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

It is currently 18 Dec 2018, 13:52

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
  • Happy Christmas 20% Sale! Math Revolution All-In-One Products!

     December 20, 2018

     December 20, 2018

     10:00 PM PST

     11:00 PM PST

    This is the most inexpensive and attractive price in the market. Get the course now!
  • Key Strategies to Master GMAT SC

     December 22, 2018

     December 22, 2018

     07:00 AM PST

     09:00 AM PST

    Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ?

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

Hide Tags

Director
Director
User avatar
B
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 536
Location: Bangladesh
Concentration: Finance, Leadership
GPA: 2.81
WE: Business Development (Real Estate)
If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ?  [#permalink]

Show Tags

New post Updated on: 12 Aug 2017, 07:52
2
Top Contributor
10
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

41% (01:37) correct 59% (01:40) wrong based on 306 sessions

HideShow timer Statistics

If \(x<0\) and \(0 < \frac{x}{y} + 1<1\), which of the following must be true ?

I. \(y > 0\)

II. \(\frac{x}{y}>-1\)

III. \(\frac{1}{x}+\frac{1}{y}<0\)


A. I only

B. I and II only

C. I and III only

D. II and III only

E. I, II and III

_________________

Md. Abdur Rakib

Please Press +1 Kudos,If it helps
Sentence Correction-Collection of Ron Purewal's "elliptical construction/analogies" for SC Challenges


Originally posted by AbdurRakib on 06 May 2017, 00:26.
Last edited by Mahmud6 on 12 Aug 2017, 07:52, edited 2 times in total.
Edited the question.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51280
Re: If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ?  [#permalink]

Show Tags

New post 06 May 2017, 09:00
6
3
AbdurRakib wrote:
If x<0 and 0 < \(\frac{x}{y}\) + 1<1 ,which of the following must be true ?

I. y > 0

II. \(\frac{x}{y}\)>-1

III. \(\frac{1}{x}\)+\(\frac{1}{y}\)<0


A. I only

B. I and II only

C. I and III only

D. II and III only

E. I,II and III


\(0 < \frac{x}{y} + 1<1\)

Subtract 1 from all 3 sides: \(-1 < \frac{x}{y}<0\). We see that II is true.

Since x < 0, then for \(\frac{x}{y}<0\) to be true y must be positive. I must be true.

Next, divide \(0 < \frac{x}{y} + 1<1\) by x and flip the signs since we know that x is negative: \(0 >\frac{1}{y} + \frac{1}{x}>\frac{1}{x}\). III must be true.

Answer: E.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
Intern
Intern
avatar
B
Joined: 29 Apr 2017
Posts: 30
Location: India
Concentration: General Management, Other
WE: Engineering (Computer Software)
Re: If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ?  [#permalink]

Show Tags

New post 06 May 2017, 01:11
AbdurRakib wrote:
If x<0 and 0 < \(\frac{x}{y}\) + 1<1 ,which of the following must be true ?

I. y > 0

II. \(\frac{x}{y}\)>-1

III. \(\frac{1}{x}\)+\(\frac{1}{y}\)<0


A. I only

B. I and II only

C. I and III only

D. II and III only

E. I,II and III


IMO, (D) should be the answer.

If statement I is true, then y > 0. Let us choose y = 1.
And it is given that, x<0 and 0 < \(\frac{x}{y}\) + 1<1

Putting y = 1, and taking any value of x < 0 (say, x = -1) , we find that, \(\frac{x}{y}\) + 1 = 0.
Now it is NOT given that 0 <= \(\frac{x}{y}\) + 1<1, but 0 < \(\frac{x}{y}\) + 1<1.
Therefore statement I cannot be true.

Only option (D) is present which does not contain statement I.
So, IMO (D) is the answer.

If you like my post, please encourage by giving KUDOS. :-D
Intern
Intern
avatar
B
Joined: 29 Apr 2017
Posts: 16
Re: If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ?  [#permalink]

Show Tags

New post 06 May 2017, 03:40
1
moutikli wrote:
AbdurRakib wrote:
If x<0 and 0 < \(\frac{x}{y}\) + 1<1 ,which of the following must be true ?

I. y > 0

II. \(\frac{x}{y}\)>-1

III. \(\frac{1}{x}\)+\(\frac{1}{y}\)<0


A. I only

B. I and II only

C. I and III only

D. II and III only

E. I,II and III


IMO, (D) should be the answer.

If statement I is true, then y > 0. Let us choose y = 1.
And it is given that, x<0 and 0 < \(\frac{x}{y}\) + 1<1

Putting y = 1, and taking any value of x < 0 (say, x = -1) , we find that, \(\frac{x}{y}\) + 1 = 0.
Now it is NOT given that 0 <= \(\frac{x}{y}\) + 1<1, but 0 < \(\frac{x}{y}\) + 1<1.
Therefore statement I cannot be true.

Only option (D) is present which does not contain statement I.
So, IMO (D) is the answer.

