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If x and y are positive integers , is x^y + (x^x)(y^y) odd?(DS)

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If x and y are positive integers , is x^y + (x^x)(y^y) odd?(DS)  [#permalink]

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New post 09 Sep 2018, 07:57
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If x and y are positive integers , is x^y + (x^x)(y^y) odd?
1) x+2y is odd
2) y+2x is odd
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Affiliations: All Day Test Prep
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Posts: 72
Location: United States (IL)
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Re: If x and y are positive integers , is x^y + (x^x)(y^y) odd?(DS)  [#permalink]

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New post 09 Sep 2018, 15:28
divyajoshi12 wrote:
If x and y are positive integers , is x^y + (x^x)(y^y) odd?
1) x+2y is odd
2) y+2x is odd


To start, just think of this as adding together two numbers where our terms are x^y & (x^x)(y^y). Our even/odd rules say that:

E + E = E
E + O = O
O + O = E

So the only way to get an odd is if one of our terms is even and the other is odd.

1) 2y will always be even since anything times an even(2 in this case) is even. therefore x has to be odd. y itself can be even or odd.

x^y will always be odd.
x^x will always be odd
y^y can be even or odd

therefore (x^x)(y^y) can be even or odd.

so we can have either:
odd + even ----> odd
or
odd + odd -----> even

INSUFFICIENT

2) 2x will always be even therefore y must be odd. x itself can be even or odd.

x^y can be even or odd
x^x can be even or odd
y^y must be odd

If x is even we have: --> even + (even)(odd) ---> even + even = even

If x is odd we have ---> odd + (odd)(odd) -----> odd+ odd = even

Regardless, each case gives us an even. Therefore this is SUFFICIENT to say "no" to our question.

Answer: B
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Re: If x and y are positive integers , is x^y + (x^x)(y^y) odd?(DS)   [#permalink] 09 Sep 2018, 15:28
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