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# If n is an integer, xy ≠ 0, and x^n

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CEO
Joined: 11 Sep 2015
Posts: 3331
If n is an integer, xy ≠ 0, and x^n  [#permalink]

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20 Oct 2016, 08:20
Top Contributor
5
00:00

Difficulty:

65% (hard)

Question Stats:

56% (01:35) correct 44% (01:42) wrong based on 107 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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Location: India
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Re: If n is an integer, xy ≠ 0, and x^n  [#permalink]

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20 Oct 2016, 09:06
4
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

Manager
Joined: 29 Aug 2008
Posts: 110
Re: If n is an integer, xy ≠ 0, and x^n  [#permalink]

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20 Oct 2016, 22:14
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.
Director
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Posts: 666
Re: If n is an integer, xy ≠ 0, and x^n  [#permalink]

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13 Jan 2019, 00:47
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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- Stne

Math Expert
Joined: 02 Sep 2009
Posts: 52231
Re: If n is an integer, xy ≠ 0, and x^n  [#permalink]

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13 Jan 2019, 02:09
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.

________________
Done. Thank you.
_________________
VP
Joined: 18 Aug 2017
Posts: 1194
Location: India
Concentration: Sustainability, Marketing
WE: Marketing (Energy and Utilities)
Re: If n is an integer, xy ≠ 0, and x^n  [#permalink]

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13 Jan 2019, 02:49
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 &nbs [#permalink] 13 Jan 2019, 02:49
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