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# If y < 0 < x, is x/y > -1?

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If y < 0 < x, is x/y > -1?  [#permalink]

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Updated on: 02 Oct 2018, 14:48
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49% (01:56) correct 51% (01:56) wrong based on 71 sessions

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If y < 0 < x, is x/y > -1?

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

IMPORTANT: After posting the question, I realized that it is faulty.
That said, there's something useful to be learned, so you might want to learn about WHY it's a faulty question (it's actually quite useful information)

Cheers,
Brent

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Originally posted by GMATPrepNow on 02 Oct 2018, 08:42.
Last edited by GMATPrepNow on 02 Oct 2018, 14:48, edited 1 time in total.
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If y < 0 < x, is x/y > -1?  [#permalink]

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02 Oct 2018, 09:10
2
If y < 0 < x, is $$\frac{x}{y}$$ > -1?

(1) x + y > 0

This means that absolute value of x is greater than absolute value of y
so absolute value of $$\frac{x}{y}$$, also x is positive, y is negative so $$\frac{x}{y}$$ < -1

SUFFICIENT

(2) 3x < -2y
Rearranging we get, $$\frac{x}{y}$$ > -$$\frac{2}{3}$$ or $$\frac{x}{y}$$ > -0.66
Hence $$\frac{x}{y}$$ > -1

SUFFICIENT

( since both statements 1&2 contradict each other, this question is flawed)

Concept used : when we divide both side of inequality by y (which is negative), the inequality sign reverses

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Re: If y < 0 < x, is x/y > -1?  [#permalink]

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02 Oct 2018, 11:13
1
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:

-------------------------------------------------------------------------------------------------------------
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.

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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Re: If y < 0 < x, is x/y > -1?  [#permalink]

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02 Oct 2018, 14:01
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GMATPrepNow wrote:
If y < 0 < x, is x/y > -1?

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

My apologies. I posted my question without noticing its FATAL FLAW.

KEY CONCEPT: On the GMAT, the two statements in a Data Sufficiency question will never contradict each other (for more on this, see the video below)

Let's examine the main issue.

Statement 1: x + y > 0
Okay, so x + y has some POSITIVE value.

Statement 2: 3x < -2y
Take: 3x < -2y
Add 2y to both sides to get: 3x + 2y < 0
Divide both sides by 3 to get: x + (2/3)y < 0
In other words, x + (2/3)y is NEGATIVE

Now recognize that, if y < 0 (given information), then (1/3)y will be negative.

We already know that x + (2/3)y is NEGATIVE.
So, if we add another negative value to x + (2/3)y, the result will be NEGATIVE.
In other words, x + (2/3)y + (1/3)y is NEGATIVE
Simplify to get: x + y is NEGATIVE

There's the problem!
Statement 1 says x + y is POSITIVE
And Statement 2 says x + y is NEGATIVE

Here's a video that discusses the fact that the two statements in a Data Sufficiency question will never contradict each other:

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Re: If y < 0 < x, is x/y > -1?  [#permalink]

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02 Oct 2018, 14:56
2
People are usually more convinced by reasons they discovered themselves than by those found by others.
(Blaise Pascal)
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Re: If y < 0 < x, is x/y > -1?  [#permalink]

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02 Oct 2018, 16:08
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For me, the response from the test-makers that sticks out the most is this: "it is highly unlikely that you would come across a question with independently sufficient statements that contradict each other"
I think the person answering the question was trying too hard to avoid taking a firm position (for whatever reason).
Also, I've certainly never seen such a question. Have you, Fabio?

For me it boils down to whether each statement is intended to provide true information.

If it's the case that the statements always provide true information, then it's impossible to have two true statements that directly contradict each other.
Conversely, if we allow for the statements to occasionally provide false information, then the entire question type falls apart.

For example:
What is the value of x?
(1) 2x = 6

If we know for certain that all statements are true, then statement 1 is clearly sufficient.
However, if we allow for the possibility that statement 1 is not true, then the equation (2x = 6) may or may not be true, which means we can't be certain of the sufficiency of statement 1.

Anyone care to weigh in on this?

Cheers,
Brent
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Re: If y < 0 < x, is x/y > -1?  [#permalink]

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02 Oct 2018, 17:58
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. 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.
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Re: If y < 0 < x, is x/y > -1?  [#permalink]

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02 Oct 2018, 18:25
GMATPrepNow wrote:
If y < 0 < x, is x/y > -1?

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

IMPORTANT: After posting the question, I realized that it is faulty.
That said, there's something useful to be learned, so you might want to learn about WHY it's a faulty question (it's actually quite useful information)

Cheers,
Brent

Another way to look at this is - the number line
Since both or on either side, x/y>-1 basically asks us whether x or y is farther from 0
If we can find this, we have our answer.

I. x+y>0
Clearly this tells us that POSITIVE value is more and x >0, so x>y and x/y>-1
Sufficient

II. 3x<-2y
3x+2y<0
Here we are adding twice of negative quantity to thrice of positive quantity and still get a negative value , so clearly negative quantity has more absolute value
Thus x/y<-1
Sufficient

'Highly unlikely' as Brent too mentioned, in my opinion, is a way for the official test makers to avoid any embarassment if any question is found having this problem sometimes later. Finally these questions are made by humans and there can be a probability of whatever small value that such an error is overlooked.
Even in CR, I have found that MOST strongly etc in almost all cases has only one choice which actually supports. So here too, use of 'most' must be for the same reason.

But the finer point, INCASE such an error is there is that it is the QUESTION that is flawed not the ANSWER.
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If y < 0 < x, is x/y > -1?  [#permalink]

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04 Oct 2018, 13:11
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.
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Re: If y < 0 < x, is x/y > -1?  [#permalink]

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04 Apr 2019, 02:25
GMATPrepNow wrote:
If y < 0 < x, is x/y > -1?

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

IMPORTANT: After posting the question, I realized that it is faulty.
That said, there's something useful to be learned, so you might want to learn about WHY it's a faulty question (it's actually quite useful information)

Cheers,
Brent

The question stem (only IF part): If $$y < 0 < x$$
Here it says that:
$$x>0$$ (the value of x is positive)
and
$$y<0$$ (the value of y is negative)

Statement 2:
--> $$3x < -2y$$
--> $$x < -\frac{2}{3}y$$
--> x < any positive value (As 'y' is negative)
So, x could be any negative value, 0 (zero), or positive value. But, the question stem (IF part) says that x is positive only. So, the question stem and the statement contradict each other. The maker of this question is liar!

Remember: The IF part is also the part of each statement.
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Re: If y < 0 < x, is x/y > -1?   [#permalink] 04 Apr 2019, 02:25
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