• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to $200 Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

## Is m+z > 0?

tagged by: Brent@GMATPrepNow

This topic has 6 expert replies and 16 member replies
Goto page
• 1,
• 2
ksutthi Newbie | Next Rank: 10 Posts
Joined
30 Mar 2008
Posted:
8 messages
1

#### Is m+z > 0?

Sun Jul 06, 2008 1:21 am
Got this from practice test 1. Can somebody help?

Is m+z > 0?

(1) m-3z > 0
(2) 4z-m > 0

Thanks a lot.

szapiszapo Junior | Next Rank: 30 Posts
Joined
30 Jun 2008
Posted:
28 messages
3
Sun Jul 06, 2008 3:08 am
does the wording states that m & z can be either positive or negative?

if m & z can be positive or negative, then i guess answer is E

ksutthi Newbie | Next Rank: 10 Posts
Joined
30 Mar 2008
Posted:
8 messages
1
Sun Jul 06, 2008 4:12 am
m and z can be anything. The question is just like that.

The answer is (C). But I was wondering how I can derive that answer.

ildude02 Master | Next Rank: 500 Posts
Joined
13 Jan 2008
Posted:
320 messages
10
Sun Jul 06, 2008 8:35 am
I solved it by plugging in numbers and it took me a while. I wonder if there is an easier way to solve it and I bet there is. Ian, Stuart or anyone, please share your thoughts with the easier approach . This questions format seems to be common and I would appreciate anyone's input on solving this question.

Now that I thought about it more, this is what I came up with when combining both the statements,

3z < m < 4z; for m and z +ve values, m > -z will always be true;
This equation cannot be solved when we consider negative values for Z. You could see that with Z as -ve value, we get,
-3Z < M < -4Z. There cannot be a value to satify this equation since something greater then -3z will always be greater then -4Z. So, that leaves us wth Z always taking a +ve value and whne Z is +ve, M is always +ve as well. That would mean, M > -Z is always TRUE .

Just wanted to make sure is this a valid assumption for not considering negative values for Z?

Last edited by ildude02 on Sun Jul 06, 2008 8:49 am; edited 2 times in total

wilderness Master | Next Rank: 500 Posts
Joined
15 Mar 2008
Posted:
102 messages
4
Sun Jul 06, 2008 8:44 am
ksutthi wrote:
Got this from practice test 1. Can somebody help?

Is m+z > 0?

(1) m-3z > 0
(2) 4z-m > 0

Thanks a lot.
Sum the 2 inequalities and we get z > 0.
If z>0 then they only way (1) is possible is if m is also positive.
Hence both numbers are positive and thus m+z > 0

So C is correct.

ildude02 Master | Next Rank: 500 Posts
Joined
13 Jan 2008
Posted:
320 messages
10
Sun Jul 06, 2008 8:54 am
I'm curious to see your logic for concluding that Z> 0 when combining both the statemets.

wilderness wrote:
ksutthi wrote:
Got this from practice test 1. Can somebody help?

Is m+z > 0?

(1) m-3z > 0
(2) 4z-m > 0

Thanks a lot.
Sum the 2 inequalities and we get z > 0.
If z>0 then they only way (1) is possible is if m is also positive.
Hence both numbers are positive and thus m+z > 0

So C is correct.

wilderness Master | Next Rank: 500 Posts
Joined
15 Mar 2008
Posted:
102 messages
4
Sun Jul 06, 2008 2:03 pm
If both (1) and (2) are separately greater than 0 then their sum must also be greater than 0.
i.e. m-3z + 4z - m > 0
which give z > 0

Hope it helps.

ildude02 Master | Next Rank: 500 Posts
Joined
13 Jan 2008
Posted:
320 messages
10
Sun Jul 06, 2008 5:06 pm
Thanks.

aj5105 Legendary Member
Joined
06 Jul 2008
Posted:
1169 messages
Followed by:
1 members
25
Tue Jun 23, 2009 2:52 am
Combine (1) + (2)

z>0. This implies m too is >0.

