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

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Joined: 28 Apr 2014
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Re: Is |4m - 3n| > |3m - n| + |m - 2n| ? [#permalink]

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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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05 Sep 2015, 05:02
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Re: Is |4m - 3n| > |3m - n| + |m - 2n| ? [#permalink]

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

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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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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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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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 $$xy<0$$. ()

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.

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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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 $$xy<0$$. ()

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.

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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Re: Is |4m - 3n| > |3m - n| + |m - 2n| ?   [#permalink] 12 Mar 2017, 23:21

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

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