Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49384

Is 4m  3n > 3m  n + m  2n ?
[#permalink]
Show Tags
06 Jul 2014, 10:11
Question Stats:
42% (01:57) correct 58% (01:56) wrong based on 403 sessions
HideShow timer Statistics




Math Expert
Joined: 02 Sep 2009
Posts: 49384

Re: Is 4m  3n > 3m  n + m  2n ?
[#permalink]
Show Tags
06 Jul 2014, 14:25
SOLUTIONIs \(3m  n + m  2n > 4m  3n\)?One of the properties of absolute values says that \(x+y\geqx+y\). Note that "=" sign holds for \(xy\geq{0}\) (or simply when \(x\) and \(y\) have the same sign). So, the strict inequality (>) holds when \(xy<0\). ( Check here: tipsandhintsforspecificquanttopicswithexamples172096.html#p1381430) Notice that if we denote \(x=3m  n\) and \(y=m  2n\), then \(x+y=4m3n\). So, the question becomes: is \(x+y>x+y\)? Thus, the qeustion basically asks whether \(x\) and \(y\), or which is the same \(3m  n\) and \(m  2n\), have the opposite signs. (1) \(m > 0\). Clearly insufficient as no info about \(n\). Not sufficient. (2) \(2n < m\). This implies that \(m2n>0\). If \(m=3\) and \(n=1\), then \(3m  n>0\) (so in this case \(3m  n\) and \(m  2n\) will have the same sign) but if \(m=4\) and \(n=3\), then \(3m  n<0\) (so in this case \(3m  n\) and \(m  2n\) will have different signs sign). Not sufficient. (1)+(2) We have that \(m > 0\), or which is the same \(5m>0\) and \(m>2n\). Add them: \(6m>2n\). Reduce by 2 and rearrange: \(3mn>0\). Thus, both \(m2n\) and \(3mn\) are positive, so we have a NO answer to the question. Sufficient. Answer: C. Try NEW Absolute Value PS question.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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: 22 Jan 2014
Posts: 176
WE: Project Management (Computer Hardware)

Re: Is 4m  3n > 3m  n + m  2n ?
[#permalink]
Show Tags
Updated on: 10 Jul 2014, 09:56
Bunuel wrote: Is \(3m  n + m  2n > 4m  3n\)? (1) \(m > 0\) (2) \(2n < m\) Kudos for a correct solution. My take is C. 1) m>0 (m,n) = (+,+);(+,);(+,0) in (+,) LHS=RHS ; so NO LHS is not > RHS in (+,+) LHS>RHS ; so YES LHS is > RHS hence, A is inconclusive. 2) 2n<m based on the aforementioned approach we again get LHS=RHS and LHS>RHS. hence, B is inconclusive. combining both shall give us a definite answer. thus C.
_________________
Illegitimi non carborundum.
Originally posted by thefibonacci on 08 Jul 2014, 10:41.
Last edited by thefibonacci on 10 Jul 2014, 09:56, edited 1 time in total.



Manager
Joined: 28 Apr 2014
Posts: 232

Re: Is 4m  3n > 3m  n + m  2n ?
[#permalink]
Show Tags
08 Jul 2014, 23:17
I am pretty sure , I posted one reply yesterday but dont see it now !!



Manager
Joined: 28 Apr 2014
Posts: 232

Re: Is 4m  3n > 3m  n + m  2n ?
[#permalink]
Show Tags
08 Jul 2014, 23:30
Sol
Putting in values to check for 1 to be sufficient
m = 10 , n =0 makes Is 30+10 > 40? No m = 10 , n = 20 makes Is 10+30 > 20 ? Yes m= 10 , n = 10 makes Is 40 + 30 > 70 ? No
So InSufficient
Case 2 Putting in values to check for 2 to be sufficient
m>2n
m = 20 , n = 5 makes Is 55 + 10 > 65 ? No m= 5 , n = 3 makes Is 12 + 1 > 11 ? Yes m= 10 , n = 10 makes Is 40 + 30 > 70 ? No
So B alone is insufficient
Taking both of them together we can see , that the contradicting scenarios are getting eliminated. Thus Both are sufficient.
Answer is C.
Algebraically :
Case 1 m>0 does not indicate anything about the sign of each term as the value of n is uncertain. So in other words 3mn could be either 3mn or n3m based on the sign of the expression. So insufficient
Case 2 m >2n again does not indicate anything about the sign of any term. So 3mn could be 3mn or n3m based on whether m and n are both positive or both negative.
Taking together  m >0 and m > 2n
will ensure that 3mn > 0 m2n > 0 4m3n > 0
so the expression after removing mod symbol becomes
Is 3mn + m2n > 4m3n ? Answer is No So sufficient.
Answer is C
PS  Not satisfied with this dirty approach and the time implications in actual GMAT test , God forbid if I get it



