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# If x and y are integers, what is the value of x?

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Re: If x and y are integers, what is the value of x? [#permalink]
nalinnair
If $$x$$ and $$y$$ are integers, what is the value of $$x$$?

(1) $$xy = 1$$
(2) $$x\neq{-1}$$

If $$x$$ and $$y$$ are integers, what is the value of $$x$$?

(1) $$xy = 1$$
(x,y)={(1,1),(-1,-1)}
NOT SUFFICIENT

(2) $$x\neq{-1}$$
Value of x is unknown
NOT SUFFICIENT

(1) + (2)
(1) $$xy = 1$$
(x,y)={(1,1),(-1,-1)}
(2) $$x\neq{-1}$$
(x,y) = (1,1)
x = 1
SUFFICIENT

IMO C
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Re: If x and y are integers, what is the value of x? [#permalink]
nalinnair
If $$x$$ and $$y$$ are integers, what is the value of $$x$$?

(1) $$xy = 1$$
(2) $$x\neq{-1}$$
Solution:

Question Stem Analysis:

We need to determine the value of x, given that x and y are integers.

Statement One Alone:

Since both x and y are integers, then both x and y are 1, or they both are -1, in order for xy = 1. However, since x can be either 1 or -1, statement one alone is not sufficient.

Statement Two Alone:

There are many integers whose values are not -1. Statement two alone is not sufficient.

Statements One and Two Together:

From statement one, we see that x is either 1 or -1. From statement two, we see that x is not -1. Therefore, x must be 1. Both statements together are sufficient.

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Re: If x and y are integers, what is the value of x? [#permalink]
what about 0? since 0 is also an integer.

If this is the case, then the answer is E. Correct?
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Re: If x and y are integers, what is the value of x? [#permalink]
silaaan
If $$x$$ and $$y$$ are integers, what is the value of $$x$$?

(1) $$xy = 1$$
(2) $$x\neq{-1}$$

what about 0? since 0 is also an integer.

If this is the case, then the answer is E. Correct?

Is 0 a solution to the equation xy = 1? Have you reviewed the previous discussion? Have you noticed that this is an official guide question?
Re: If x and y are integers, what is the value of x? [#permalink]
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