? (1) x > 5 + y. (2) y < 0.  [#permalink]

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14 Mar 2011, 18:16
From (1) we have :

x > 5 + 5 - x => x > 5 so sufficient

From (2) we have :

y < 0, so x = 5 - ( a negative number) will be always positive. Hence sufficient.

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Re: 286. If x = 5 – y, is x > 0? (1) x > 5 + y. (2) y < 0.  [#permalink]

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14 Mar 2011, 18:19
1) Sufficient
x> 5+y => x>5+5-x
=> 2x>10 => x>5 = x>0

2) Sufficient
x = 5- y
given y <0, so no matter what the value of y is x = 5 - (-ve number)= 5+postive number >0

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Re: If x = 5 y, is x > 0?  [#permalink]

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23 Feb 2014, 04:23
Bumping for review and further discussion.
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Re: If x = 5 y, is x > 0?  [#permalink]

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13 Mar 2016, 07:06
Nice Question...
Classical equality inequality relation..
Here Statement is sufficient as X>5+y and Y=5-x => x>5 =>Sufficient
Statement 2 is sufficient for the same reason
Hence D
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If x = 5 y, is x > 0?  [#permalink]

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23 Jan 2020, 02:57
In this question, we are to find out if x>0. Since x = 5-y, the question becomes “Is 5-y>0?” which can be simplified to “Is 5>y?” or “Is y<5?”.

So, the question we are trying to answer is “Is y<5?”.

From statement I alone, x>5+y. Substituting the value of x, we have 5-y > 5+y which gives us 2y<0 on simplification. Since 2 is a positive value, the only way in which 2y is less than ZERO is if y<0. So, from statement I alone, y<0. This essentially means y<5 as well.

Statement I is sufficient to answer the question. Answer options B, C and E can be eliminated. Possible answer options are A or D.

From statement II alone, y<0. Clearly, if y<0, y has to be less than 5. Statement II alone is sufficient.
Answer option A can be eliminated. The correct answer option is D.

Use the question data and the question stem to rephrase the question asked, to a simpler question. The rephrased question will tell you what to look for in the statements.

Here are a few Quant resources for your reference:

8 Solid Ways To Get A 50-51 Raw Score In GMAT Quant

The Ultimate Guide to GMAT Inequalities

Hope that helps!
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If x = 5 y, is x > 0?   [#permalink] 23 Jan 2020, 02:57
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