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Is |4m - 3n| > |3m - n| + |m - 2n| ?

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Re: Is |4m - 3n| > |3m - n| + |m - 2n| ? [#permalink]

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New post 18 Jul 2014, 10:59
vietmoi999 wrote:
this is not og questions and should not be studied


If Bunuel is presenting a question , I would definitely study it


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Re: Is |4m - 3n| > |3m - n| + |m - 2n| ? [#permalink]

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Re: Is |4m - 3n| > |3m - n| + |m - 2n| ? [#permalink]

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New post 03 Nov 2016, 12:19
Hello from the GMAT Club BumpBot!

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Re: Is |4m - 3n| > |3m - n| + |m - 2n| ? [#permalink]

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New post 23 Nov 2016, 14:39
Statement 2 says 2n<m which translates to m-2n>0. I thought, by filling in numbers, this would mean that 3m-n certainly is bigger than 0. However, in the explanation above m=-4 and n=-3 are given as an example to fill in. But if m =-4 and n=-3 then 2n is not smaller than m. This would mean that these numbers could not be used with this premise right? m has to be bigger than 2n so m has to be >0. I'd say statement 2 is sufficient to answer the question. Could someone help me please?
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Re: Is |4m - 3n| > |3m - n| + |m - 2n| ? [#permalink]

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New post 23 Nov 2016, 23:47
esmeeaugustijn wrote:
Statement 2 says 2n<m which translates to m-2n>0. I thought, by filling in numbers, this would mean that 3m-n certainly is bigger than 0. However, in the explanation above m=-4 and n=-3 are given as an example to fill in. But if m =-4 and n=-3 then 2n is not smaller than m. This would mean that these numbers could not be used with this premise right? m has to be bigger than 2n so m has to be >0. I'd say statement 2 is sufficient to answer the question. Could someone help me please?


If m =-4 and n=-3, then \((2n = -6) < (m = -4)\)
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Re: Is |4m - 3n| > |3m - n| + |m - 2n| ? [#permalink]

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New post 12 Mar 2017, 19:41
Bunuel wrote:
SOLUTION

Is \(|3m - n| + |m - 2n| > |4m - 3n|\)?

One of the properties of absolute values says that \(|x|+|y|\geq|x+y|\). 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: http://gmatclub.com/forum/tips-and-hint ... l#p1381430)

Notice that if we denote \(x=3m - n\) and \(y=m - 2n\), then \(x+y=4m-3n\). 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 \(m-2n>0\). 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 re-arrange: \(3m-n>0\). Thus, both \(m-2n\) and \(3m-n\) 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.


Could someone please help to explain \(x=3m - n\) and \(y=m - 2n\), then \(x+y=4m-3n\). 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?

I thought it needs to be the same sign.
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Re: Is |4m - 3n| > |3m - n| + |m - 2n| ? [#permalink]

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New post 12 Mar 2017, 23:21
ziyuen wrote:
Bunuel wrote:
SOLUTION

Is \(|3m - n| + |m - 2n| > |4m - 3n|\)?

One of the properties of absolute values says that \(|x|+|y|\geq|x+y|\). 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: http://gmatclub.com/forum/tips-and-hint ... l#p1381430)

Notice that if we denote \(x=3m - n\) and \(y=m - 2n\), then \(x+y=4m-3n\). 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 \(m-2n>0\). 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 re-arrange: \(3m-n>0\). Thus, both \(m-2n\) and \(3m-n\) 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.


Could someone please help to explain \(x=3m - n\) and \(y=m - 2n\), then \(x+y=4m-3n\). 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?

I thought it needs to be the same sign.


Plug the numbers and check. Try x=1 and y=2 AND x=1 and y=-2.
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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?
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Re: Is |4m - 3n| > |3m - n| + |m - 2n| ?   [#permalink] 12 Mar 2017, 23:21

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