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

It is currently 13 Dec 2018, 12:17

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
  • GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

     December 14, 2018

     December 14, 2018

     09:00 AM PST

     10:00 AM PST

    10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.
  • 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 x+y+z > 0, is z > 1 ?

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

Hide Tags

Intern
Intern
avatar
Joined: 21 Dec 2010
Posts: 2
If x+y+z > 0, is z > 1 ?  [#permalink]

Show Tags

New post 05 Feb 2011, 08:33
5
32
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

62% (01:22) correct 38% (01:25) wrong based on 856 sessions

HideShow timer Statistics

If x+y+z > 0, is z > 1 ?

(1) z > x + y + 1
(2) x + y + 1 < 0

This is a question from OG 10, could someone please explain this. The explanation in the OG is not clear enough.

Thanks,
Eddy
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51185
Re: is z > 1 ?  [#permalink]

Show Tags

New post 05 Feb 2011, 08:45
41
26
eddyed911 wrote:
If x+y+z > 0, is z > 1 ?

1) z > x + y + 1
2) x + y + 1 < 0

this is a question from OG 10, could someone please explain this. The explanation in the OG is not clear enough.

Thanks,
Eddy


Welcome to Gmat Club Eddy!

Note that:
You can only add inequalities when their signs are in the same direction:

If \(a>b\) and \(c>d\) (signs in same direction: \(>\) and \(>\)) --> \(a+c>b+d\).
Example: \(3<4\) and \(2<5\) --> \(3+2<4+5\).

You can only apply subtraction when their signs are in the opposite directions:

If \(a>b\) and \(c<d\) (signs in opposite direction: \(>\) and \(<\)) --> \(a-c>b-d\) (take the sign of the inequality you subtract from).
Example: \(3<4\) and \(5>1\) --> \(3-5<4-1\).

Back to the original question:

If x+y+z > 0, is z > 1?

(1) z > x + y + 1 --> as the signs are in the same direction we can add two inequalities: \((x+y+z)+z>x+y+1\) --> \(2z>1\) --> \(z>\frac{1}{2}\), so z may or may not be more than 1. Not sufficient.

(2) x + y + 1 < 0 --> as the signs are in the opposite direction we can subtract two inequalities: \((x+y+z)-(x+y+1)>0\) --> \(z-1>0\) --> \(z>1\). Sufficient.

Answer: B.

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

Most Helpful Community Reply
Director
Director
User avatar
Status: -=Given to Fly=-
Joined: 04 Jan 2011
Posts: 800
Location: India
Concentration: Leadership, Strategy
Schools: Haas '18, Kelley '18
GMAT 1: 650 Q44 V37
GMAT 2: 710 Q48 V40
GMAT 3: 750 Q51 V40
GPA: 3.5
WE: Education (Education)
Re: is z > 1 ?  [#permalink]

Show Tags

New post 05 Feb 2011, 08:52
6
1
Statement 1:
Given:
z>x+y+1 <---- Equ. 1
&
x+y+z>0

Now add z to both sides of Equ. 1
2z>x+y+z+1
Since x+y+z > 0
2z>GT0+1 (GT0 means a quantity greater than 0)
2z>GT1
z>GT(1/2)
So we cannot conclude that z>1
Therefore, insufficient!

Statement 2:
x+y+1<0
Adding z to both sides of the Equation
x+y+z+1<Z
GT0+1<z
or
GT1<z
Therefore, z>1
Sufficient!

Ans: 'B'

I hope the explanation is clear enough :)
_________________

"Wherever you go, go with all your heart" - Confucius

Useful Threads

1. How to Review and Analyze your Mistakes (Post by BB at GMAT Club)

2. 4 Steps to Get the Most out out of your CATs (Manhattan GMAT Blog)

My Experience With GMAT

1. From 650 to 710 to 750 - My Tryst With GMAT

2. Quest to do my Best - My GMAT Journey Log

General Discussion
Retired Moderator
avatar
Joined: 20 Dec 2010
Posts: 1820
Re: is z > 1 ?  [#permalink]

Show Tags

New post 05 Feb 2011, 08:56
2
If x+y+z > 0, is z > 1 ?

