Data Sufficiency

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

OA : E

With statement II, I arrived at x + y > 0. But why is this not correct to deduce that II is sufficient?

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

1. (x+y)(x-y) > 1 so (x+y)=1 (x-y)=2 as well as (x+y) = -1 (x-y) = -2 both satisy it. Not suff

2. x+y)/y > 0 so if y>0 then x+y > 0 if y<0 then x+y<0 if y=0 not defined. Not suff

Using 1&2

If (x+y)(x-y) > 1 means if (x+y) > 0 x-y need be > 0 or x>y

Even combining 1&2 we can not deduce anything as we are only sure x>y and not that y>0

E

From 1, ( x+y) ( x-y) > 1... both x and y can be -ve or +ve to acheive the result.

Hence it is not sufficient

From 2, x > -y.

From this, x can be +ve or -ve.. hence it is not sufficient.

From both (1) and (2), it can't be determined whether x and y are +ve or -ve. Hence answer is E.

Regards,
Viju