(C)

rah_pandey Master | Next Rank: 500 Posts
Joined
22 May 2009
Posted:
122 messages
8
Test Date:
15/07/2009
GMAT Score:
700
Tue Jun 23, 2009 4:01 am
Please note a>0 and b>0 =>a+b>0

but same is not true about substraction and also if sign of one of the inequality is different from the other

Domnu Master | Next Rank: 500 Posts
Joined
24 May 2009
Posted:
385 messages
11
Test Date:
2011. Practicing now
Target GMAT Score:
800
GMAT Score:
740
Thu Jun 25, 2009 2:14 pm
I would just graph it with x = m, y = z and look at the regions.

_________________
Have you wondered how you could have found such a treasure? -T

El Nino Newbie | Next Rank: 10 Posts
Joined
22 Sep 2009
Posted:
5 messages
1
Tue Sep 22, 2009 8:14 am
There are values of m and z fulfilling both conditions, some of which result in m+z>0, and others which result in m+z<0.

E.g. m=-2, z=-1 --> m+z<0
m=2, z=-1 --> m+z<0

Similarly, using the graph method suggested, there are values m+z can be positive or negative.

So, I think the statements are insufficient, answer E.

However, the GMAT software and contributors to this site have answer C.

Can someone pls explain??

Thanks

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
11516 messages
Followed by:
1229 members
5254
GMAT Score:
770
Tue Sep 22, 2009 8:25 am
ksutthi wrote:
Got this from practice test 1. Can somebody help?

Is m+z > 0?

(1) m-3z > 0
(2) 4z-m > 0

Thanks a lot.
ildude02 has it correct (see a few posts above).

When we combine (1) and (2) we get 3z < m < 4z

Now some people see this and conclude that the value of m lies between 3z and 4z (true). They also conclude that z (and thus m) can be either positive or negative (false).

The only time that 3z<4z is when z is positive. When z is negative, then 3z>4z.
So, in addition to telling us that the value of m is between 3z and 4z, the inequality 3z < m < 4z also tells us that z must be positive.
If z is positive, then m must also be positive, in which case m+z must be positive.

_________________
Brent Hanneson â€“ Founder of GMATPrepNow.com
Use our video course along with

Check out the online reviews of our course
Come see all of our free resources

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months!
sashish007 Senior | Next Rank: 100 Posts
Joined
13 May 2009
Posted:
72 messages
Followed by:
2 members
7
Target GMAT Score:
750+
Thu Dec 16, 2010 9:10 am
@brent, great explanation. but i was a little apprehensive in combining the two at the beginning and thought of the following solution:

the question asks, IS m+z>0? .... i.e. IS m+z +ve?

this can only happen if either
[i] both m & z are +ve OR
[ii] m and z have dissimilar signs with the +ve no. greater in magnitude than the -ve no.
...... [A]

[1] m>3z
m-3z>0
2 variables - 1 equation - NO soln - INS
(since, no. of equations should equal the no. of variables to solve for the variables!)

[2] 4z-m>0
Again, 2 variables - 1 equation - NO soln - INS

COMBINE 1, 2 i.e. Add 1 & 2,
m-3z>0
-m+4z>0 ... ensure that the direction of inequalities are same
---------
z>0 ... z is +ve;
thus, as per [A] m is +ve or -ve

BUT, m > 3z
so, if z is +ve, then m HAS to be +ve
THUS, m+z IS +ve (>0) hence, SUFF (C)

Ashish

_________________
Ashish
Share not just why the right answer is right, but also why the wrong ones are not.

ankurmit Legendary Member
Joined
02 Nov 2009
Posted:
516 messages
Followed by:
1 members
14
Test Date:
06-06-2011
GMAT Score:
710
Sun Dec 19, 2010 8:28 am
Grt man!!

_________________
--------
Ankur mittal

### Top First Responders*

1 GMATGuruNY 67 first replies
2 Rich.C@EMPOWERgma... 44 first replies
3 Brent@GMATPrepNow 40 first replies
4 Jay@ManhattanReview 25 first replies
5 Terry@ThePrinceto... 10 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 GMATGuruNY

The Princeton Review Teacher

132 posts
2 Rich.C@EMPOWERgma...

EMPOWERgmat

112 posts
3 Jeff@TargetTestPrep

Target Test Prep

95 posts
4 Scott@TargetTestPrep

Target Test Prep

92 posts
5 Max@Math Revolution

Math Revolution

91 posts
See More Top Beat The GMAT Experts