If you like my post, please encourage by giving KUDOS. :-D

Hello

If we simplify the given equation
0<x/y +1 < 1

It equals 0<x+y < y
Which implies y>0
Hence I is true

Is this correct? Or am i doing something wrong

Thanks

Sent from my SM-N9200 using GMAT Club Forum mobile app
Intern
Intern
avatar
B
Joined: 23 Apr 2017
Posts: 20
Location: India
GMAT 1: 720 Q50 V36
WE: Marketing (Manufacturing)
Re: If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ?  [#permalink]

Show Tags

New post 06 May 2017, 05:54
2
IMO the answer is E

0<x/y +1<1
-1<x/y<0

As x<0 and x/y <0
Y must be positive

As mod value of x/y lesser than 1, mod value of y is greater than mod value of x

So mod value of 1/x is greater than mod value of 1/y

x < 0, so 1/x < 0
As |1/x |>|1/y|
1/x+1/y<0

So all the conditions are correct
Ans E




Sent from my BLN-L22 using GMAT Club Forum mobile app
Current Student
avatar
B
Joined: 11 Sep 2016
Posts: 65
Location: India
Concentration: General Management, Leadership
GMAT 1: 710 Q47 V40
GPA: 3
WE: Sales (Manufacturing)
Re: If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ?  [#permalink]

Show Tags

New post 13 May 2017, 22:57
Bunuel Please let me know whether my method of deriving III as true is valid ?

From the question stem we know that x<0 and and \(\frac{x}{y}\) lies between 0 and -1 i.e. -1<\(\frac{x}{y}\)<0

Hence we necessarily have to have y>0

Multiplying Y on both sides (without changing signs because y>0)

\(x>-y\) result 1

Given in III is \(\frac{1}{x}+\frac{1}{y}<0\)

Therefore, \(\frac{1}{x}<-\frac{1}{y}\)

Taking resiprocals

\(\frac{x}{1}\)>-\(\frac{y}{1}\)
Hence \(x >-y\) result 2

result 1 and result 2 are the same

Hence III is correct
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51280
Re: If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ?  [#permalink]

Show Tags

New post 14 May 2017, 00:43
KM2018AA wrote:
Bunuel Please let me know whether my method of deriving III as true is valid ?

From the question stem we know that x<0 and and \(\frac{x}{y}\) lies between 0 and -1 i.e. -1<\(\frac{x}{y}\)<0

Hence we necessarily have to have y>0

Multiplying Y on both sides (without changing signs because y>0)

\(x>-y\) result 1

Given in III is \(\frac{1}{x}+\frac{1}{y}<0\)

Therefore, \(\frac{1}{x}<-\frac{1}{y}\)

Taking resiprocals

\(\frac{x}{1}\)>-\(\frac{y}{1}\)

Hence \(x >-y\) result 2

result 1 and result 2 are the same

Hence III is correct


Your solution missing steps. In the highlighted part, do you know the sign of y? How? If not then you cannot do that.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Current Student
avatar
B
Joined: 11 Sep 2016
Posts: 65
Location: India
Concentration: General Management, Leadership
GMAT 1: 710 Q47 V40
GPA: 3
WE: Sales (Manufacturing)
Re: If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ?  [#permalink]

Show Tags

New post 14 May 2017, 03:01
Bunuel wrote:
KM2018AA wrote:
Bunuel Please let me know whether my method of deriving III as true is valid ?

From the question stem we know that x<0 and and \(\frac{x}{y}\) lies between 0 and -1 i.e. -1<\(\frac{x}{y}\)<0

Hence we necessarily have to have y>0

Multiplying Y on both sides (without changing signs because y>0)

\(x>-y\) result 1

Given in III is \(\frac{1}{x}+\frac{1}{y}<0\)

Therefore, \(\frac{1}{x}<-\frac{1}{y}\)

Taking resiprocals

\(\frac{x}{1}\)>-\(\frac{y}{1}\)

Hence \(x >-y\) result 2

result 1 and result 2 are the same

Hence III is correct


Your solution missing steps. In the highlighted part, do you know the sign of y? How? If not then you cannot do that.


So then what is the rule with taking reciprocals in inequalities?
(if any)
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51280
Re: If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ?  [#permalink]

Show Tags

New post 14 May 2017, 04:36
KM2018AA wrote:
Bunuel wrote:
KM2018AA wrote:
Bunuel Please let me know whether my method of deriving III as true is valid ?

From the question stem we know that x<0 and and \(\frac{x}{y}\) lies between 0 and -1 i.e. -1<\(\frac{x}{y}\)<0

Hence we necessarily have to have y>0

Multiplying Y on both sides (without changing signs because y>0)

\(x>-y\) result 1

Given in III is \(\frac{1}{x}+\frac{1}{y}<0\)

Therefore, \(\frac{1}{x}<-\frac{1}{y}\)

Taking resiprocals

\(\frac{x}{1}\)>-\(\frac{y}{1}\)

Hence \(x >-y\) result 2

result 1 and result 2 are the same

Hence III is correct


Your solution missing steps. In the highlighted part, do you know the sign of y? How? If not then you cannot do that.