Intern
Joined: 23 Jun 2014
Posts: 4
WE: Operations (Energy and Utilities)

Re: Is 4m  3n > 3m  n + m  2n ?
[#permalink]
Show Tags
12 Jul 2014, 06:01
Why not just 'B,? We just need the second statement to know the sign of Modulus expressions. IMO it should be just "B"



Manager
Joined: 28 Apr 2014
Posts: 232

Re: Is 4m  3n > 3m  n + m  2n ?
[#permalink]
Show Tags
12 Jul 2014, 12:00
I have done by putting in values. It is not answering conclusively



Intern
Joined: 02 Jun 2014
Posts: 14
Location: India
Concentration: Strategy, Operations
GPA: 3.7
WE: Sales (Energy and Utilities)

Re: Is 4m  3n > 3m  n + m  2n ?
[#permalink]
Show Tags
13 Jul 2014, 00:03
Not sure  I got E, as it was still inconclusive even after trying values....and the silly timer doesnt help too... god forbid i get it too....



Intern
Joined: 24 Jan 2013
Posts: 38

Re: Is 4m  3n > 3m  n + m  2n ?
[#permalink]
Show Tags
13 Jul 2014, 06:23
Answer must be C. Opening the mod we get if 4m>3n? Statement 1 says m>0 but we know nothing about n Eg: if m=3 and n= 1 it is true but if m=1 and n=2 the answer is no
Statement 2 says m>2n but we know nothing about m and n in terms of whether they are positive or negative. Eg: if m =5 and n =0.5 the answer is yes but if m=2 and if n=1.5 the answer is no
Combining both the statements we get that m>0 and m>2n we get m>n and therefore 4m>3n.



Manager
Joined: 28 Apr 2014
Posts: 232

Re: Is 4m  3n > 3m  n + m  2n ?
[#permalink]
Show Tags
13 Jul 2014, 21:51
Waiting for the Bunuel post with some new twist and dollops of learning.



Manager
Joined: 21 Sep 2012
Posts: 218
Location: United States
Concentration: Finance, Economics
GPA: 4
WE: General Management (Consumer Products)

Re: Is 4m  3n > 3m  n + m  2n ?
[#permalink]
Show Tags
14 Jul 2014, 00:40
Bunuel wrote: Is \(3m  n + m  2n > 4m  3n\)? (1) \(m > 0\) (2) \(2n < m\) Kudos for a correct solution. I am getting A as answer, but took too long to solve by plugging numbers. For statement A, any combination of values of m and n is getting the same answer. Statement 2 is not sufficient. We get two different answers if we take values as m=10,n=4 and m=3 and n=2. Hence insufficient. Experts please suggest a faster approach to solve such problem.



