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Is 4m  3n > 3m  n + m  2n ?
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06 Jul 2014, 10:11
Question Stats:
39% (02:18) correct 61% (02:30) wrong based on 328 sessions
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Is \(3m  n + m  2n > 4m  3n\)? (1) \(m > 0\) (2) \(2n < m\) Kudos for a correct solution.
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Re: Is 4m  3n > 3m  n + m  2n ?
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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.
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Re: Is 4m  3n > 3m  n + m  2n ?
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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.
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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.



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



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Re: Is 4m  3n > 3m  n + m  2n ?
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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



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Re: Is 4m  3n > 3m  n + m  2n ?
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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"



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



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Re: Is 4m  3n > 3m  n + m  2n ?
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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....



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Re: Is 4m  3n > 3m  n + m  2n ?
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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.



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



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Re: Is 4m  3n > 3m  n + m  2n ?
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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.



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Re: Is 4m  3n > 3m  n + m  2n ?
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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.
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Re: Is 4m  3n > 3m  n + m  2n ?
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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]
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Re: Is 4m  3n > 3m  n + m  2n ?
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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.



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Re: Is 4m  3n > 3m  n + m  2n ?
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16 Jul 2014, 02:22
peacewarriors wrote: 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. I don't understand your solution...
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Re: Is 4m  3n > 3m  n + m  2n ?
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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



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Re: Is 4m  3n > 3m  n + m  2n ?
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16 Jul 2014, 02:36
peacewarriors wrote: 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 How do you know that 4m  3n = 4m3n, 3m  n = 3m+n and m  2n =  m+2n???
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Re: Is 4m  3n > 3m  n + m  2n ?
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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.



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Re: Is 4m  3n > 3m  n + m  2n ?
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17 Jul 2014, 11:01
this is not og questions and should not be studied
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Re: Is 4m  3n > 3m  n + m  2n ?
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17 Jul 2014, 11:03
vietmoi999 wrote: this is not og questions and should not be studied This is GMAT Club's question.
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Re: Is 4m  3n > 3m  n + m  2n ?
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