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## If x and y are positive integers . . .

tagged by: M7MBA

This topic has 1 expert reply and 0 member replies

### Top Member

M7MBA Master | Next Rank: 500 Posts
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#### If x and y are positive integers . . .

Mon Nov 06, 2017 6:49 am
If x and y are positive integers, what is the remainder when y^x is divided by 2?

(1) y^2 is an odd integer.
(2) xy is an even integer.

The OA is A.

Why is A the correct? I don't know how to prove that statement 1 is sufficient.

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
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Mon Nov 06, 2017 12:34 pm
Hi M7MBA,

We're told that X and Y are positive integers. We're asked for the remainder when Y^X is divided by 2.

This question can be solved by TESTing VALUES and/or by using Number Properties. It's worth noting that when dividing an integer by 2, the only possible remainders are 0 and 1.

1) Y^2 is an ODD integer.

Fact 1 tells us that Y^2 is an ODD integer - and we already know that X and Y are both POSITIVE INTEGERS.

(Even)^2 = Even
(Odd)^2 = Odd

This means that Y MUST be ODD. By extension, an ODD number raised to an INTEGER power will ALWAYS be ODD. Fact 1 essentially tells us that Y^X will ALWAYS be an ODD number. Dividing ANY odd number by 2 will ALWAYS give us a remainder of 1.
Fact 1 is SUFFICIENT

2) XY is an EVEN integer.

The information in Fact 2 means that one - or both - of the two integers are EVEN.

IF....
X=2, Y=1, then Y^X = 1 and the answer to the question is 1.
X=1, Y=2, then Y^X = 2 and the answer to the question is 0.
Fact 2 is INSUFFICIENT

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

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