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If x and y are integers, is x^y odd?

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If x and y are integers, is x^y odd?  [#permalink]

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New post 27 Aug 2018, 05:21
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If x and y are integers, is xy odd?

(1) x^y is odd.

(2) x + y is even.
Intern
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Re: If x and y are integers, is x^y odd?  [#permalink]

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New post 27 Aug 2018, 05:26
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Found the answer to this as E on manhattan.
My solution:
1.
Since x^y is odd so X has to be odd.
Insufficient


2. If x + y is even

X and Y are either both odd or even.

Combining these two we can say since X is odd so Y is also odd, hence xy is also odd.
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If x and y are integers, is x^y odd?  [#permalink]

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New post 27 Aug 2018, 05:39
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pratik2018 wrote:
If x and y are integers, is xy odd?

(1) x^y is odd.

(2) x + y is even.


OA: E

(1) \(x^y\) is odd
Take \(x =2 , y =0\) then \(x^y\) will be \(2^0=1\) odd
is xy odd? : No as 2*0=0 , Zero is even

Take \(x =3 , y =1\) then \(x^y\) will be \(3^1=3\) odd
is xy odd? : Yes as 3*1=3 , Three is odd
Statement 1 alone is not sufficient.

(2) x + y is even
Take \(x =2 , y =0\) then \(x+y\) will be \(2+0=2\) even
is xy odd? : No as 2*0=0 , Zero is even

Take \(x =3 , y =1\) then \(x+y\) will be \(3+1=4\) even
is xy odd? : Yes as 3*1=3 , Three is odd
Statement 2 alone is not sufficient.

Combining 1 and 2 will also be insufficient as we have used the same value(3,1) for yes answer and (2,0) for no answer in both statements.
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Re: If x and y are integers, is x^y odd?  [#permalink]

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New post 27 Aug 2018, 05:45
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If x and y are integers, is xy odd?

(1) \(x^y\) is odd.

X is odd or/and Y = 0

Insufficient

(2) x + y is even.

X and Y are either both odd or even.

Insufficient

(1)+(2)

If Y =0 > X = even. So, xy = 0 even

If X = odd, Y = odd. So, xy = odd

Insufficient


Option E
Re: If x and y are integers, is x^y odd? &nbs [#permalink] 27 Aug 2018, 05:45
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