1) z > x + y + 1

z - 1 > x+ y
and
x+y > -z

z-1 > -z
2z>1

z>1/2

There are infinite real numbers between 1/2 and 1.

Not sufficient.

2)
x + y + 1 < 0
x+y < -1

To make x+y+z>0; z should be greater than 1 because x+y is less than -1.

Sufficient.

Ans: "B"
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Intern
Intern
avatar
Joined: 21 Dec 2010
Posts: 2
Re: is z > 1 ?  [#permalink]

Show Tags

New post 05 Feb 2011, 08:58
Thanks guys ! these explanations really clarify things :)
Manager
Manager
User avatar
Joined: 27 Jun 2008
Posts: 52
Location: United States (AL)
Concentration: General Management, Technology
GMAT 1: 660 Q48 V34
WE: Consulting (Computer Software)
Re: is z > 1 ?  [#permalink]

Show Tags

New post 07 Feb 2011, 06:43
1
thanks for the expalanation bunuel
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8673
Location: Pune, India
Re: is z > 1 ?  [#permalink]

Show Tags

New post 16 Feb 2011, 18:41
6
2
eddyed911 wrote:
If x+y+z > 0, is z > 1 ?

1) z > x + y + 1
2) x + y + 1 < 0



this is a question from OG 10, could someone please explain this. The explanation in the OG is not clear enough.

Thanks,
Eddy


In case you get confused with addition/subtraction of inequalities, you can stick with addition only, if you like. Just rewrite one inequality to give them the same sign. Remember that you can add inequalities only when they have the same sign.

Ques: Is z > 1?
Given: x+y+z > 0 .......... (I)

Stmnt 1: z > x + y + 1 .........(II)
(I) and (II) both have the same inequality sign '>' so we can add them.
x + y + 2z > x + y + 1
We get, z > (1/2)
z may or may not be greater than 1. Not sufficient.

Stmnt 2: x + y + 1 < 0
We can re-write this as 0 > x + y + 1 .......(III)
Now, (I) and (III) have the same sign '>' so you can add them.
x + y + z > x + y + 1
We get z > 1. Sufficient.

Answer (B)
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Senior Manager
Senior Manager
avatar
Status: Up again.
Joined: 31 Oct 2010
Posts: 493
Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40
GMAT 2: 740 Q49 V42
Re: is z > 1 ?  [#permalink]

Show Tags

New post 16 Feb 2011, 23:36
eddyed911 wrote:
If x+y+z > 0, is z > 1 ?

1) z > x + y + 1
2) x + y + 1 < 0



this is a question from OG 10, could someone please explain this. The explanation in the OG is not clear enough.

Thanks,
Eddy


Statement 1: just tells us z-1>x+y. Tells us nothing about the signs of any variable. Insufficient.
Statement 2: tells us x+y<-1. Now for x+y+z>0, minimum quantity we have to add has to be greater than one. Test numbers. Sufficient.

Answer B.
_________________

My GMAT debrief: http://gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html

Director
Director
User avatar
B
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 521
CAT Tests
Re: is z > 1 ?  [#permalink]

Show Tags

New post 03 Mar 2011, 06:13
Bunuel wrote:
eddyed911 wrote:
If x+y+z > 0, is z > 1 ?

1) z > x + y + 1
2) x + y + 1 < 0

this is a question from OG 10, could someone please explain this. The explanation in the OG is not clear enough.

Thanks,
Eddy


Welcome to Gmat Club Eddy!

Note that:
You can only add inequalities when their signs are in the same direction:

If \(a>b\) and \(c>d\) (signs in same direction: \(>\) and \(>\)) --> \(a+c>b+d\).


Example: \(3<4\) and \(2<5\) --> \(3+2<4+5\).

You can only apply subtraction when their signs are in the opposite directions:

If \(a>b\) and \(c<d\) (signs in opposite direction: \(>\) and \(<\)) --> \(a-c>b-d\) (take the sign of the inequality you subtract from).
Example: \(3<4\) and \(5>1\) --> \(3-5<4-1\).

