Last visit was: 19 Nov 2025, 21:02 It is currently 19 Nov 2025, 21:02
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
   1   2 
avatar
zanaik89
avatar
Joined: 19 Aug 2016
Last visit: 29 Nov 2019
Posts: 54
Own Kudos:
8
Given Kudos: 30
Posts: 54
Kudos: 8
Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 22 Jul 2018, 17:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Is m+z > 0

(1) m - 3z > 0. Insufficient on its own.

(2) 4z - m > 0. Insufficient on its own.


(1)+(2) Remember we can add inequalities with the sign in the same direction:

\((m-3z)+(4z-m)>0\);

\(z>0\), so \(z\) is positive.

From (1) \(m>(3z=positive)\), so \(m\) is positive too (\(m\) is more than some positive number \(3z\), so it's positive). Therefore, \(m+z=positive+positive>0\). Sufficient.

Answer: C.

For graphic approach refer to: https://gmatclub.com/forum/is-m-z-0-1-m- ... 75657.html
Show more

Hi Bunuel...

From statement 2 we know that 4z>m in which case lets say.. 4(1)>1 the statement is suff that m+z>0

But 4(1)>-2 in which case M+z>0 is not true

Thanks For ur help in advance
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,389
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,389
Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 22 Jul 2018, 20:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
zanaik89
Bunuel
Is m+z > 0

(1) m - 3z > 0. Insufficient on its own.

(2) 4z - m > 0. Insufficient on its own.


(1)+(2) Remember we can add inequalities with the sign in the same direction:

\((m-3z)+(4z-m)>0\);

\(z>0\), so \(z\) is positive.

From (1) \(m>(3z=positive)\), so \(m\) is positive too (\(m\) is more than some positive number \(3z\), so it's positive). Therefore, \(m+z=positive+positive>0\). Sufficient.

Answer: C.

For graphic approach refer to: https://gmatclub.com/forum/is-m-z-0-1-m- ... 75657.html

Hi Bunuel...

From statement 2 we know that 4z>m in which case lets say.. 4(1)>1 the statement is suff that m+z>0

But 4(1)>-2 in which case M+z>0 is not true

Thanks For ur help in advance
Show more

Yes, (2) is not sufficient because it gives an YES and a NO answers to the question whether m + z > 0 but what is your doubt?
User avatar
ProfChaos
User avatar
Joined: 11 Apr 2020
Last visit: 06 Dec 2020
Posts: 122
Own Kudos:
352
Given Kudos: 630
GMAT 1: 660 Q49 V31
GMAT 1: 660 Q49 V31
Posts: 122
Kudos: 352
Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 21 Sep 2020, 02:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
kman
Is m + z > 0?

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

Hi Bunuel

Help me with what is wrong in my approach

Q.Stem : is m+z>0
Since we dont know anything about m and z we cannot do anything with the stem.
m/z can be 0/+ve/-ve

Statement 1: m-3z>0 ==> m>3z
Let z=0 ==> 3z=0 ==> m>0, let m=1 ==> m+z = 1+0 = 1 > 0 (YES)
Let z=1 ==> 3z=3 ==> m>3, let m=4 ==> m+z = 4+1 = 5 > 0 (YES)
Let z=-1 ==> 3z=-3 ==> m>-3. let m=-2 ==> m+z = (-2)+(-1) = -3 < 0 (NO)
INSUFFICIENT

Statement 2: 4z - m > 0 ==> 4z>m ==> m<4z
Let z=0 ==> 4z=0 ==> m<0, let m=-1 ==> m+z = -1+0 = -1 < 0 (NO)
Let z=1 ==> 4z=4 ==> m<4, let m=3 ==> m+z = 3+1 = 4 > 0 (YES)
Let z=-1 ==> 4z=-4 ==> m<-4. let m=-5 ==> m+z = (-5)+(-1) = -6 < 0 (NO)
INSUFFICIENT

Combining 1 and 2
We get, m>3z and m<4z, let m=3.5z ==> m+z = 3.5z+z = 4.5z
Let z=0 ==> 4.5z = 0 ==> 0 = 0 (NO)
Let z=1 ==> 4.5z = 4.5 ==> 4.5 > 0 (YES)
Let z=-1 ==> 4.5z = -4.5 ==> -4.5 < 0 (NO)
INSUFFICIENT

Hence (E)
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,389
 [1]
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,389
 [1]
Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 21 Sep 2020, 02:28
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ProfChaos
kman
Is m + z > 0?

