Data Sufficiency

Can someone explain these please?

[quote="UmanG"]Hi,

My answer is B. Explaination is as follow,

1. Y < X,

Here if both X & Y holds the same sign either positive or negative will change the above equation to |X-Y| = |X| - |Y|

And if both have oppsite signs then since Y < X it holds the equation,
|X-Y| > |X| - |Y|

It means this option gives us |X-Y| >= |X| - |Y|.

Stetement 1 alone is NOT SUFFICIENT.

2. XY<0

This equation tells us that X & Y has oppsite signs.

Now for +ve X & -ve Y
|X-(-Y)| > |X| - |(-Y)|
--> |X+Y| > |X| - |Y|-----------(A)
(clearly X+Y in either condition will grater then X-Y.)

Or for -ve X & +ve Y
|(-X)-Y| > |(-X)| - |Y|
--> |-X-Y| > |X| - |Y|
--> |X+Y| > |X| - |Y|-----------(B)
(Same as A)

Thus using stetement 2, in either condition (+ve X & -ve Y, -ve X & +ve Y)we clearly able to say that |X-Y| > |X| - |Y|.

And so stetement 2 alone is SUFFICIENT.[/quote]

Question2:

Statement1 says: y > 1/2(x+10) , in other words the question itself.

statement2: can be contradicted by picking x as 1

y = 5

(x+10)/2 would be 5.5 greater than y

so the answer is A

question 3:

Z^n = 1

what is Z?

statement 1: n<> 0

if n = 2

Z could be +1 or -1

not conclusive

statement 2:

Z>0

not enough by itself.
but this statement with statement 1 means that z = 1

hence c