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

 It is currently 19 Jun 2019, 00:09

### 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

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

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

Author Message
TAGS:

### Hide Tags

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

### Show Tags

05 Feb 2011, 09:33
6
39
00:00

Difficulty:

55% (hard)

Question Stats:

63% (01:53) correct 37% (02:04) wrong based on 1060 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
Math Expert
Joined: 02 Sep 2009
Posts: 55681
Re: is z > 1 ?  [#permalink]

### Show Tags

05 Feb 2011, 09:45
47
31
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.

Hope it's clear.
_________________
Director
Status: -=Given to Fly=-
Joined: 04 Jan 2011
Posts: 799
Location: India
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

05 Feb 2011, 09:52
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
_________________
##### General Discussion
Retired Moderator
Joined: 20 Dec 2010
Posts: 1745
Re: is z > 1 ?  [#permalink]

### Show Tags

05 Feb 2011, 09:56
3
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"
_________________
Intern
Joined: 21 Dec 2010
Posts: 2
Re: is z > 1 ?  [#permalink]

### Show Tags

05 Feb 2011, 09:58
Thanks guys ! these explanations really clarify things
Intern
Joined: 27 Jun 2008
Posts: 47
Location: United States (AL)
Concentration: General Management, Technology
GMAT 1: 660 Q48 V34
WE: Consulting (Computer Software)
Re: is z > 1 ?  [#permalink]

### Show Tags

07 Feb 2011, 07:43
1
thanks for the expalanation bunuel
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9331
Location: Pune, India
Re: is z > 1 ?  [#permalink]

### Show Tags

16 Feb 2011, 19:41
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.

_________________
Karishma
Veritas Prep GMAT Instructor

Senior Manager
Status: Up again.
Joined: 31 Oct 2010
Posts: 483
Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40
GMAT 2: 740 Q49 V42
Re: is z > 1 ?  [#permalink]

### Show Tags

17 Feb 2011, 00:36
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.

_________________
My GMAT debrief: http://gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html
Senior Manager
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 490
Re: is z > 1 ?  [#permalink]

### Show Tags

03 Mar 2011, 07:13
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.

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.
_________________
Senior Manager
Joined: 30 Aug 2009
Posts: 261
Location: India
Concentration: General Management

### Show Tags

12 Jan 2012, 00:44
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:
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
Joined: 14 Dec 2010
Posts: 41
Re: If x+y+z > 0, is z > 1 ? 1) z > x + y + 1 2) x + y  [#permalink]

### Show Tags

19 Jan 2012, 09:02
Thanks Bunuel...bcoz of the property u told this Q took 30 seconds to solve...
Manager
Joined: 10 Jan 2010
Posts: 146
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

20 Jan 2012, 05:54
Thanks Bunuel, makes the questions clear and easy to solve!
Manager
Joined: 22 Feb 2009
Posts: 160
Re: If x+y+z > 0, is z > 1 ?  [#permalink]

### Show Tags

22 Jul 2014, 16:42
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
Joined: 09 Sep 2013
Posts: 11396
Re: If x+y+z > 0, is z > 1 ?  [#permalink]

### Show Tags

16 Oct 2018, 04:03
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.
_________________
Re: If x+y+z > 0, is z > 1 ?   [#permalink] 16 Oct 2018, 04:03
Display posts from previous: Sort by