Math Expert
Joined: 02 Sep 2009
Posts: 49384

Re: Is 4m  3n > 3m  n + m  2n ?
[#permalink]
Show Tags
15 Jul 2014, 11:33
SOLUTIONIs \(3m  n + m  2n > 4m  3n\)?One of the properties of absolute values says that \(x+y\geqx+y\). Note that "=" sign holds for \(xy\geq{0}\) (or simply when \(x\) and \(y\) have the same sign). So, the strict inequality (>) holds when \(xy<0\). ( Check here: tipsandhintsforspecificquanttopicswithexamples172096.html#p1381430) Notice that if we denote \(x=3m  n\) and \(y=m  2n\), then \(x+y=4m3n\). So, the question becomes: is \(x+y>x+y\)? Thus, the qeustion basically asks whether \(x\) and \(y\), or which is the same \(3m  n\) and \(m  2n\), have the opposite signs. (1) \(m > 0\). Clearly insufficient as no info about \(n\). Not sufficient. (2) \(2n < m\). This implies that \(m2n>0\). If \(m=3\) and \(n=1\), then \(3m  n>0\) (so in this case \(3m  n\) and \(m  2n\) will have the same sign) but if \(m=4\) and \(n=3\), then \(3m  n<0\) (so in this case \(3m  n\) and \(m  2n\) will have different signs sign). Not sufficient. (1)+(2) We have that \(m > 0\), or which is the same \(5m>0\) and \(m>2n\). Add them: \(6m>2n\). Reduce by 2 and rearrange: \(3mn>0\). Thus, both \(m2n\) and \(3mn\) are positive, so we have a NO answer to the question. Sufficient. Answer: C. Kudos points given to correct solutions above.Try NEW Absolute Value PS question.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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: 28 Apr 2014
Posts: 232

Re: Is 4m  3n > 3m  n + m  2n ?
[#permalink]
Show Tags
15 Jul 2014, 20:32
Wow. A kudos from Bunuel. GMAC should consider Bunuel's kudos in its exam process [SMILING FACE WITH SMILING EYES][SMILING FACE WITH SMILING EYES]
Sent from my iPhone using Tapatalk



Intern
Joined: 24 Jan 2013
Posts: 38

Re: Is 4m  3n > 3m  n + m  2n ?
[#permalink]
Show Tags
15 Jul 2014, 20:34
Hi bunuel, Is my solution incorrect? Quote: Answer must be C. Opening the mod we get if 4m>3n? Statement 1 says m>0 but we know nothing about n Eg: if m=3 and n= 1 it is true but if m=1 and n=2 the answer is no
Statement 2 says m>2n but we know nothing about m and n in terms of whether they are positive or negative. Eg: if m =5 and n =0.5 the answer is yes but if m=2 and if n=1.5 the answer is no
Combining both the statements we get that m>0 and m>2n we get m>n and therefore 4m>3n.



Math Expert
Joined: 02 Sep 2009
Posts: 49384

Re: Is 4m  3n > 3m  n + m  2n ?
[#permalink]
Show Tags
16 Jul 2014, 02:22



Intern
Joined: 24 Jan 2013
Posts: 38

Re: Is 4m  3n > 3m  n + m  2n ?
[#permalink]
Show Tags
16 Jul 2014, 02:30
HI, Opening the modulus I mean 4m  3n > 3m  n + m  2n: 4m3n>3m+n  m+2n= Consolidating the similar terms,we get 8m>6n? dividing by 2 we get 4m>3n



Math Expert
Joined: 02 Sep 2009
Posts: 49384

Re: Is 4m  3n > 3m  n + m  2n ?
[#permalink]
Show Tags
16 Jul 2014, 02:36



Intern
Joined: 24 Jan 2013
Posts: 38

Re: Is 4m  3n > 3m  n + m  2n ?
[#permalink]
Show Tags
16 Jul 2014, 02:54
Got my mistake. I assumed that lhs = rhs and followed the approach lhs=rhs or lhs=rhs or vice versa.



Manager
Joined: 08 Apr 2013
Posts: 180

Re: Is 4m  3n > 3m  n + m  2n ?
[#permalink]
Show Tags
17 Jul 2014, 11:01
this is not og questions and should not be studied
_________________
If anyone in this gmat forum is in England,Britain, pls, email to me, (thanghnvn@gmail.com) . I have some questions and need your advise. Thank a lot.



Math Expert
Joined: 02 Sep 2009
Posts: 49384

Re: Is 4m  3n > 3m  n + m  2n ?
[#permalink]
Show Tags
17 Jul 2014, 11:03




Re: Is 4m  3n > 3m  n + m  2n ? &nbs
[#permalink]
17 Jul 2014, 11:03



Go to page
1 2
Next
[ 32 posts ]



