GMATPrepNow wrote:
If y < 0 < x, is x/y > -1?
(1) x + y > 0
(2) 3x < -2y
VERY important problem, Brent. Congrats!
(I believe it is a 650-700 level, by the way.)
\(y < 0 < x\,\,\,\, \Leftrightarrow \,\,\,\,\,\left\{ \matrix{
\,y < 0\,\,\,\,\left( * \right) \hfill \cr
\,x > 0 \hfill \cr} \right.\)
\(\frac{x}{y}\,\,\,\mathop > \limits^? \,\, - 1\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\,\boxed{\,\,x\,\mathop < \limits^? \, - y\,\,\,}\,\,\,\)
\(\left( 1 \right)\,\,x + y > 0\,\,\,\,\,\mathop \Rightarrow \limits^{{\text{FOCUS}}\,\,!} \,\,\,\,\,x > - y\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle\)
\(\left( 2 \right)\,\,\,\,3x < - 2y\,\,\,\,\,\mathop \Rightarrow \limits^{{\text{FOCUS}}\,\,!} \,\,\,\,\,x < - \frac{2}{3}y\,\,\,\mathop < \limits^{\left( {**} \right)} \,\,\, - y\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\)
\(\left( {**} \right)\,\,\, - \frac{2}{3} > - 1\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\, - \frac{2}{3}y < - 1 \cdot y\,\,\,\, \Rightarrow \,\,\,\, - \frac{2}{3}y < - y\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
P.S.: 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: *I* have asked this question to an official GMAT representant in 2012. My question and the full official answer are below:
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Question: I´ve been teaching students in Brazil for the quantitative section of the GMAT for more than a decade and although the (D) alternative in data sufficiency does NOT necessarily mean EXPLICITLY that both statements answers in the same way to the question asked it is usually the case in official problems. After many years thinking about this small (but interesting) detail and having read good arguments for the fact that the answers (in this (D) right choice case) "must" be the same.
Well, my question is: could you please tell me/us the "official" position in this matter? In other words, may we (students/teachers) be 100% sure all GMAT data sufficiency problems are created in the following sense: there is one single scenario presented pre-statements and both statements must refer to the same scenario and, therefore, all info given in the statements are "coherent" between them without any possible situation in which one statement could give us a conclusion that is not compatible to any possible conclusion taken from the other statement?
I hope I could make my question clear.
Thanks a lot,
Fabio.
Answer:Hello, Fabio! There are not any "official" rules with regard to your scenario.
DS has been on the GMAT exam since 1991 and it is certainly possible that someone very familiar with DS would be able to find a counter example in one of the OGs.
That said, it is highly unlikely that you would come across a question with independently sufficient statements that contradict each other.
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Fabio Skilnik ::
GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here:
https://gmath.net