Help me solv this?

[disturbedmimi]

If both x and y are positive integers then which of the following expressions must also be even?
i.. y^x-1
ii.y-1
iii. x/2

(a) i only
(b) ii only
(c) iii. only
(d) i and iii only
(e) i, ii, and iii

[everything's eventual]

I feel that some info is missing here.

Lets take (ii) and (iii) into consideration first.

(ii) will be even if y is odd and odd is y is even.

(iii) will be even if x is even and odd is x is odd.

Now considering(i)

y ^ (x-1)

Consider x as odd ( say 3) and y as even ( say 2). So after substituting in the equation we get value as 4 viz even. Now consider, x as even ( say 2) and y as odd ( say 3). Now we get value as 3 viz odd.

According to my solution none of them "must" be even.

[everything's eventual]

I think that the problem states that both x and y are even positive integers. In this case the answer is (d) : (i) and (iii) only

[Shalabh's Quants]

I think that the problem states that both x and y are even positive integers. In this case the answer is (d) : (i) and (iii) only

(iii) is not necessarily an even. Take x=6, then x/2 would be Odd.

[Brent@GMATPrepNow]

If both x and y are positive integers then which of the following expressions must also be even?
i.. y^x-1
ii.y-1
iii. x/2

(a) i only
(b) ii only
(c) iii. only
(d) i and iii only
(e) i, ii, and iii

This question could use some clarification before we try to answer it.

First, there's some uncertainty with ". . . which of the following expressions must also be even?"
Also?
Is one or both of the given variables (x, y) supposed to be even?

Second, there's some possible ambiguity with the first expresson: y^x-1
Does this mean (y^x) - 1 or y^(x-1)?
Some brackets (or even some spaces) would help prevent any ambiguity.

Cheers,
Brent

[everything's eventual]

@ Shalabh...yes very silly of me...in that case we have only (i)