GMAT Prep questions... Explanation please!!!

[LunaticAnagha]

Positive integers X, Y and Z are such that; X is a factor of Y and Y is a factor of Z. Is Z even?
1. XZ is even
2.Y is even
ANSWER: Each statement alone is sufficient.

I understand if Y is even as Z has to be even as its a multiple of Y. But how is statement 1 sufficient? Any quick explanation?

ALSO

If X is positive which of the following can be correct orders:
1.X^2<2X<1/X
2.X^2<1/X<2X
3.2X<X^2<1/X

ANSWER: 1 and 2 both are correct.

1 is clear. How is 2 correct? Even if I plug Integers or Fractions, its not giving me order no 2.

Please HELP!!!

[NikolayZ]

hey there !
1)
stmt 2 is an easy one.

stmt 1:
xz is even.
So, either one of those is even or they are both even.
Notice that x is a factor of y, and y is a factor of y.
If both ==> z is even.
If just z is even, so z is even.
If x is even, and is a factor of y, then y is even either. Therefore, if y is a factor of z, z is got to be even too.

2)
As for the second inequality to be true. Try plugging in 8/10 or 9/10.

[LunaticAnagha]

Thanks a ton...
That really helped...
The 1st problem is clear now..

In the second one, is there a trick or method of plugging some special values so that we can cover all possibl outcomes???

I tried positive integers and fractions, still missed this one