Question

If xy < zy < 0, is y positive? x < z x is negative

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient

Answer 1

Both statements (1) and (2) TOGETHER are sufficient to answer the question asked

Explanation:

Given statement 1 :

xy < zy < 0,

The product of two numbers are negative if either of the numbers are negative.

∵ if xy < 0 ⇒ Case 1 : x > 0 and y < 0

Case 2 : x < 0 and y > 0,

Thus, Statement is not sufficient to prove y is positive,

Now, Statement 2 :

x < z, x is negative,

That is, x < 0

Combining statements (1) and (2),

We get,

xy < 0, x < 0,

⇒ y > 0

That is, y is positive.

Hence, Both statements (1) and (2) TOGETHER are sufficient to answer the question asked