Interesting question II.II wrote:If x, y, and z are positive integeres, is x-y odd ?
(1) x = z^2
(2) y = (z - 1)^2
Thanks.
This is the very essence of Data Sufficiency. Within 10-20 seconds you should be able to eliminte A / B and D as possible answers.
Why?
Since the relationship being tested requires us to look for the outcome of X - Y, it becomes obvious that Statement 1 and Statement 2 by themselves are not going to pull it off (they only have X and Z, and Y and Z respectively.
If on test-da your time is running out (or even if it is not), something like this is really going to help you.
Now to decide between C and E:
Together:
X - Y = Z^2 - (Z-1)^2.................(This is the classic difference of squares rule)
Therfore, X- Y = ( Z - (Z-1)) ( Z+(Z+1))
which is then = (Z - Z +1) (2Z+1)
which simplifies as = (1) (2Z +1) = 2Z +1
The odd number kingdom is defined as 2(integer) + 1 OR 2(Integer) - 1.
Since Z is an integer, 2Z+1 MUST be odd. This answers the question with an ALWAYS YES, and hence sufficiency.
C is the answer.