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

Hi Bunuel

Help me with what is wrong in my approach

Q.Stem : is m+z>0
Since we dont know anything about m and z we cannot do anything with the stem.
m/z can be 0/+ve/-ve

Statement 1: m-3z>0 ==> m>3z
Let z=0 ==> 3z=0 ==> m>0, let m=1 ==> m+z = 1+0 = 1 > 0 (YES)
Let z=1 ==> 3z=3 ==> m>3, let m=4 ==> m+z = 4+1 = 5 > 0 (YES)
Let z=-1 ==> 3z=-3 ==> m>-3. let m=-2 ==> m+z = (-2)+(-1) = -3 < 0 (NO)
INSUFFICIENT

Statement 2: 4z - m > 0 ==> 4z>m ==> m<4z
Let z=0 ==> 4z=0 ==> m<0, let m=-1 ==> m+z = -1+0 = -1 < 0 (NO)
Let z=1 ==> 4z=4 ==> m<4, let m=3 ==> m+z = 3+1 = 4 > 0 (YES)
Let z=-1 ==> 4z=-4 ==> m<-4. let m=-5 ==> m+z = (-5)+(-1) = -6 < 0 (NO)
INSUFFICIENT

Combining 1 and 2
We get, m>3z and m<4z, let m=3.5z ==> m+z = 3.5z+z = 4.5z
Let z=0 ==> 4.5z = 0 ==> 0 = 0 (NO)
Let z=1 ==> 4.5z = 4.5 ==> 4.5 > 0 (YES)
Let z=-1 ==> 4.5z = -4.5 ==> -4.5 < 0 (NO)
INSUFFICIENT

Hence (E)
Show more

Notice that 3z < m < 4z implies that z is positive (3z < 4z --> 0 < z), so you should not use negative numbers for z. Positive z on the other hand implies that m is positive too. So, m + z = positive + positive = positive.

Hope it helps.
User avatar
ProfChaos
User avatar
Joined: 11 Apr 2020
Last visit: 06 Dec 2020
Posts: 122
Own Kudos:
352
Given Kudos: 630
GMAT 1: 660 Q49 V31
GMAT 1: 660 Q49 V31
Posts: 122
Kudos: 352
Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 21 Sep 2020, 02:33
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
ProfChaos
kman
Is m + z > 0?

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

Hi Bunuel

Help me with what is wrong in my approach

Q.Stem : is m+z>0
Since we dont know anything about m and z we cannot do anything with the stem.
m/z can be 0/+ve/-ve

Statement 1: m-3z>0 ==> m>3z
Let z=0 ==> 3z=0 ==> m>0, let m=1 ==> m+z = 1+0 = 1 > 0 (YES)
Let z=1 ==> 3z=3 ==> m>3, let m=4 ==> m+z = 4+1 = 5 > 0 (YES)
Let z=-1 ==> 3z=-3 ==> m>-3. let m=-2 ==> m+z = (-2)+(-1) = -3 < 0 (NO)
INSUFFICIENT

Statement 2: 4z - m > 0 ==> 4z>m ==> m<4z
Let z=0 ==> 4z=0 ==> m<0, let m=-1 ==> m+z = -1+0 = -1 < 0 (NO)
Let z=1 ==> 4z=4 ==> m<4, let m=3 ==> m+z = 3+1 = 4 > 0 (YES)
Let z=-1 ==> 4z=-4 ==> m<-4. let m=-5 ==> m+z = (-5)+(-1) = -6 < 0 (NO)
INSUFFICIENT

Combining 1 and 2
We get, m>3z and m<4z, let m=3.5z ==> m+z = 3.5z+z = 4.5z
Let z=0 ==> 4.5z = 0 ==> 0 = 0 (NO)
Let z=1 ==> 4.5z = 4.5 ==> 4.5 > 0 (YES)
Let z=-1 ==> 4.5z = -4.5 ==> -4.5 < 0 (NO)
INSUFFICIENT

Hence (E)

Notice that 3z < m < 4z implies that z is positive (3z < 4z --> 0 < z), so you should not use negative numbers for z. Positive z on the other hand implies that m is positive too. So, m + z = positive + positive = positive.

Hope it helps.
Show more

Thank you so much for replying this quickly!

I understood. Thanks a lot Bunuel. You are a saviour!
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,070
Own Kudos:
19,393
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,070
Kudos: 19,393
Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 28 Sep 2020, 05:09
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

DS question with 2 variables: Let the original condition in a DS question contain 2 variables . In other words, there are two fewer equations than variables. Now, we know that each condition (1) and (2) would usually give us an equation, however, since we need 2 equations to match the numbers of variables and equations in the original condition, the unequal number of equations and variables should logically give us an answer C.

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

We have to find whether m + z > 0 .


Second and the third step of Variable Approach: From the original condition, we have 2 variables (m and z).To match the number of variables with the number of equations, we need 2 equations. Since conditions (1) and (2) will provide 1 equation each, C would most likely be the answer.

Let’s take a look at both conditions together .

Condition(1) tells us that m - 3z > 0 or m > 3z .

Condition(2) tells us that 4z - m > 0.

=> 4z - m > 0 or m < 4z

Adding both inequalities: m - 3z + 4z - m > 0 => z > 0 [Hence, z is positive]

Combining both: 3z < m < 4z

When z > 0 then m + z will also be greater than '0' - is m +z > 0 - YES

Since the answer is unique YES , both conditions together are sufficient by CMT 1.


So, C is the correct answer.

