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If n is an integer, xy ≠ 0, and x^n

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If n is an integer, xy ≠ 0, and x^n  [#permalink]

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New post 20 Oct 2016, 09:20
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Difficulty:

  65% (hard)

Question Stats:

54% (02:04) correct 46% (02:08) wrong based on 128 sessions

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If n is an integer, xy ≠ 0, and x^n = y^n, then what is the value of n?

(1) x/y = 2

(2) n < y < x

Our video solution can be found here: https://www.gmatprepnow.com/module/gmat ... video/1053

NOTE: Kudos for all correct solutions

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Re: If n is an integer, xy ≠ 0, and x^n  [#permalink]

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New post 20 Oct 2016, 10:06
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1
x^n = y^n --> We can have 3 different cases:
Case 1) \(x = y\) and n is any value
Case 2) \(|x| \neq {|y|}\) and n = 0
Case 3) \(x = -y\) and n is even

St1: x/y = 2 --> \(|x| \neq {|y|}\) --> n = 0
Sufficient

St2: n < y < x --> Can have 2 possibilities
\(x \neq {y}\) --> n = 0
or
\(y = -x\) --> n is even and negative
Not Sufficient

Answer: A
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Re: If n is an integer, xy ≠ 0, and x^n  [#permalink]

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New post 20 Oct 2016, 23:14
1
From question we know.

xy ≠ 0 - which means none of them can be equal to zero.

and x^n = y^n meaning either n can be zero or even.

1. Statement 1 : x/y = 2, which means (2)^n = 1, this is only possible for one value of n =0. Sufficient

2. Statement 2 : n < y < x, this means that y would be negative (y = -x) and n would be smaller than y, as we are given
that x^n = y^n, so n would be even negative integer and we can have multiple solutions. So not sufficient.

Option A.
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Re: If n is an integer, xy ≠ 0, and x^n  [#permalink]

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New post 13 Jan 2019, 01:47
GMATPrepNow wrote:
If n is an integer, xy ≠ 0, and x^n = y^n, then what is the value of n?

(1) x/y = 2

(2) n < y < x

Our video solution can be found here: https://www.gmatprepnow.com/module/gmat ... video/1053

NOTE: Kudos for all correct solutions


Dear Moderator,
Another DS question in the incorrect section, hope you will do the needful. Thank you.
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Re: If n is an integer, xy ≠ 0, and x^n  [#permalink]

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New post 13 Jan 2019, 03:09
stne wrote:
GMATPrepNow wrote:
If n is an integer, xy ≠ 0, and x^n = y^n, then what is the value of n?

(1) x/y = 2

(2) n < y < x

Our video solution can be found here: https://www.gmatprepnow.com/module/gmat ... video/1053

NOTE: Kudos for all correct solutions


Dear Moderator,
Another DS question in the incorrect section, hope you will do the needful. Thank you.

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Done. Thank you.
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Re: If n is an integer, xy ≠ 0, and x^n  [#permalink]

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New post 13 Jan 2019, 03:49
GMATPrepNow wrote:
If n is an integer, xy ≠ 0, and x^n = y^n, then what is the value of n?

(1) x/y = 2

(2) n < y < x


Our video solution can be found here: https://www.gmatprepnow.com/module/gmat ... video/1053

NOTE: Kudos for all correct solutions


#1:
only way
x^n = y^n
when n=0
sufficeint
#2
n <y<x can be -ve or +ve
we would get both values
in sufficient

IMO A
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Re: If n is an integer, xy ≠ 0, and x^n   [#permalink] 13 Jan 2019, 03:49
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