Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 08 Apr 2012
Posts: 454

Re: Is m+z > 0 ? [#permalink]
Show Tags
24 Nov 2013, 09:10
Bunuel wrote: smitakokne wrote: Is m+z > 0
1. m3z > 0 2. 4zm > 0
OA : C
Need help in underdstanding how we arrive at C. (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 > \(m3z+4zm>0\) > \(z>0\), 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) > \(m+z=positive+positive>0\). Sufficient. Answer: C. For graphic approach refer to: ismz01m3z024zm75657.htmlHi Bunuel, When I took both statements and in my head made the stipulations, I ended up with 3z<m<4z, but that did not yield the right answer. Can you tell me what I am missing doing this vs. actually adding the equations?



Math Expert
Joined: 02 Sep 2009
Posts: 39597

Re: Is m+z > 0 ? [#permalink]
Show Tags
24 Nov 2013, 09:13
ronr34 wrote: Bunuel wrote: smitakokne wrote: Is m+z > 0
1. m3z > 0 2. 4zm > 0
OA : C
Need help in underdstanding how we arrive at C. (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 > \(m3z+4zm>0\) > \(z>0\), 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) > \(m+z=positive+positive>0\). Sufficient. Answer: C. For graphic approach refer to: ismz01m3z024zm75657.htmlHi Bunuel, When I took both statements and in my head made the stipulations, I ended up with 3z<m<4z, but that did not yield the right answer. Can you tell me what I am missing doing this vs. actually adding the equations? You missed the last step: from 3z<4z it follows that z>0, thus 3z=positive > (3z=positive)<m > m=positive > m+z=positive.
_________________
New to the Math Forum? Please read this: 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? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 03 Dec 2012
Posts: 340

Re: Is m+z > 0 ? [#permalink]
Show Tags
30 Nov 2013, 01:34
Bunuel wrote: smitakokne wrote: Is m+z > 0
1. m3z > 0 2. 4zm > 0
OA : C
Need help in underdstanding how we arrive at C. (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 > \(m3z+4zm>0\) > \(z>0\), 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) > \(m+z=positive+positive>0\). Sufficient. Answer: C. For graphic approach refer to: ismz01m3z024zm75657.htmlI have a doubt: 1 & 2 are obviously insuff. Combining 1 & 2 we get z>0. Now according to 1) m3z>0 (so we get m>0). My doubt starts here 2) says 4zm>0 so when z>0, m>0 or m<0. For eg z=2 & m=2, we will still get 4zm>0 So according to me answer should be E or am I missing something here.



Math Expert
Joined: 02 Sep 2009
Posts: 39597

Re: Is m+z > 0 ? [#permalink]
Show Tags
30 Nov 2013, 04:07
mohnish104 wrote: Bunuel wrote: smitakokne wrote: Is m+z > 0
1. m3z > 0 2. 4zm > 0
OA : C
Need help in underdstanding how we arrive at C. (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 > \(m3z+4zm>0\) > \(z>0\), 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) > \(m+z=positive+positive>0\). Sufficient. Answer: C. For graphic approach refer to: ismz01m3z024zm75657.htmlI have a doubt: 1 & 2 are obviously insuff. Combining 1 & 2 we get z>0. Now according to 1) m3z>0 (so we get m>0). My doubt starts here 2) says 4zm>0 so when z>0, m>0 or m<0. For eg z=2 & m=2, we will still get 4zm>0 So according to me answer should be E or am I missing something here. Please read the whole thread before posting: ismz01m3z024zm106381.html#p1248558ismz01m3z024zm10638120.html#p1296461
_________________
New to the Math Forum? Please read this: 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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 18 Jul 2013
Posts: 73
Location: Italy
GMAT 1: 600 Q42 V31 GMAT 2: 700 Q48 V38

Re: Is m+z > 0 (1) m3z > 0 (2) 4zm > 0 [#permalink]
Show Tags
23 Jul 2014, 13:15
Is that correct?
1) \(m3z>0\) <=> \(m>3z\) Insuff 2) \(4zm>0\) <=> \(m<4z\) Insuff
1+2) we multiply 1) by 4, \(4m>12z\) we multiply 2) by 3, \(3m<12z\) <=> \(3m>12z\)
As we can add two inequalities \(4m3m>0\) so \(m>0.\)
from1), \(m>3z\) from 2), \(m<4z\) <=> \(m>4z\)
As we can add two inequalities \(0>z\) so \(z>0\)
so \(m+z>0\)



Math Expert
Joined: 02 Sep 2009
Posts: 39597

Re: Is m+z > 0 (1) m3z > 0 (2) 4zm > 0 [#permalink]
Show Tags
23 Jul 2014, 18:03



Manager
Joined: 18 Jul 2013
Posts: 73
Location: Italy
GMAT 1: 600 Q42 V31 GMAT 2: 700 Q48 V38

Re: Is m+z > 0 (1) m3z > 0 (2) 4zm > 0 [#permalink]
Show Tags
24 Jul 2014, 10:39
thank you for the link!



