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# If x ≠ 0 and x^y = 1 what is the value of x?

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Math Expert
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If x ≠ 0 and x^y = 1 what is the value of x?  [#permalink]

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08 Sep 2019, 21:52
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35% (medium)

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68% (01:04) correct 32% (01:21) wrong based on 68 sessions

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If $$x ≠ 0$$ and $$x^y = 1$$ what is the value of x?

(1) y is an integer

(2) x is a positive number

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Re: If x ≠ 0 and x^y = 1 what is the value of x?  [#permalink]

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08 Sep 2019, 23:05
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Re: If x ≠ 0 and x^y = 1 what is the value of x?  [#permalink]

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09 Sep 2019, 00:03
1
Given x!=0, and x^y=1
We are to determine the value of x.

From statement 1, we know that y is an integer.
Let y=2
Then x^2=1 means either x=1 or x=-1,
Hence not sufficient.

From statement 2, we know that x>0.
Let y=0
Then x^0=1, This means that x can have an infinite number of positive numbers which satisfy the equation x^0=1.
Hence 2 is also not sufficient.

(1)+(2)
x>0 and y is an integer.
y is an integer means y can still equal 0,
in which case x^0=1 and x still having an infinite number of possibilities that satisfy the given equation.

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Re: If x ≠ 0 and x^y = 1 what is the value of x?  [#permalink]

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09 Sep 2019, 02:02
1
If x ≠ 0 and xy=1 what is the value of x?
$$x^y = 1$$

 Y = 0 for any value of x
OR
 Y = 1 or x = 1

(1) y is an integer

since y can take any value among 0 and 1,
x can have any value when y = 0

INSUFFICIENT.

(2) x is a positive number

For y = 0, x can take any positive integer values

INSUFFICIENT.

Together 1) and 2)
Still y can have 0 or 1 as its values and x can take any positive integer values

INSUFFICIENT.

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Re: If x ≠ 0 and x^y = 1 what is the value of x?  [#permalink]

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09 Sep 2019, 04:05
If x≠0 and x^y=1 what is the value of x?

(1) y is an integer
if y be 0, x can be any integers
more than one answer of x therefore
insufficient

(2) x is a positive number
we still do not know y
insufficient

together, still insufficient because x and y can still be many number that suits the condition.

therefore, E
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Re: If x ≠ 0 and x^y = 1 what is the value of x?  [#permalink]

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09 Sep 2019, 07:01
It's E because even after combining we will get two conditions: 1^0=1 and 1^1=1, Hence both together are insufficient.

If
x≠0 and x^y=1

what is the value of x?

(1) y is an integer

(2) x is a positive number
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Re: If x ≠ 0 and x^y = 1 what is the value of x?  [#permalink]

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30 Sep 2019, 19:20
If x≠0x≠0 and xy=1xy=1 what is the value of x?

(1) y is an integer
if x^y must equal zero, then Y can be zero and X can be any number. Even if we could get a single X out of this that isn't 1, Y could still be any positive number and X could be one, and you would still end up with two values of X.

(2) x is a positive number

Again, X can be 1 and Y be anything, or X can be any other positive number and Y be zero - therefore there are an infinite amount of Xs that make this statement true.

E.
Re: If x ≠ 0 and x^y = 1 what is the value of x?   [#permalink] 30 Sep 2019, 19:20
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