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# M28-37

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Math Expert
Joined: 02 Sep 2009
Posts: 46305

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16 Sep 2014, 01:31
00:00

Difficulty:

65% (hard)

Question Stats:

38% (00:41) correct 63% (00:45) wrong based on 48 sessions

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If $$x$$ is not equal to 0 and $$x^y=1$$, then which of the following must be true?
I. $$x=1$$

II. $$x=1$$ and $$y=0$$

III. $$x=1$$ or $$y=0$$

A. $$I$$ only
B. $$II$$ only
C. $$III$$ only
D. $$I$$ and $$III$$ only
E. $$None$$

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Math Expert
Joined: 02 Sep 2009
Posts: 46305

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16 Sep 2014, 01:31
1
Official Solution:

If $$x$$ is not equal to 0 and $$x^y=1$$, then which of the following must be true?
I. $$x=1$$

II. $$x=1$$ and $$y=0$$

III. $$x=1$$ or $$y=0$$

A. $$I$$ only
B. $$II$$ only
C. $$III$$ only
D. $$I$$ and $$III$$ only
E. $$None$$

Notice that if $$x=-1$$ and $$y$$ is any even number, then $$(-1)^{even}=1$$, thus none of the options must be true.

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Intern
Joined: 02 Aug 2014
Posts: 4

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16 Jul 2015, 04:25
Bunuel wrote:
Official Solution:

If $$x$$ is not equal to 0 and $$x^y=1$$, then which of the following must be true?
I. $$x=1$$

II. $$x=1$$ and $$y=0$$

III. $$x=1$$ or $$y=0$$

A. $$I$$ only
B. $$II$$ only
C. $$III$$ only
D. $$I$$ and $$III$$ only
E. $$None$$

Notice that if $$x=-1$$ and $$y$$ is any even number, then $$(-1)^{even}=1$$, thus none of the options must be true.

Dear Bunuel,

Please explain why C is incorrect. Even that satisfies the must condition.
Math Expert
Joined: 02 Sep 2009
Posts: 46305

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16 Jul 2015, 04:38
shanti47 wrote:
Bunuel wrote:
Official Solution:

If $$x$$ is not equal to 0 and $$x^y=1$$, then which of the following must be true?
I. $$x=1$$

II. $$x=1$$ and $$y=0$$

III. $$x=1$$ or $$y=0$$

A. $$I$$ only
B. $$II$$ only
C. $$III$$ only
D. $$I$$ and $$III$$ only
E. $$None$$

Notice that if $$x=-1$$ and $$y$$ is any even number, then $$(-1)^{even}=1$$, thus none of the options must be true.

Dear Bunuel,

Please explain why C is incorrect. Even that satisfies the must condition.

III says $$x=1$$ or $$y=0$$. This is NOT necessarily true: consider x = -1 and y = 2 --> (-1)^2 = 1.
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Joined: 12 Aug 2015
Posts: 291
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)

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12 Feb 2016, 00:22
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KUDO me plenty

Intern
Joined: 12 Nov 2016
Posts: 29
Location: Nepal
Concentration: Accounting, Economics
GPA: 3.63
WE: Account Management (Accounting)

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18 Jun 2017, 03:33
Hi Bunuel, I didn't understand why B is incorrect. When x=1 and y=0, then the answer is always 1. Please clarify.
Math Expert
Joined: 02 Sep 2009
Posts: 46305

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18 Jun 2017, 03:37
Romannepal wrote:
Hi Bunuel, I didn't understand why B is incorrect. When x=1 and y=0, then the answer is always 1. Please clarify.

The question asks which of the following MUST be true? Not COULD be true.

II says: $$x=1$$ and $$y=0$$.

This is not necessarily true. Consider x = -1 and y = 0.
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Intern
Joined: 30 Nov 2013
Posts: 7
Location: India
GMAT 1: 770 Q51 V42
GPA: 3.4
WE: Engineering (Energy and Utilities)

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05 Oct 2017, 07:58
Hi Bunuel, why is C incorrect. It says X=1 or Y=0. Now if X=1, x^y will always be 1 irrespective of Y and if Y = 0, then x^y will be 1 as well since X cannot be 0. Can you please explain.
Math Expert
Joined: 02 Sep 2009
Posts: 46305

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05 Oct 2017, 08:00
mansi20081990 wrote:
Hi Bunuel, why is C incorrect. It says X=1 or Y=0. Now if X=1, x^y will always be 1 irrespective of Y and if Y = 0, then x^y will be 1 as well since X cannot be 0. Can you please explain.

This is explained above:

III says $$x=1$$ or $$y=0$$. This is NOT necessarily true: consider x = -1 and y = 2 --> (-1)^2 = 1.
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Re: M28-37   [#permalink] 05 Oct 2017, 08:00
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# M28-37

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