Brent@GMATPrepNow wrote:If y < 0 < x, is x/y > -1?

(1) x + y > 0
(2) 3x < -2y

Source: www.gmatprepnow.com

VERY important problem, Brent. Congrats!
(I believe it is a 650-700 level, by the way.)

$$y < 0 < x\,\,\,\, \Leftrightarrow \,\,\,\,\,\left\{ \matrix{
\,y < 0\,\,\,\,\left( * \right) \hfill \cr
\,x > 0 \hfill \cr} \right.$$
$$\frac{x}{y}\,\,\,\mathop > \limits^? \,\, - 1\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\,\boxed{\,\,x\,\mathop < \limits^? \, - y\,\,\,}\,\,\,$$

$$\left( 1 \right)\,\,x + y > 0\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{FOCUS}}\,\,!} \,\,\,\,\,x > - y\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle $$

$$\left( 2 \right)\,\,\,\,3x < - 2y\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{FOCUS}}\,\,!} \,\,\,\,\,x < - {2 \over 3}y\,\,\,\mathop < \limits^{\left( {**} \right)} \,\,\, - y\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,$$
$$\left( {**} \right)\,\,\, - \frac{2}{3} > - 1\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\, - \frac{2}{3}y < - 1 \cdot y\,\,\,\, \Rightarrow \,\,\,\, - \frac{2}{3}y < - y$$

Obs.: this problem is PERFECTLY stated. More explicitly: some people believe (D) must have statements "answering the same" but this belief is simply NOT true.
Proof: https://www.beatthegmat.com/data-suffic ... 16453.html


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

People are usually more convinced by reasons they discovered themselves than by those found by others.
(Blaise Pascal)

Hi, Brent.

First of all, thank you for the reply.

I am not an English-native speaker, therefore let me say, first-hand, that I do not mean to be rude in anything that follows.

01. The GMAT representative wrote a post on 27 Jul 2012 saying the following:

Thank you for asking this Data Sufficiency question. I have forwarded your question to one of our psychometricians in order to get the best answer possible. When I receive a response I will post it on this thread.

The answer came only on 06 Ago 2012, therefore I do believe the question WAS given to the people who are REALLY in charge of the "rules of the game".

In my opinion, the answer is absolutely clear.

02. I agree that it is helpful to use the fact that it is highly unlikely to have "incoherent" answers to help students qualify for the test.
(I myself do that, too.) But this is NOT the same as making a statement that contradicts official rules, though.

03. I have already seen an official question like that. In the next few days I will try to find it (and bring it here). It is probably in the Official Guide 10th edition (the first I used when I started teaching for the exam). Please do not argue that it is an old edition, for instance.
The fact is that finding it is not the issue at all. The issue deals with the possibility of something to occur, not if it has already occurred previously.

04. I respect your arguments, your preferences.
I agree statements are always true. The question is whether there is a unique "common reality" to both of them when each alone is sufficient.
The official answer is NO.

My intention was only to give facts to clarify a common misunderstanding. I do not want to go into this further.

Thank you again for your time and your attention.

Kind Regards,
Fabio.

Hi there!

I would discreetly edit my last post to present an official example of (D) with contradicting statements.
The fact that I did not find it made me feel "ethically compromised" to open this new post and let you all know that.

Anyway,

1. The absence of evidence is not evidence of absence.

2. I also believe non-contradicting statements for the (D) answer is much more elegant (and avoids refuting (C) at first glance).
This is the first time I put my own preferences into this discussion, by the way.

Regards,
Fabio.