GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 11 Dec 2018, 10:07

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Free GMAT Prep Hour

     December 11, 2018

     December 11, 2018

     09:00 PM EST

     10:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3231
Location: Canada
If y < 0 < x, is x/y > -1?  [#permalink]

Show Tags

New post Updated on: 02 Oct 2018, 13:48
Top Contributor
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

59% (01:28) correct 41% (01:38) wrong based on 54 sessions

HideShow timer Statistics

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

_________________

Test confidently with gmatprepnow.com
Image


Originally posted by GMATPrepNow on 02 Oct 2018, 07:42.
Last edited by GMATPrepNow on 02 Oct 2018, 13:48, edited 1 time in total.
Senior DS Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1118
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
If y < 0 < x, is x/y > -1?  [#permalink]

Show Tags

New post 02 Oct 2018, 08:10
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

Answer D


( 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


_________________

Win GMAT CLUB Test- Weekly Quant Quiz Contest
Weekly Quant Quiz Questions- Direct Download
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

GMATH Teacher
User avatar
G
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 534
Re: If y < 0 < x, is x/y > -1?  [#permalink]

Show Tags

New post 02 Oct 2018, 10:13
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.

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.
-------------------------------------------------------------------------------------------------------------
_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3231
Location: Canada
Re: If y < 0 < x, is x/y > -1?  [#permalink]

Show Tags

New post 02 Oct 2018, 13:01
Top Contributor
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:

_________________

Test confidently with gmatprepnow.com
Image

GMATH Teacher
User avatar
G
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 534
Re: If y < 0 < x, is x/y > -1?  [#permalink]

Show Tags

New post 02 Oct 2018, 13:56
1
People are usually more convinced by reasons they discovered themselves than by those found by others.
(Blaise Pascal)
_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3231
Location: Canada
Re: If y < 0 < x, is x/y > -1?  [#permalink]

Show Tags

New post 02 Oct 2018, 15:08
Top Contributor
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
_________________

Test confidently with gmatprepnow.com
Image

GMATH Teacher
User avatar
G
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 534
Re: If y < 0 < x, is x/y > -1?  [#permalink]

Show Tags

New post 02 Oct 2018, 16:58
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.
_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7099
Re: If y < 0 < x, is x/y > -1?  [#permalink]

Show Tags

New post 02 Oct 2018, 17:25
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

D....but opposite answers

'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.
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

GMATH Teacher
User avatar
G
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 534
If y < 0 < x, is x/y > -1?  [#permalink]

Show Tags

New post 04 Oct 2018, 12:11
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.
_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

GMAT Club Bot
If y < 0 < x, is x/y > -1? &nbs [#permalink] 04 Oct 2018, 12:11
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron
Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.