If x = 5 y, is x > 0?

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

please explain statement (1)
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?

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.

fair enough x>0, thanks

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.

So the answer is D.

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

Answer is D.

Bumping for review and further discussion.

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

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!