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by disturbedmimi » Thu Sep 06, 2012 7:01 pm
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
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by everything's eventual » Thu Sep 06, 2012 7:30 pm
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.
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by everything's eventual » Thu Sep 06, 2012 7:32 pm
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
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by Shalabh's Quants » Fri Sep 07, 2012 7:15 am
everything's eventual wrote: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.
Shalabh Jain,
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by Brent@GMATPrepNow » Fri Sep 07, 2012 8:46 am
disturbedmimi wrote: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
Brent Hanneson - Creator of GMATPrepNow.com
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by everything's eventual » Fri Sep 07, 2012 9:14 am
@ Shalabh...yes very silly of me...in that case we have only (i)
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