GMAT Quantitative Reasoning Practice Test 7

Question : 98 of 100

Marks: +1, -0

What is the value of

(X^2+Y^2)

?
(1)

4 X^2-7=17-4 Y^2

.
(2)

(X+Y)^2=6+2 X Y

Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
Either statement BY ITSELF is sufficient to answer the question.
Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

Solution:

Statement (1) can be written as

4 X^2+4 Y^2=24

X^2+Y^2=6

Statement (1) is sufficient.
Statement (2) can be simplified:

X^2+2 X Y+Y^2=6+2 X Y X^2 +Y^2=6

.
This statement is also sufficient.

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