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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If x is not equal to 0 and x^y=1, then which of the followin

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Intern  Joined: 27 Aug 2012
Posts: 3
If x is not equal to 0 and x^y=1, then which of the followin  [#permalink]

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10 00:00

Difficulty:   85% (hard)

Question Stats: 27% (01:12) correct 73% (01:08) wrong based on 169 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

Answer is None of the Above, According to me III option should be correct. Because if X=1 or Y=0 satisfies the given condition in all circumstances.

Originally posted by gmathacker1 on 02 Aug 2014, 08:19.
Last edited by Bunuel on 02 Aug 2014, 10:32, edited 1 time in total.
Renamed the topic, edited the question and the OA.
Math Expert V
Joined: 02 Sep 2009
Posts: 59588

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gmathacker1 wrote:
If x is not equal to 0 and x^y=1(X to the power y), then which of the following must be true?

I. x=1

II. x=1 and y=0

III. x=1 or y=0

IV. None of the above three

Answer is None of the Above, According to me III option should be correct. Because if X=1 or Y=0 satisfies the given condition in all circumstances.

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.

As for your doubt: x=1 or y=0 indeed satisfies x^y=1, but the question asks "which of the following must be true". But this option is NOT necessarily true, because x could be -1 and y any even number, not necessarily 0.

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Manager  Joined: 22 Feb 2009
Posts: 153
Re: If x is not equal to 0 and x^y=1, then which of the followin  [#permalink]

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gmathacker1 wrote:
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

Answer is None of the Above, According to me III option should be correct. Because if X=1 or Y=0 satisfies the given condition in all circumstances.

I can't see why this question difficulty is 5% low. It is not hard but tricky. C is really tempting after you see I and II are false, and you see III, you seems to forget one more alternative that x can be -1
Manager  Joined: 02 May 2012
Posts: 65
If x is not equal to 0 and x^y=1, then which of the followin  [#permalink]

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I am not able to completely understand this solution such as in 2) x=1 and y=0
it's not correct because : it may be the case that x=4 and y= 0 is also = 1. As not unique solution so not must be true ?

Bunuel
Also I totally don't understand the use of following
Notice that if x=-1 and y is ANY even number, then (-1)^{even}=1, thus none of the options MUST be true.

Must be true here means --> Only eq 1 , or 2 or 3 is a unique solution and no other solution which will give results as x^y =1 ?
Math Expert V
Joined: 02 Sep 2009
Posts: 59588
Re: If x is not equal to 0 and x^y=1, then which of the followin  [#permalink]

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aashu4uiit wrote:
I am not able to completely understand this solution such as in 2) x=1 and y=0
it's not correct because : it may be the case that x=4 and y= 0 is also = 1. As not unique solution so not must be true ?

Bunuel
Also I totally don't understand the use of following
Notice that if x=-1 and y is ANY even number, then (-1)^{even}=1, thus none of the options MUST be true.

Must be true here means --> Only eq 1 , or 2 or 3 is a unique solution and no other solution which will give results as x^y =1 ?

For example, if x = -1 and y = 2, then $$x^y=(-1)^2=1$$, so none of the options MUST be true.
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Senior Manager  P
Joined: 17 Mar 2014
Posts: 426
If x is not equal to 0 and x^y=1, then which of the followin  [#permalink]

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Bunuel,

Is option D wrong because of "Only" word ?
If $$X = 1$$ or $$Y =0$$ then $$X^Y$$ $$= 1$$
If $$X= -1$$ and $$Y=$$ any even number then $$X^Y = 1$$

Above both cases are must be true.

Regards,
Ammu
Manager  B
Joined: 07 Oct 2018
Posts: 59
If x is not equal to 0 and x^y=1, then which of the followin  [#permalink]

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chetan2u can you explain this question please. In option B f x=1 and y=0 then clearly x will be equal to 1 and even in option A if x=1 then whatever is the value of y we will always get value 1. I don't get it how the ans is E. What am I missing here?
Math Expert V
Joined: 02 Aug 2009
Posts: 8284
Re: If x is not equal to 0 and x^y=1, then which of the followin  [#permalink]

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Shreshtha55 wrote:
chetan2u can you explain this question please. In option B f x=1 and y=0 then clearly x will be equal to 1 and even in option A if x=1 then whatever is the value of y we will always get value 1. I don't get it how the ans is E. What am I missing here?

Hi,

The question is asking for MUST be true.
Say x=-1 and y=2, $$(-1)^2=1$$..
Thus none of the options is necessarily or MUST be true, as we can get x^y=1 from other values too.

Now, what mistake you are doing is taking MUST be true as CAN be true.

In CAN, we will take all possibilities as true, while in MUST we will take a choice to be true, if only that possibility exists.
_________________ Re: If x is not equal to 0 and x^y=1, then which of the followin   [#permalink] 04 Jun 2019, 20:34
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