Answer: C
User avatar
CrackverbalGMAT
User avatar
Major Poster
Joined: 03 Oct 2013
Last visit: 19 Nov 2025
Posts: 4,844
Own Kudos:
8,945
Given Kudos: 225
Affiliations: CrackVerbal
Location: India
Expert
Expert reply
Posts: 4,844
Kudos: 8,945
Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 01 Jul 2021, 03:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The question pertains to the sign of an addition of terms. This should give us a clue that if we have to combine the inequalities, we need to add the inequalities.

From statement I alone, m – 3z > 0.
Therefore, m > 3z

If z = -1 and m = 1, m > 3z but m + z = 0. The main question can be answered with a NO.
If z = -1 and m = 2, m > 3z but m + z > 0. The main question can be answered with a YES.
Statement I alone is insufficient. Answer options A and D can be eliminated.

From statement II alone, 4z – m > 0.
Therefore, 4z > m or m < 4z.

If z = 0, m = -1, m <4z but m + z < 0. The main question can be answered with a NO
If z = 1, m = 1, m < 4z but m + z > 0. The main question can be answered with a YES.
Statement II alone is insufficient. Answer option B can be eliminated.

Combining statements I and II, we have the following:
From statement I alone, m > 3z; from statement II alone, m < 4z. Therefore, 3z < m < 4z.

Adding the two inequalities given, m – 3z + 4z – m > 0, we can see that z > 0. Therefore, m has to be positive.
Since both m and z are positive, m + z > 0.
The combination of statements is sufficient. Answer option E can be eliminated.

The correct answer option is C.

Hope that helps!
Aravind B T
User avatar
adityaganjoo
User avatar
Joined: 10 Jan 2021
Last visit: 04 Oct 2022
Posts: 148
Own Kudos:
32
Given Kudos: 154
Posts: 148
Kudos: 32
Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 10 Jul 2021, 07:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
kman
Is m + z > 0?

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

Statement 1: m>3z
m=1; z=-1;
m-3z>0; sure
m+z = 0; So, no

m=8, z=1;
m>3z? yes
m+z>0? yes

So, Statement 1 is insufficient

Statement 2: 4z>m
z=1; m=2
4z>m? Yes
m+z>0? Yes

z=1, m=-2
4z>m? Yes
m+z>0? No

So, Statement 2 is insufficient

Combining both:
(1) m>3z
(2)m<4z

Multiply (1) with -1: -m<-3z
Add (1) to (2)
0<z
i.e. z>0
Put this in original (1)
m>0
Therefore, m+z> 0

Therefore, (C)

We are going to Tahiti
User avatar
RastogiSarthak99
User avatar
Joined: 20 Mar 2019
Last visit: 10 Aug 2024
Posts: 141
Own Kudos:
23
Given Kudos: 282
Location: India
Posts: 141
Kudos: 23
Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 03 Jun 2022, 22:23
Kudos
Add Kudos
Bookmarks
Bookmark this Post
My 2 cents on this:

For me, the best way to solve this was to realize that both statements alone were not giving any answer. Goal is to find whether m + z > 0

Jumping ahead to St 1 and 2 together, By adding both statements:

m - 3z> 0
-m + 4z> 0
-------------
z>0

Therefore, if m - 3z >0

m>3z

m> 3 (z, which is some positive number)

hence m is positive and m+z > 0

C
User avatar
SomeOneUnique
User avatar
Joined: 17 Mar 2019
Last visit: 26 Dec 2024
Posts: 122
Own Kudos:
117
Given Kudos: 41
Location: India
Posts: 122
Kudos: 117
Is m + z > 0 (1) m - 3z > 0 (2) 4z - m > 0 01 Nov 2024, 18:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Is m + z > 0?

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

To answer whether m+z is positive, we need at least some information about the signs of m and z.
Let's dive deep in each of the given information statements.

(1) m - 3z > 0
In inequalities, we can add and subtract without knowing the sign of the variables but to multiply and divide one has to be cautious about the sign of the variables.
Thus, m - 3z > 0 can also be written as m > 3z.
m+z will be greater than 3z+z i.e. 4z. (Only calculation for this statement)
If z is positive then 4z will be greater than 0.
If z is negative then 4z will be less than 0.
Because we are yet to get a confirmation on the sign of z, the statement I is insufficient.


(2) 4z - m > 0
Using the same logic as used in statement I, 4z - m > 0 can be written as 4z > m.
It can be further divided by 4, z>m/4. (Only calculation for this statement)
Because we are yet to get a confirmation on signs of m and z, the statement II is insufficient.


(Both)
m - 3z > 0
4z - m > 0
4z - m > 0 can be re-written as -m + 4z >0

m - 3z > 0
-m + 4z >0
----------------
Adding the 2 equations, we get z > 0.
Wallah, this is what we were looking for; the sign of z is now known to us.

We can proceed further to fill the gap of statement 1 but we will not as we have the answer that data is sufficient.
Hence C is the correct option for this question.
   1   2 
Moderators:
Bunuel
Math Expert
105390 posts
kingbucky
496 posts