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gmathacker1
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If x is not equal to 0 and x^y=1, then which of the followin Updated on: 02 Aug 2014, 10:32
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.
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E
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Difficulty:

85% (hard)

Question Stats:

33% (01:05) correct 67% (01:03) wrong based on 835 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

Show Spoiler
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.

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Bunuel
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If x is not equal to 0 and x^y=1, then which of the followin 02 Aug 2014, 10:39
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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

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

Answer: E.

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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vad3tha
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If x is not equal to 0 and x^y=1, then which of the followin 02 Aug 2014, 23:57
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gmathacker1
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

Show Spoiler
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.
Show more

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
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If x is not equal to 0 and x^y=1, then which of the followin 04 Dec 2014, 10:52
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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 ?
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If x is not equal to 0 and x^y=1, then which of the followin 04 Dec 2014, 10:56
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aashu4uiit
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 ?
Show more

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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If x is not equal to 0 and x^y=1, then which of the followin 04 Dec 2014, 11:36
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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,
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If x is not equal to 0 and x^y=1, then which of the followin 03 Jun 2019, 11:33
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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?
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GMAT Focus 1: 735 Q90 V89 DI81
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If x is not equal to 0 and x^y=1, then which of the followin 04 Jun 2019, 20:34
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Shreshtha55
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?
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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.
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If x is not equal to 0 and x^y=1, then which of the followin 20 Jun 2021, 00:01
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If we have conditions confirming the equation than why we are going out of question?
Question statement is must be true if below conditions satisfy
in that second satisfy the condition and 0 is even no
If it were following condition satisfy than imo ans would be e
Any view on this

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If x is not equal to 0 and x^y=1, then which of the followin 25 Jun 2024, 23:11
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@gmathacker1If x is not equal to 0 and x^y=1, then which of the following must be true?

(-1)ˆ(y=2n) = 1
If x = -1; xˆy = 1 if y is even.

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

IMO E
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If x is not equal to 0 and x^y=1, then which of the followin 24 Oct 2024, 14:11
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Hello,

So if we have an answer choice x = +1 or (x = -1 and y even) or y=0, it can be considered as the right answer ?
Bunuel
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.

Answer: E.

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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If x is not equal to 0 and x^y=1, then which of the followin 25 Oct 2024, 06:43
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GMATLola
Hello,

So if we have an answer choice x = +1 or (x = -1 and y even) or y=0, it can be considered as the right answer ?
Bunuel
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.

Answer: E.

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.
Show more

Yes, x = 1 or x = -1 or y = 0 would be correct.
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If x is not equal to 0 and x^y=1, then which of the followin 20 Nov 2025, 06:55
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