is x > |y|?

okay, here is how I did it.

by picking different numbers and trying positive and -ve values

Given in problem - x+y>0

Option 1: x>y

1)Pick a +ve numbers for both

x=8, y=7
x>|y|

2)Pick one positive and one negative,

I ) x=8, y=-7 (making sure x+y>0 and x>y)
we get x>|y|. [Note you cannot pick y=-9 or anything since x+y has to be > 0, given in the problem.

II) We cannot take any other combinations like x=-8,y=7 or x=0,y=-1 or x=-1,y=0 since they do not satisfy given conditions.

Seems like this option gives us only one answer x>|y|

So SUFFICIENT

Option 2:y<0


1)x=8, y = -7 [already tried this one and yields the answer as yes

2)x=-8, y=-7 [cant pick these numbers for obvious reasons]


this option gives us only one answer x>|y|

SUFFICIENT

Ans is D.

Anyone has any better method than picking numbers. This method seems a little risky, for we really need to trust ourselves on picking all right numbers to test on. Also its laborious. But right now, I know only one way to solve it

vivekjaiswal wrote:If x + y >0, is x > |y|?
(1) x > y
(2) y < 0


OA is [spoiler](D)[/spoiler]

I dont prefer picking numbers as its time consuming. Here is how I did it.

Given, x + y > 0 ie x > - y.

Question is asking x > |y|. So rephrase is,

x > y (if y is positive) or x > -y (if y is negative)

1. We got the rephrase
2. We already know that x > - y. We need to know whether Y is negative. Stmt 2 says that

Hence D

Can you please elaborate you algebric expression for 2 part
We already know that x > - y. We need to know whether Y is negative How knowing Y is negative will solve it

navdeepbajwa wrote:Can you please elaborate you algebric expression for 2 part
We already know that x > - y. We need to know whether Y is negative How knowing Y is negative will solve it

if y is a negative number, |y| is nothing but -(-y). Let y = -2. Absolute value of y, |y| = -(-2).

Rephrase of the question is nothing but x > -(-y) (this is the same as |y|). Since we know that x > - y (based on x+y>0), all we need is another negative sign; in other words, whether y is negative..

Hope its clear now.

Hi Crackgmat 2007
Is this makes sense
If x + y >0, is x > |y|?
(1) x > y
(2) y < 0

Since x > |y|
which means
-x<y<x by def

from statement 1 since x>y
and x+y>0 x>-y
so -x<y<x
Statement 1 is sufficient
from statement 2 since y<0
and x+y>0 x>-y
from stem x>-y and y<0

x>-(-y)
so x>y
and x>-y
so -x<y<x
Statement 2 is sufficient

navdeepbajwa wrote:Hi Crackgmat 2007
Is this makes sense
If x + y >0, is x > |y|?
(1) x > y
(2) y < 0

Since x > |y|
which means
-x<y<x by def

from statement 1 since x>y
and x+y>0 x>-y
so -x<y<x
Statement 1 is sufficient
from statement 2 since y<0
and x+y>0 x>-y
from stem x>-y and y<0

x>-(-y)
so x>y
and x>-y
so -x<y<x
Statement 2 is sufficient

This appears to be fine. But, I would try to make things as simple as possible. Specially the below one, which in other words we can rephrase as I did earlier. But if it works for you, go for it. All we need to solving quickly & correctly.

Since x > |y|
which means
-x<y<x by def

If x + y >0, is x > |y|?
(1) x > y
(2) y < 0

Hi guys!

Let's use some critical reasoning and maybe a bit of picking numbers too. Let's first focus on the question stem and the info in the question stem, trying to make deductions.

The question tells us that the sum of x and y is positive. Therefore, either x or y (or both) is positive; at least one of them must be positive (as punitkaur pointed out). This must be true because if they were both negative, their sum would be negative. The question is asking:

Is x >|y|?

Or Is left side > right side?

Because the right hand side is an absolute value, it must be positive (or zero). Therefore, if the answer to the question is "yes" it would mean x is positive for sure. (Because absolute value is always positive or zero, if x is bigger than the absolute value of something, then x is necessarily positive).

Let's look at statement 2 first: it tells us y is negative; therefore, x must be positive (remember that at least one of them is positive). Furthermore, because their sum is positive, x must be larger than the absolutve value of y. Here, you can pick numbers quickly to confirm this. If x is 8 and y is -5, then their sum is positive. But if x is 5 and y is -8, their sum is negative, which would betray the information given in the question stem. (That is to say, it is impossible for x to be a "small" positive number and y a "large" negative number without violating "x+y>0" given in the question stem). So, the answer to the question is "definitely yes". Statement 2 is sufficient.

For statement 1: x is bigger than y. Remember our deduction that at least one out of x and y is positive. So if x is bigger than y, and at least one is positive, there are two possible cases:

case 1: x is positive and y is negative (ie, one positive and one negative)
This case is the same as statement 2: x must have a larger absolute value than y. (Again, x is positive and y is negative but because their sum is positive x must be bigger than y.) In this case, the answer to the question is "yes" x is bigger than the absolute value of y.

case 2: x is a larger positive number than y, which is also a positive number (ie, both positive)
In this case, x is clearly larger than the absolute value of y, and again the answer to the question is "yes".

Under both possible cases, we get a "yes" answer to the question. Therefore, statement 1 yields a "definitely yes" answer to the question. Statement 1 is sufficient.

Because both statements are independenly sufficient, we should choose D.