M7MBA wrote:x is a nonzero number. Is xy < 0?

(1) y is not negative.
(2) y is not positive.

The OA is C.

Experts, may you give me some help here? Please. How can I prove that the correct answer is C?

x ≠ 0

Question : Is xy < 0?

Statement 1: y is not negative.

But the sign of x and y are unknown therefore we can't conclude the sign of x*y hence
NOT SUFFICIENT


Statement 1: y is not Positive.
But the sign of x and y are unknown therefore we can't conclude the sign of x*y hence
NOT SUFFICIENT

Combining the two statements

Since y is neither positive nor Negative therefore y must be ZERO

i.e. y = 0
hence xy = 0
hence, x*y is NOT less than Zero
SUFFICIENT

Answer: Option C

I hope this helps!!!

Hello M7MBA.

We know that $$x\ne0.$$ Now, let's take a look at each statement: $$\left(1\right)\ y\ is\ not\ negative,\ this\ implies\ that\ y\ \ge0$$ Since we don't know anything about x, we cannot say anything about xy. INSUFFICIENT. $$\left(2\right)\ y\ is\ not\ positive,\ this\ implies\ that\ y\ \le0$$ again, we cannot say anything about xy.

Now, using both statements we have: $$y\ \le0\ and\ y\ge0\ \Rightarrow\ y=0.$$ Now, since y=0, then xy=0. In conlcusion xy is not negative. SUFFICIENT.

Therefore, the answer is C.

M7MBA wrote:x is a nonzero number. Is xy < 0?

(1) y is not negative.
(2) y is not positive.

We are given that x is a nonzero number and need to determine whether xy < 0.

Statement One Alone:

y is not negative.

If y is zero, then xy is not less than zero. If y is positive and x is negative, then xy is less than zero. Statement one alone is not sufficient.

Statement Two Alone:

y is not positive.

If y is zero, then xy is not less than zero. If y is negative and x is positive, then xy is less than zero. Statement two alone is not sufficient.

Statements One and Two Together:

Using our statements together we see that y is not negative and also not positive so y must be zero, thus xy must be zero, which is not less than 0. The two statements together are sufficient to answer the question.

Answer: C