Senior Manager
Joined: 28 Apr 2014
Posts: 282

Re: Is m+z > 0 (1) m3z > 0 (2) 4zm > 0 [#permalink]
Show Tags
28 Jul 2014, 01:37
Bunuel my line of reasoning was that the numbers are aligned like 3z<m<4z. Now m falls between 3z and 4z which can only be possible if both m and z are positive ( as the multiplier is positive). Now adding two positive numbers will always be more than 0 . Hence both are sufficient to prove



Intern
Joined: 29 Sep 2012
Posts: 13

Re: Is m+z > 0 (1) m3z > 0 (2) 4zm > 0 [#permalink]
Show Tags
07 Sep 2014, 08:41
Hi Bunuel, I have a doubt in this question. it is asked whether m+z>0 this implies that is m>z?
Statement 1 says: m3Z>0 then m>3z and 3z is definitely greater than z then isnt m>z. Please clarify.



Math Expert
Joined: 02 Sep 2009
Posts: 39597

Re: Is m+z > 0 (1) m3z > 0 (2) 4zm > 0 [#permalink]
Show Tags
07 Sep 2014, 08:56



Manager
Joined: 06 Aug 2013
Posts: 92

Re: Is m+z > 0 (1) m3z > 0 (2) 4zm > 0 [#permalink]
Show Tags
30 Nov 2014, 06:48
Bunuel wrote: smitakokne wrote: Is m+z > 0
1. m3z > 0 2. 4zm > 0
OA : C
Need help in underdstanding how we arrive at C. (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 > \(m3z+4zm>0\) > \(z>0\), 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) > \(m+z=positive+positive>0\). Sufficient. Answer: C. For graphic approach refer to: ismz01m3z024zm75657.htmlbunuel, i have a doubt here... z > 0, plugging this in statement 1 gives us m > 0 but plugging this is statement 2, 4z > m , if z=1, m=0, 4 > 0, m+z > 0 yes but when z = 1, m = 1, 4 > 1, but m + z is not greater than 0. NO in that case, how is C the answer. in conditions like these, do we plug in either of the statemnts and check. would really appreciate your help on this.



Intern
Joined: 26 Jun 2012
Posts: 6

Is m+z > 0 (1) m3z > 0 (2) 4zm > 0 [#permalink]
Show Tags
15 Nov 2015, 07:21
from I we get as follows
m  z  m3z  m+z  4  1  1  5  this case true 1  8  23  9  this case fails
from II we get as follows
z  m  4zm  m+z  4  1  15  5  this case true 1  8  8  9  this case fails
1+2 also both values give yes and no so option is E If i am wrong please correct me



Math Expert
Joined: 02 Sep 2009
Posts: 39597

Re: Is m+z > 0 (1) m3z > 0 (2) 4zm > 0 [#permalink]
Show Tags
15 Nov 2015, 09:22



Senior Manager
Joined: 29 Oct 2013
Posts: 296
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)

Is m+z > 0 (1) m3z > 0 (2) 4zm > 0 [#permalink]
Show Tags
23 Dec 2015, 18:17
Bunuel, Skywalker18, Engr2012, and other experts : Do you think algebraic approach works even if an answer choice is E in such similar questions? Or do we have to resort to graphic approach/number picking then? Any tips on how to attack these questions in general? Thanks
_________________
Please contact me for super inexpensive quality private tutoring
My journey V46 and 750 > http://gmatclub.com/forum/myjourneyto46onverbal750overall171722.html#p1367876



Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2642
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: Is m+z > 0 (1) m3z > 0 (2) 4zm > 0 [#permalink]
Show Tags
23 Dec 2015, 18:50
NoHalfMeasures wrote: Bunuel, Skywalker18, Engr2012, and other experts : Do you think algebraic approach works even if an answer choice is E in such similar questions? Or do we have to resort to graphic approach/number picking then? Any tips on how to attack these questions in general? Thanks IMO, these questions require a combination of algebraic and number plugging in order to arrive at the final answer. Without looking at a particular question, it is very dangerous to define your strategy. I did not use any graphical method as such but did employ number plugging for proving that statements 1 and 2 are not sufficient on their own and then use algebra to show that when the 2 statements are combined, we get z>0.
_________________
Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidatedthursdaywithronlistforallthesections201006.html#p1544515 Rules for Posting in Quant Forums: http://gmatclub.com/forum/rulesforpostingpleasereadthisbeforeposting133935.html Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rulesforpostingpleasereadthisbeforeposting133935.html#p1096628 GMATCLUB Math Book: http://gmatclub.com/forum/gmatmathbookindownloadablepdfformat130609.html Everything Related to Inequalities: http://gmatclub.com/forum/inequalitiesmadeeasy206653.html#p1582891 Inequalities tips: http://gmatclub.com/forum/inequalitiestipsandhints175001.html Debrief, 650 to 750: http://gmatclub.com/forum/650to750a10monthjourneytothescore203190.html



