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

Question

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

(1)  xy = 1 
(2)  x
eq{-1}

OptimusPrepJanielle · Answer

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
eq{-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

Ndkms · Answer

(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
eq{-1}  
This is quite easy as both x and y can have any value insufficient

(1) + (2) Give the right answer hence C

Kinshook · Answer

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
eq{-1} 
Value of x is unknown
NOT SUFFICIENT

(1) + (2)
(1)  xy = 1 
(x,y)={(1,1),(-1,-1)}
(2)  x
eq{-1} 
(x,y) = (1,1)
x = 1
SUFFICIENT

IMO C

ScottTargetTestPrep · Answer

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.

Answer: C

silaaan · Answer

what about 0? since 0 is also an integer.

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

Bunuel · Answer

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?

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

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