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If x and y are integers, is y divisible by 2? (1) x^y = 1 (2) x is

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Bunuel
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If x and y are integers, is y divisible by 2? (1) x^y = 1 (2) x is [#permalink] New post   23 Apr 2021, 01:30
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If x and y are integers, is y divisible by 2?

(1) \(x^y=1\)
(2) x is negative.


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If x and y are integers, is y divisible by 2? (1) x^y = 1 (2) x is [#permalink] New post   26 Apr 2021, 01:15
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If x and y are integers, is y divisible by 2?

(1) \(x^y=1\). If x=1, then y could be any integer even or odd. Not sufficient.

(2) x is negative. No info about y. Not sufficient.

(1)+(2) x is negative and \(x^y=1\). We can have the following two cases

i. If \(x=-1\), then y must be even: \((-1)^{even}=1\).
ii. If x is any other negative integer, then y must be 0: \((non-zero \ integer)^{0}=1\).

In either case y is even, so divisible by 2. Sufficient.

Answer: C.

Hope it's clear.
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If x and y are integers, is y divisible by 2? (1) x^y = 1 (2) x is [#permalink] New post   Updated on: 24 Apr 2021, 02:08
If x and y are integers, is y divisible by 2?

Statement (1) x^y=1

x=1 y=any integer
x=any integer y=0
x=-1 y=2..etc

Not sufficient

Statement (2) x is negative.
Not sufficient

Combined
x=-1 y=2
x=-1 y=0

Hence, sufficient as both 2 and 0 are divisible by 2 as remainder is 0 in both cases
C is the answer

Originally posted by sumitkrocks on 23 Apr 2021, 03:05.
Last edited by sumitkrocks on 24 Apr 2021, 02:08, edited 1 time in total.
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Re: If x and y are integers, is y divisible by 2? (1) x^y = 1 (2) x is [#permalink] New post   23 Apr 2021, 06:03
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If x and y are integers, is y divisible by 2?

Stat1: \(x^y\)=1
\(x^0\) = 1; y= even and if \(1^1\) = 1; y= odd. Not sufficient

Stat2: x is negative.
But, we have no idea of y. Not sufficient

Combining both,\( (-1)^2\) = 1; y= 2= even; if \((-n)^0\)\(\) = 1; y= 0 = even. Sufficient

So, I think C. :)
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Re: If x and y are integers, is y divisible by 2? (1) x^y = 1 (2) x is [#permalink] New post   23 Apr 2021, 08:56
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If x and y are integers, is y divisible by 2?

(1) x^y=1

1^1 =1
(Anything)^0=1
Not sufficient

(2) x is negative.
Not about y. Eliminate. Not sufficient.

Combining both statement
X^y =1 and x = negative
Clearly y = 2
Sufficient

IMO C

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Re: If x and y are integers, is y divisible by 2? (1) x^y = 1 (2) x is [#permalink] New post   23 Apr 2021, 23:39
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IMO C

St. 1 x^y = 1 implies that either x can be 1 or Y can be zero hence, insufficient
St. 2 x is negative. Clearly no conclusion on Y
Combining both we get X is Negative and 1 x^y = 1 implies that
Either,
x is -1 and y is either 0 or multiple of 2
or
x any negative integer and y is Zero
in both above case y is divisible by 2 hence both together is sufficient.
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If x and y are integers, is y divisible by 2? (1) x^y = 1 (2) x is [#permalink] New post   25 Apr 2021, 23:16
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imo C .
If x and y are integers, is y divisible by 2?

Stat1: \(x^y\)=1
x and y can be 1 . Or
x can be anything and y can be 0 .
so y = 0 or 1 may or may not divisible by 2 .
Not sufficient

Stat2: x is negative.
But, we have no idea of y. Not sufficient

Combining both,\( (-1)^{even}\) = 1; y= even; so divisible by 2 . Sufficient
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Re: If x and y are integers, is y divisible by 2? (1) x^y = 1 (2) x is [#permalink] New post   10 Feb 2023, 07:54
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Re: If x and y are integers, is y divisible by 2? (1) x^y = 1 (2) x is [#permalink]
10 Feb 2023, 07:54
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