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 3447
GPA: 3.82

Re: Is m+z > 0 (1) m3z > 0 (2) 4zm > 0 [#permalink]
Show Tags
23 Dec 2015, 23:28
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. Is m+z > 0 (1) m3z > 0 (2) 4zm > 0 In the original condition, there are 2 variables(m,z), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. In 1)&2), add the 2 equations, which is m3z+4z+m>0, z>0. Then m>z>0 is derived from m>3z>z, which is m>0. So, m+z>0 is always yes and sufficient. Therefore, the answer is C. > For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Find a 10% off coupon code for GMAT Club members. “Receive 5 Math Questions & Solutions Daily” Unlimited Access to over 120 free video lessons  try it yourself See our Youtube demo



Intern
Joined: 12 Nov 2014
Posts: 23

Re: Is m+z > 0 (1) m3z > 0 (2) 4zm > 0 [#permalink]
Show Tags
24 Dec 2015, 09:48
with the first statement, if you apply the numbers 1,0 and 1. You will conclude that m is positive when z is positive. Hence I thought one is sufficient.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7440
Location: Pune, India

Re: Is m+z > 0 (1) m3z > 0 (2) 4zm > 0 [#permalink]
Show Tags
09 May 2016, 21:55
smitakokne wrote: Is m+z > 0
(1) m3z > 0 (2) 4zm > 0 Responding to a pm: Quote: When I look at such question, I know I will figure out something if I consider both statements together. I feel comfortable with applying inequalities rules there. But I find it harder to approach individual statements in such cases. I get lost in figuring out cases to reject (or approve) one statement on its own. At times, I take time and eventually rush onto considering both statements together.
Can you please help me out if I'm lacking some approach or concepts?
There really isn't one suitable method for all inequality questions. The approach depends on the kind of question. Very rarely will I plug in numbers here to find cases where the inequality holds or does not hold. This is how I will do this question: "Is m+z > 0?" Here I think that m and z could both be positive or one of them could be positive with greater absolute value than the other. If both are negative, this doesn't hold. Go on to stmnts. (1) m3z > 0 Here, I will try to segregate the variables to get relation between them. m > 3z The moment I see this, I naturally go to the number line. (z positive): ______________________________ 0 ____z_________________3z___________m____________________ OR (z negative): __3z_________(m)______________z___(m)__ 0 _______________(m)____________________ Both z and m could be positive, both negative or z negative m positive. Not sufficient. (2) 4zm > 0 4z > m (z positive): __________________(m)____________ 0 __(m)_______z_____________________(m)_____4z______ OR (z negative): ______m_______4z____________________z_____ 0 _______________________ Both z and m could be positive, both negative or m negative z positive. Not sufficient. Both together, 3z < m < 4z (z positive): ______________________________ 0 ____z_________________3z_____m_______4z___________ OR (z negative): ___________4z________3z___________________z_____ 0 _______________________ m has to be to the left of 4z but right of 3z. Not possible. So m and z both must be positive. So m + z > 0 Answer (C)
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Intern
Joined: 21 Oct 2015
Posts: 47

Is m+z > 0 (1) m3z > 0 (2) 4zm > 0 [#permalink]
Show Tags
09 May 2016, 22:52
Thank you so much Karishma. You're a saviour!
Is it possible to visualise such problems rather than drawing on number line? I think that will be prone to errors.
Besides, I have noticed that problem statements concerning number line involves too many possibilities as you explained in detail. For the same reason, I feel these questions are designed to put the test taker in a situation where it consumes more than required time? My gut will always push me to rush on these questions therefore.
Rephrasing the question is vital I guess. Let me know if the only way through such questions is to draw the number line and analyze?
Cheers!
Posted from my mobile device



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7440
Location: Pune, India

Re: Is m+z > 0 (1) m3z > 0 (2) 4zm > 0 [#permalink]
Show Tags
10 May 2016, 20:43
HarisinghKhedar wrote: Thank you so much Karishma. You're a saviour!
Is it possible to visualise such problems rather than drawing on number line? I think that will be prone to errors.
Besides, I have noticed that problem statements concerning number line involves too many possibilities as you explained in detail. For the same reason, I feel these questions are designed to put the test taker in a situation where it consumes more than required time? My gut will always push me to rush on these questions therefore.
Rephrasing the question is vital I guess. Let me know if the only way through such questions is to draw the number line and analyze?
Cheers!
Posted from my mobile device Most questions can be solved using many different methods. You can use the graphical approach discussed by walker here: http://gmatclub.com/forum/ismz75657.htmlAs for too many possibilities on the number line, it seems that way when I draw it out but here is how I see it in my mind. Stmtn 1: There are only 2 cases: z is positive (or 0) or z is negative. If z is to the right of 0, 3z is further to the right of z and m is further to the right of 3z. m has to be positive. If z is to the left of 0, 3z is further to the left of z but m is anywhere on the right of 3z. m could be negative or positive. That's all I need to know.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews




Re: Is m+z > 0 (1) m3z > 0 (2) 4zm > 0
[#permalink]
10 May 2016, 20:43



Go to page
Previous
1 2 3
Next
[ 46 posts ]




