Number Properties...

[ii]

If x, y, and z are positive integeres, is x-y odd ?

(1) x = z^2
(2) y = (z - 1)^2

Thanks.

[dshelly77]

I think the answer is C.

Question: is x-y = odd
Rationale

1) x=z^2
if z=even, then x=Even
If z=odd, then x=Odd
Therefore, Not sufficient

2) y=(z-1)^2
If z=even, then y=odd
If z=odd, then y=even
Therefore, not sufficient

Together:
x=z^2
y=(z-1)^2

x-y=z^2-(z-1)^2
x-y= z^2-(z^2-2z+1)
x-y=z^2-z^2+2z-1
x-y=2z-1

Since any number times an even number yields and even number, and an even number minus 1 yields an odd number, the x-y=odd.

Therefore the answer is c.
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[rfernandez]

Nice work, dshelley77! I'll just add one point:

You can conclude right away that (1) in insufficient simply because it only mentions x and z and says nothing about y. Ditto for (2): it relates y and z, but says nothing about x.

Rey

[try-it]

I differ here, the question asks that whether x-y is odd or not, if a statement can establish a define yes or no, it should be sufficent.

Let see

Statement 1 says x= Z ^ 2

Now there are two cases

a) Z can be odd, since odd. odd = odd so X is also odd. Now odd- odd = even so answer is no.
b) Z can be even, since even.even = even so X is also even. Now even-even = even so answer is again no.

So since answer is no in all cases the staement is sufficent to answer the question.

Am i missing something here?

[Guest]

[quote="try-it"]

[JonathanSchneider]

try-it, you're missing the fact that the question asks for x-y, not x-z.