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# If x is a positive integer, is (x+y) even?

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Intern
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If x is a positive integer, is (x+y) even? [#permalink]

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05 Aug 2012, 23:02
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If x is a positive integer, is (x+y) even?

(1) K^x*K^y =1
(2) K is not equal to 1
[Reveal] Spoiler: OA

Last edited by stonecold on 20 Nov 2016, 08:07, edited 2 times in total.
Edited the question.

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Re: If x is a positive integer, is (x+y) even? [#permalink]

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06 Aug 2012, 00:54
ananthpatri wrote:
If x is a positive integer, is (x+y) even?

(1) K^x*K^y =1
(2) K is not equal to 1

(1) States $$K^{x+y}=1$$. If $$K = 1, x + y$$ can be odd or even. Not sufficient.

(2) Nothing about $$x + y$$. Not sufficient.

(1) and (2) together: Sufficient, because necessarily $$x + y = 0$$.

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Re: If x is a positive integer, is (x+y) even? [#permalink]

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06 Aug 2012, 01:03
1
KUDOS
Expert's post
EvaJager wrote:
ananthpatri wrote:
If x is a positive integer, is (x+y) even?

(1) K^x*K^y =1
(2) K is not equal to 1

(1) States $$K^{x+y}=1$$. If $$K = 1, x + y$$ can be odd or even. Not sufficient.

(2) Nothing about $$x + y$$. Not sufficient.

(1) and (2) together: Sufficient, because necessarily $$x + y = 0$$.

x+y is not necessarily zero. If k=-1, then x+y can be ANY even number.
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Re: If x is a positive integer, is (x+y) even? [#permalink]

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06 Aug 2012, 01:08
Bunuel wrote:
EvaJager wrote:
ananthpatri wrote:
If x is a positive integer, is (x+y) even?

(1) K^x*K^y =1
(2) K is not equal to 1

(1) States $$K^{x+y}=1$$. If $$K = 1, x + y$$ can be odd or even. Not sufficient.

(2) Nothing about $$x + y$$. Not sufficient.

(1) and (2) together: Sufficient, because necessarily $$x + y = 0$$.

x+y is not necessarily zero. If k=-1, then x+y can be ANY even number.

You are absolutely right. Nothing stated about K! At least the answer is still C.
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Re: If x is a positive integer, is (x+y) even? [#permalink]

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06 Aug 2012, 01:09

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Re: If x is a positive integer, is (x+y) even? [#permalink]

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28 Oct 2016, 17:03
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Re: If x is a positive integer, is (x+y) even? [#permalink]

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29 Oct 2016, 11:00
ananthpatri wrote:
If x is a positive integer, is (x+y) even?

(1) K^x*K^y =1
(2) K is not equal to 1

FROM STEM , X IS +VE but x+y doesnt have to be +ve , is x+y even??

from 1

k = 1 and x+y = anything or k= -1 , x+y = even or k is anything and x+y = 0 ... insuff

from 2

k is not 1 ... insuff

both together

k can = 1 and (x+y = even ) or k = anything and (x+y = 0) .... in either case x+y is even ... suff

C

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Re: If x is a positive integer, is (x+y) even? [#permalink]

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20 Nov 2016, 08:12
Okay
so we need to get if x+y is even or not
x=> integer
remember => y is not specified as to being an integer.
Lets ook at statements

Statement 1
k^x*k^y=> k^(x+y)=> 1
okay if k is one then x+y can be anything => even/odd/fraction etc
hence not sufficient.
Statement 2
k≠1
no clue of x and y hence not sufficient
Lets Combine the statements
Hmm
K≠1
if k=-1 => x+y must be even as (-1)^even =1 and (-1)odd = -1
if k is any other integer except 1 and -1 then x+y must be zero.
But hey, zero is an even too.
BINGO
x+y must be always either 0 or even
Hence C
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Re: If x is a positive integer, is (x+y) even?   [#permalink] 20 Nov 2016, 08:12
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