Need help on this DS ques

[AnuragRatna]

If x and y are integers and x<y, what is the value of x+y?
(1) xy=4

(2) |x|=|y|

A Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D EACH statement ALONE is sufficient.
E Statements (1) and (2) TOGETHER are not sufficient.

[GMATGuruNY]

I believe that the problem should read as follows:

If x and y are integers and x<y, what is the value of x+y?
(1) x^y=4

(2) |x|=|y|

Statement 1: x^y = 4
Since x<y, only one case is possible:
x=-2 and y=2, with the result that x^y = (-2)² = 4.
Thus:
x+y = -2+2 = 0.
SUFFICIENT.

Statement 2: |x| = |y|
Since x<y, we get the following cases:
x=-2 and y=2.
x=-1 and y=1.
x=-10 and y=10.
And so on.
In every case, x+y = 0.
SUFFICIENT.

The correct answer is D.

[GMATinsight]

If x and y are integers and x<y, what is the value of x+y?
(1) xy=4

(2) |x|=|y|

Statement 1) xy=4
x=1, y=4 then x+y = 5 or
x=-4, y=-1 then x+y = -5 or

INSUFFICIENT

Statement 2) |x|=|y|

i.e. x and y have same absolute values irrespective of their signs
but since x < y therefore
either both positive or
both negative
or x negative and y positive

Combining the two statements

Result of Statement 2 is contradicting with the inference of statement 1 therefore the question is not properly phrased.

[GMATinsight]

AnuragRatna wrote:
If x and y are integers and x<y, what is the value of x+y?
(1) x^y=4 (CONSIDERING THE CORRECTION TO BE DONE)

(2) |x|=|y|

Statement 1) x^y=4
i.e. x = -2 and y = 2 is the only Solution under the given constraint

therefore x+y = 0

SUFFICIENT

Statement 2) |x|=|y|

i.e. x and y have same absolute values

but since x < y therefore

X will be negative and Y will be positive

i.e. x = -y
i.e. x+y = 0

SUFFICIENT

Answer: Option D