once you rule out 1 and 2 independently and combine them,
what you get is
1) 4z>m>3z
2) by adding two inequalities
z>0
hence m>0
and m+z>0
C
BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
Redeem
Featured Course
Target Test Prep GMAT OnDemand
Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.
- 715+ score guarantee — highest in the industry (99th percentile)
- 52 chapters · 1,500+ lessons · 4,000+ practice questions
- 400 hours of video · 1,500+ instructor-led HD smartboard lessons
- 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
- 24/7 live support + weekly Zoom office hours with GMAT instructors
- TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
- 1,200+ flashcards + AI-powered study assistant & daily calendar
- OnDemand, LiveTeach & GMAT Bootcamp formats available
- Also: GRE, SAT Math & Executive Assessment courses
- MBA Admissions Consulting now available
- 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
- 200,000+ students served
- 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★
5.0
(559 reviews)
130-pt guarantee
$0 to start
then $127/mo
M+Z>0
Source: Beat The GMAT — Data Sufficiency |
From what i could make out..
1. says m>3z.. in which case either of m or z or both can be negative.
same is the case with statement 2.
If u consider both the statements..
m>3z but m<4z
this can happen only when both the variables are positve because when z is negative for ex: -3 ..there exists no solution for m which will be
>-9 but <-12 so for the inequality to hold true.. z should be positve n therefore m also positve.
and hence the addition of 2 positive numbers positive
Hope that gave a better insight.
1. says m>3z.. in which case either of m or z or both can be negative.
same is the case with statement 2.
If u consider both the statements..
m>3z but m<4z
this can happen only when both the variables are positve because when z is negative for ex: -3 ..there exists no solution for m which will be
>-9 but <-12 so for the inequality to hold true.. z should be positve n therefore m also positve.
and hence the addition of 2 positive numbers positive
Hope that gave a better insight.
Can someone plz. help me understand this problem
If m-3z>0
Then m>3z only if m and z are positive.
And m<3z if m and z are negative
So 1st is insufficient
2) Similarly for 2nd
4z>m only if m and z are positive
Else 4z<m
Now combining 1 and 2 we get
3z<m<4z
Now m and z can be positive as well as negative
So how we reached conclusion that m+z>0
Also I am not sure this is right way to solve this problem
If m-3z>0
Then m>3z only if m and z are positive.
And m<3z if m and z are negative
So 1st is insufficient
2) Similarly for 2nd
4z>m only if m and z are positive
Else 4z<m
Now combining 1 and 2 we get
3z<m<4z
Now m and z can be positive as well as negative
So how we reached conclusion that m+z>0
Also I am not sure this is right way to solve this problem
GMAT/MBA Expert
-
Ian Stewart
- GMAT Instructor
- Posts: 2623
- Location: Montreal
- Thanked: 1090 times
- GMAT Score:780
If m-3z > 0, then m > 3z. It does not matter whether m and z are positive or negative. We're only adding 3z to both sides of the inequality here, and you never need to worry about reversing an inequality when you add or subtract the same quantity on both sides.gmattester wrote:Can someone plz. help me understand this problem
If m-3z>0
Then m>3z only if m and z are positive.
And m<3z if m and z are negative
I expect you're thinking about multiplying (or dividing) on both sides of an inequality- if you multiply or divide by a negative, you must reverse the inequality.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
ianstewartgmat.com
if you combine I & IIgmattester wrote: Now combining 1 and 2 we get
3z<m<4z
Now m and z can be positive as well as negative
So how we reached conclusion that m+z>0
Also I am not sure this is right way to solve this problem
m-3z>0
4z-m>0
If you add these two inequalities
m-3z+4z-m>0
-3z+4z>0
z>0
if z > 0, then m will also be greater than 0 because m>3z
Hence m+z>0, answer is C.
Always remember the following rule for inequalities.
1. Inequalities can only be added to each other, they cannot be subtracted.
2. When adding two inequalities, the signs of both the inequalities should be in the same direction.
Like we did in this case.
Hope this helps. Let me know if you still have any problems.
Thanks Ian. I read one of your post where it was x/y>1 and you explained this reversing an inequality thing. So I applied same concept here but forgot this rule is only true for multiplication and division. Thanks for clearing that.Ian Stewart wrote:If m-3z > 0, then m > 3z. It does not matter whether m and z are positive or negative. We're only adding 3z to both sides of the inequality here, and you never need to worry about reversing an inequality when you add or subtract the same quantity on both sides.gmattester wrote:Can someone plz. help me understand this problem
If m-3z>0
Then m>3z only if m and z are positive.
And m<3z if m and z are negative
I expect you're thinking about multiplying (or dividing) on both sides of an inequality- if you multiply or divide by a negative, you must reverse the inequality.
Thanks chase.........parallel_chase wrote:if you combine I & IIgmattester wrote: Now combining 1 and 2 we get
3z<m<4z
Now m and z can be positive as well as negative
So how we reached conclusion that m+z>0
Also I am not sure this is right way to solve this problem
m-3z>0
4z-m>0
If you add these two inequalities
m-3z+4z-m>0
-3z+4z>0
z>0
if z > 0, then m will also be greater than 0 because m>3z
Hence m+z>0, answer is C.
Always remember the following rule for inequalities.
1. Inequalities can only be added to each other, they cannot be subtracted.
2. When adding two inequalities, the signs of both the inequalities should be in the same direction.
Like we did in this case.
Hope this helps. Let me know if you still have any problems.
Now it is more clear to me.
-
codesnooker
- Legendary Member
- Posts: 543
- Thanked: 43 times
- GMAT Score:580
Suyog, the link that you have given, in that post, the question is wrongly posted. Check again the inequalities sign for the second statement.
And yes answer (C) is correct answer.
