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.
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- AnuragRatna
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I believe that the problem should read as follows:
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.
Statement 1: x^y = 4AnuragRatna wrote:If x and y are integers and x<y, what is the value of x+y?
(1) x^y=4
(2) |x|=|y|
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.
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- GMATinsight
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Statement 1) xy=4AnuragRatna wrote:If x and y are integers and x<y, what is the value of x+y?
(1) xy=4
(2) |x|=|y|
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.
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- GMATinsight
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Statement 1) x^y=4AnuragRatna 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|
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
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