So then what is the rule with taking reciprocals in inequalities?
(if any)


You should know the signs. Check the links below for more:

Inequalities Made Easy!

Solving Quadratic Inequalities - Graphic Approach
Inequality tips
Wavy Line Method Application - Complex Algebraic Inequalities

DS Inequalities Problems
PS Inequalities Problems

700+ Inequalities problems

http://gmatclub.com/forum/inequalities-trick-91482.html
http://gmatclub.com/forum/data-suff-ine ... 09078.html
http://gmatclub.com/forum/range-for-var ... 09468.html
http://gmatclub.com/forum/everything-is ... 08884.html
http://gmatclub.com/forum/graphic-appro ... 68037.html

Hope this helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4317
Location: United States (CA)
Re: If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ?  [#permalink]

Show Tags

New post 18 May 2017, 19:02
2
AbdurRakib wrote:
If \(x<0\) and \(0 < \frac{x}{y} + 1<1\), which of the following must be true ?

I. \(y > 0\)

II. \(\frac{x}{y}>-1\)

III. \(\frac{1}{x}+\frac{1}{y}<0\)


A. I only

B. I and II only

C. I and III only

D. II and III only

E. I,II and III


We can simplify the given inequality:

0 < x/y + 1 < 1

-1 < x/y < 0

Since x is negative, y must be positive.

Let’s now analyze our Roman numeral answer choices:

I. y > 0

Since we’ve mentioned y must be positive, Roman numeral I is correct.

II. x/y > -1

Since -1 < x/y < 0 also means that x/y > -1, Roman numeral II is correct.

III. 1/x + 1/y < 0

We can multiply both sides of the inequality by x to obtain:

1 + x/y > 0

Notice that we switch the inequality sign since x is negative. Now let’s subtract 1 from both sides:

x/y > -1

Roman numeral III is correct also.

Answer: E
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Director
Director
User avatar
P
Joined: 14 Dec 2017
Posts: 518
Location: India
Premium Member
Re: If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ?  [#permalink]

Show Tags

New post 16 Jun 2018, 11:31
AbdurRakib wrote:
If \(x<0\) and \(0 < \frac{x}{y} + 1<1\), which of the following must be true ?

I. \(y > 0\)

II. \(\frac{x}{y}>-1\)

III. \(\frac{1}{x}+\frac{1}{y}<0\)


A. I only

B. I and II only

C. I and III only

D. II and III only

E. I, II and III



Given \(x<0\) .............(i)
&
\(0 < \frac{x}{y} + 1<1\)......(ii)

can be simplified as,

\(-1 < \frac{x}{y} < 0\) ................(iii)


I. \(y > 0\) - from (iii), we can say since \(x<0\), \(y>0\) is true

II. \(\frac{x}{y}>-1\) - from (iii), we can say this is true

III. \(\frac{1}{x}+\frac{1}{y}<0\) - multiply (ii) with \(\frac{1}{x}\) & since \(x<0\), we need to flip the signs. Hence III is also true.


Answer E.



Thanks,
GyM
_________________

New to GMAT Club - https://gmatclub.com/forum/new-to-gmat-club-need-help-271131.html#p2098335

Intern
Intern
avatar
B
Joined: 12 Dec 2016
Posts: 12
Re: If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ?  [#permalink]

Show Tags

New post 28 Sep 2018, 08:32
Bunuel wrote:
AbdurRakib wrote:
If x<0 and 0 < \(\frac{x}{y}\) + 1<1 ,which of the following must be true ?

I. y > 0

II. \(\frac{x}{y}\)>-1

III. \(\frac{1}{x}\)+\(\frac{1}{y}\)<0


A. I only

B. I and II only

C. I and III only

D. II and III only

E. I,II and III


\(0 < \frac{x}{y} + 1<1\)

Subtract 1 from all 3 sides: \(-1 < \frac{x}{y}<0\). We see that II is true.

Since x < 0, then for \(\frac{x}{y}<0\) to be true y must be positive. I must be true.

Next, divide \(0 < \frac{x}{y} + 1<1\) by x and flip the signs since we know that x is negative: \(0 >\frac{1}{y} + \frac{1}{x}>\frac{1}{x}\). III must be true.

Answer: E.

Hope it's clear.


Even though Statement II is true in this context, it is not true for values of \(\frac{x}{y}\)>0 because that contradicts the statement in the question stem after manipulating it (\(-1 < \frac{x}{y}<0\)). But then again, it is true in the context of this question. So if we get something similar in that sense, do we consider the statement to be true or not (Choice 'C' vs. Choice 'E')? How does that fit in the "must be true" VS. "could be true" context? Does anyone share the same misunderstanding in GMAT questions? I would appreciate if anyone could clarify this concept.
GMAT Club Bot
Re: If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ? &nbs [#permalink] 28 Sep 2018, 08:32
Display posts from previous: Sort by

If x < 0 and 0 < x/y + 1 < 1, which of the following must be true ?

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


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®.