Data Sufficiency

Question # 35
Is x + y > 0 ?
(I) x² - y² > 1
(II) x/y + 1 > 0

(A) Statement (I) ALONE is sufficient, but statement (II) alone is not sufficient

(B) Statement (II) ALONE is sufficient, but statement (I) is not sufficient

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient

(D) Each statement ALONE is sufficient

(E) Statements (I) and (II) TOGETHER are NOT sufficient

[spoiler]my Answer : B
Actual Answer : E

Explanation
From statement I x² - y² > 1
This can be written as (x + y)(x - y) > 1
There is no other available information to determine if (x + y) is greater than or less than 0.
Thus statement 1 alone is not sufficient to answer the question.

From statement 2, x/y + 1 > 0 or (x + y)/y > 0.
This will be true when either both x + y > 0 and y > 0 or x + y < 0 and y < 0.
Since there is no other available information, this statement alone is also not sufficient to answer the question.

Combining the two statements also we do not get any definite information about, x, y or x + y.
Thus the two statements together are also not sufficient to answer the question.
Therefore, we cannot say for sure whether x + y> 0.

Hence (E) is the correct answer.[/spoiler]