Back to the original question:

If x+y+z > 0, is z > 1?

(1) z > x + y + 1 --> as the signs are in the same direction we can add two inequalities: \((x+y+z)+z>x+y+1\) --> \(2z>1\) --> \(z>\frac{1}{2}\), so z may or may not be more than 1. Not sufficient.

(2) x + y + 1 < 0 --> as the signs are in the opposite direction we can subtract two inequalities: \((x+y+z)-(x+y+1)>0\) --> \(z-1>0\) --> \(z>1\). Sufficient.

Answer: B.

Hope it's clear.




is the option (1) is like : x+y+z+z>0+x+y+1 (as a>b+c>d= a+c>b+d), and option 2
(2) x+y+z -(x+y+z)>0-0 (as a>b -c<d = a-b>c-d)
Help me for my understanding.
_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Senior Manager
Senior Manager
avatar
Joined: 30 Aug 2009
Posts: 270
Location: India
Concentration: General Management
Re: DS inequalities  [#permalink]

Show Tags

New post 11 Jan 2012, 23:44
Smita04 wrote:
If x + y + z > 0, is z > 1?

(1) z > x + y + 1
(2) x + y + 1 < 0


stmnt1: adding z to both sides of the equation

2z >x+y+z+1
2z>1 or z> 0.5. this can give us any value for z (0.6,1,1.5).

taking numeric values
assume
x= - 0.2
y= - 0.3
z= + 0.6

z> x+y+1 but z<1

for x= 1, y= 2 and z= 5

we have x+y+z>0

and z> x+y+1 and z>1. Hence insuff

stmnt2:
adding z to either sides
x+y+1+z<0+z
or z>1

also given x+y+1<0 or x+y < -1
we have x+y+z>0 or -1 + z >0 or z>1

hence suff

so B
Intern
Intern
avatar
Joined: 14 Dec 2010
Posts: 43
Re: If x+y+z > 0, is z > 1 ? 1) z > x + y + 1 2) x + y  [#permalink]

Show Tags

New post 19 Jan 2012, 08:02
Thanks Bunuel...bcoz of the property u told this Q took 30 seconds to solve...
Manager
Manager
avatar
Joined: 10 Jan 2010
Posts: 156
Location: Germany
Concentration: Strategy, General Management
Schools: IE '15 (M)
GPA: 3
WE: Consulting (Telecommunications)
Re: If x+y+z > 0, is z > 1 ? 1) z > x + y + 1 2) x + y  [#permalink]

Show Tags

New post 20 Jan 2012, 04:54
Thanks Bunuel, makes the questions clear and easy to solve!
Manager
Manager
User avatar
Joined: 22 Feb 2009
Posts: 171
GMAT ToolKit User
Re: If x+y+z > 0, is z > 1 ?  [#permalink]

Show Tags

New post 22 Jul 2014, 15:42
Entwistle wrote:
Statement 1:
Given:
z>x+y+1 <---- Equ. 1
&
x+y+z>0

Now add z to both sides of Equ. 1
2z>x+y+z+1
Since x+y+z > 0
2z>GT0+1 (GT0 means a quantity greater than 0)
2z>GT1
z>GT(1/2)
So we cannot conclude that z>1
Therefore, insufficient!

Statement 2:
x+y+1<0
Adding z to both sides of the Equation
x+y+z+1<Z
GT0+1<z
or
GT1<z
Therefore, z>1
Sufficient!

Ans: 'B'

I hope the explanation is clear enough :)


Yeah, Add z to the both sides of the equation is the fastest way :)
_________________

.........................................................................
+1 Kudos please, if you like my post

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9151
Premium Member
Re: If x+y+z > 0, is z > 1 ?  [#permalink]

Show Tags

New post 16 Oct 2018, 03:03
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: If x+y+z > 0, is z > 1 ? &nbs [#permalink] 16 Oct 2018, 03:03
Display posts from previous: Sort by

If x+y+z > 0, is z > 1 ?

  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®.