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# Allegation on 3+ values?

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Intern
Joined: 18 Sep 2011
Posts: 8
Concentration: Strategy, General Management
GMAT Date: 11-29-2011
WE: Corporate Finance (Retail)

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02 Oct 2011, 14:32
Hi,

I've just learned the allgegation method for weighted average/mixture questions and it is very fast when computing mixture questions with two different values!
Does anyone know if this method works for 3 or more values?
If so, how?

Thanks
Intern
Joined: 20 Jun 2013
Posts: 9
Re: Allegation on 3+ values?  [#permalink]

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02 Aug 2013, 03:20
In what ratio must a person mix three kinds of metal costing Rs.60/kg, Rs.75/kg and Rs.100 /kg so that the resultant alloy when sold at Rs.96/kg results in a gain of 20%?
(1) 1 : 2 : 4 (2) 3 : 7 : 6 (3) 1 : 4 : 2 (4) 1 : 4 : 1

How can we solve this as it involves 3 quantities ?
Manager
Joined: 10 Apr 2013
Posts: 106
Re: Allegation on 3+ values?  [#permalink]

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02 Aug 2013, 03:43
Hi,

Happy to help

The fastest way would be to plug in the values in the options:

1. gives (60*1+75*2+100*4)/7=610/7

2. gives (60*3+75*7+100*6)=1205/7

3. gives (60*1+75*4+100*2)=560/7

4. gives ((60*1+75*4+100*1)=460/7

Now, desired rate= Rs. 80. So option 3.

In case you are interested in a detailed mathematical solutioning, substitute the basic ratio as "x"

Thus in option 1, the ratios would be x, 2x and 4x and so on in the other options

Regards

Argha
Intern
Joined: 20 Jun 2013
Posts: 9
Re: Allegation on 3+ values?  [#permalink]

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02 Aug 2013, 07:47
Yes, agreed that plugging in the choices is the best method but using allegation technique to find ratios of metals
M1 : M3= 1 : 1 and M2 : M3 = 4 : 1 so according to that M1 : M2 : M3 = 1: 4 : 1 should be the ratio of metals in the alloy ... could you point out what i'm missing ??
Manager
Joined: 10 Apr 2013
Posts: 106
Re: Allegation on 3+ values?  [#permalink]

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02 Aug 2013, 10:31
Hi,

Sorry but did not understand your question.

Why are you assuming this: M1 : M3= 1 : 1 and M2 : M3 = 4 : 1???

Regards

Argha
Intern
Joined: 20 Jun 2013
Posts: 9
Re: Allegation on 3+ values?  [#permalink]

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02 Aug 2013, 23:19
argha wrote:
Hi,

Sorry but did not understand your question.

Why are you assuming this: M1 : M3= 1 : 1 and M2 : M3 = 4 : 1???

Regards

Argha

M1 = metal costing 60/kg , M2 = metal costing 75/ kg and M3= 100/ kg.
sp = 96
profit = 20%
thus cp = 96/1.2 = 80

Using allegation, M1 : M3 = (100-80)/(80-60) = 20/20= 1:1
similarly, M2 : M3 = (100-80)/ ( 80-75) = 20/5 = 4: 1

Thus, M1 : M2 : M3 = 1: 4 : 1
where am i wrong ?
Intern
Joined: 19 Nov 2016
Posts: 1
Re: Allegation on 3+ values?  [#permalink]

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19 Nov 2016, 21:31
hsb91 wrote:
Yes, agreed that plugging in the choices is the best method but using allegation technique to find ratios of metals
M1 : M3= 1 : 1 and M2 : M3 = 4 : 1 so according to that M1 : M2 : M3 = 1: 4 : 1 should be the ratio of metals in the alloy ... could you point out what i'm missing ??

M1 : M3 = 1 : 1 and
M2 : M3 = 4 : 1
===> M1:M2:M3 = 1:4:2(1+1)

You should add it in 3 value allegation
Intern
Joined: 21 Jan 2018
Posts: 1
Re: Allegation on 3+ values?  [#permalink]

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02 Feb 2018, 13:34
I have the same doubt. Can @bunnel or karishma help with this?

Using allegation, M1 : M3 = (100-80)/(80-60) = 20/20= 1:1
similarly, M2 : M3 = (100-80)/ ( 80-75) = 20/5 = 4: 1

Thus, M1 : M2 : M3 = 1: 4 : 1

But actually, the common value is added in alligation. M1:M2:M3 = 1:4:2(1+1)

Manager
Joined: 17 Jul 2016
Posts: 55
Re: Allegation on 3+ values?  [#permalink]

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04 Feb 2018, 17:11
60---------1-------0-------->1

75---------0-------4-------->4

100---------1-------1-------->2

You can use allegation. You must first compare something below 80 to something above 80. So first we compare 60 to 100. One of each will average to 80. Then we compare 75 to 100. We must have them in a 4 to 1 ratio in order to average to 80. The above "chart" breaks it down.
Manager
Joined: 04 Jun 2018
Posts: 157
GMAT 1: 610 Q48 V25
GMAT 2: 690 Q50 V32
GMAT 3: 710 Q50 V36
Re: Allegation on 3+ values?  [#permalink]

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07 Aug 2018, 02:37
Can some expert please shed some light on this concept of using allegations in 3 variables.
Bunuel????
Re: Allegation on 3+ values?   [#permalink] 07 Aug 2018, 02:37
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