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Current Student B
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Joined: 09 Jan 2016
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If x and y are integers, what is the value of x?  [#permalink]

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Difficulty:   5% (low)

Question Stats: 77% (00:45) correct 23% (00:41) wrong based on 501 sessions

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

(1) $$xy = 1$$
(2) $$x\neq{-1}$$
SVP  B
Joined: 06 Nov 2014
Posts: 1873
Re: If x and y are integers, what is the value of x?  [#permalink]

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1
nalinnair wrote:
If $$x$$ and $$y$$ are integers, what is the value of $$x$$?

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

We know that x and y are integers.

Statement 1: $$xy = 1$$
Case 1, x = 1 and y = 1
Case 2, x = - 1 and y = -1
INSUFFICIENT

Statement 2: $$x\neq{-1}$$
Nothing can be said about the value of x
INSUFFICIENT

Combining both statements:
We know that xy = 1 and x ≠ -1
Hence x = 1
SUFFICIENT

Correct Option: C
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Joined: 09 Aug 2016
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Re: If x and y are integers, what is the value of x?  [#permalink]

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

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

(1) x*y = 1 and (x, y) = integers
Since x,y are integers the only integer pair that gives 1 as a product should be (1, 1) or (-1, -1) . Although since we cannot decide which pair fits our case insufficient

(2) Actually here if you now only $$x\neq{-1}$$
This is quite easy as both x and y can have any value insufficient

(1) + (2) Give the right answer hence C
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Re: If x and y are integers, what is the value of x?  [#permalink]

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x,y integers
value of x = ?
1, xy=1
(Negative)(Negative) = Positive
(Positive)(Positive) = Positive
x = -1 or x = 1
BCE
2, x # - 1
Eliminate B
Combine
x = 1, true
C
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Re: If x and y are integers, what is the value of x?  [#permalink]

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Ans C
St 1 : xy=1 this gives 2 cases (1,1) &(-1,-1). ambiguous and hence INSUFFICIENT.
St 2: x not equal -1 ....pick any integer except that... INSUFFICIENT.

Together : well together st 2 will diminish the ambiguity in st 1 and will lead to only one choice as x=1. Hence SUFFICIENT
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Re: If x and y are integers, what is the value of x?  [#permalink]

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

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

Statement 1) tells us x and y must be of the same sign (-1)(-1) or (1) (1) so we cannot tell if x = 1 or -1.

Insufficient.

Eliminate A/D

Try statement 2) it tells us x cannot be -1

well then x can be anything else? so it is insufficient.

Eliminate B

now try combining statement (1) and (2)

we get that x cannot be -1 then x must be 1.

Sufficient.

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

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

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

Given,

x and y are integers.

Statement 1:

xy = 1

x = 1

y = 1

or

x = -1

y = -1

So, we don't have the specific value for x.

NOT sufficient.

Statement 2:

x is not equal to -1.

infinite values for x except -1.

NOT sufficient.

Combining both statements;

Now we know from 1 that x is either 1 or -1. statement 2 helps to +1.

The best answer is C.
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Posts: 1691
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Re: If x and y are integers, what is the value of x?  [#permalink]

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nalinnair wrote:
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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E-mail : kinshook.chaturvedi@gmail.com Re: If x and y are integers, what is the value of x?   [#permalink] 16 Sep 2019, 04:49
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