x is a nonzero number. Is xy < 0?

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Fri Mar 09, 2018 9:38 am

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?

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Source: Beat The GMAT — Data Sufficiency | Fri Mar 09, 2018 9:38 am

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Fri Mar 09, 2018 10:04 am

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 â‰ 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!!!

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Thu Mar 22, 2018 3:04 am

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.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Fri Mar 23, 2018 11:56 am

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

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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