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A rabbit on a controlled diet is fed daily 300 grams of a [#permalink]
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26 Jul 2007, 09:45
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A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10% protein and food Y contains 15% protein. If the rabbit's diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture. A. 100 B. 140 C. 150 D. 160 E. 200
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Last edited by Bunuel on 06 Jun 2014, 02:39, edited 1 time in total.
Edited the question and added the OA.



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Set up two equations.
We know that 10%x+15%y=38 grams or .1x+.15y=38
We also know that x+y=300 grams.
2 eq. with 2 variables. Solve them and you should get it.



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Re: Mixture Problem. Please explain [#permalink]
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26 Jul 2007, 10:17
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tinman1412 wrote: A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10% protein and food Y contains 15% protein. If the rabbit's diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture.
a)100 b)140 c)150 d)160 e)200
The answer is B)140, but I do not understand the OG explanation. Can someone provide their approach to this question in detail
Thanks,
in fact one eq is enough: .1x + .15(300x) = 38
solve for x, x = 140



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Re: Mixture Problem. Please explain [#permalink]
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26 Jul 2007, 10:35
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tinman1412 wrote: A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10% protein and food Y contains 15% protein. If the rabbit's diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture.
a)100 b)140 c)150 d)160 e)200
The answer is B)140, but I do not understand the OG explanation. Can someone provide their approach to this question in detail
Thanks,
Much simpler method is there...
38 gms means approx. 12.66%. Then use the mixture alligation formula to calculate the ratio of X to Y, ie,
X/Y= (1512.66)/(12.6610)=2.33/2.66.
Hence amt of X in total mixture is 300*2.33/(2.33+2.66)=139.2~140
Answer B.



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D
Assume x grams is of mixture A and 300x is of mixture B
Eqn is:
(300x)*.1 + .15x = 38 (10% and 15% protein in Mixtures A and B respectively)
Solve for x =160



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0.1x + 0.15y = 38
x+y = 300
x = 300y
so 0.1(300y) + 0.15y = 38
300.1y + 0.15y = 38
0.05y = 8
y = 160 grams
then x = 140 grams.
Ans B



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tinman1412 wrote: I was just wondering. I know there are many different ways to solve math problems, but is there a prefer method when solving Mixture Problems?
Its wat you feel comfortable with or the one which you do faster and accurately. You have to develop that approach by practice.
Atleast I think so. I solved the problem using Mixtures & Alligation formula coz I feel comfortable with that.
Sunil



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Re: Mixture Problem. Please explain [#permalink]
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13 Aug 2009, 05:37
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MGMAT has a great method that has really helped me to do these problems quickly.
For mixture problems, set up a chart:
the two different mixtures go on the right hand side, the quantities of each go on the top:
Protein Other X
Y
The problem says the two mixtures are added together to produce a new mixture totaling 300 grams, so add to the chart:
Protein Other Total X X
Y Y
X+Y 300
Now add the information about how much protein is in each mixture
Protein Other Total X .1X X
Y .15Y Y
X+Y 38 300
Now there are two equations with 2 variables:
.1X + .15Y=38 X + Y = 300
Simple method, but it really helps break down harder questions.



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Re: Mixture Problem. Please explain [#permalink]
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22 Jun 2010, 17:23
can someone explain the logic of the mixture and allegation formula?
the ratio of (difference between the high value and new percentage) over (diff b/t high and new) + (diff b/t new and low value)
what does this ratio represent and why, when multiplying the whole to it does it give you the amount in final.....



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Re: Mixture Problem. Please explain [#permalink]
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23 Sep 2010, 02:13
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We know that 1.00x+1.00y=300
and that 0.10x+0.15y=38
so 0.10x+0.15y=38 *10= 1.00x+1.50y=380
Align them under eachother 1.00x+1.50y=380 1.00x+1.00y=300
Means 0.50y=80 80*2=160 y=160 x=300y x=300160 x=140



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Re: Mixture Problem. Please explain [#permalink]
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24 Sep 2010, 03:21
let x= mixture A ,, then 300x is Mixture B
.0.1 x + (300x)0.15=38
after the solving the equation ,,x=140



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Re: Mixture Problem. Please explain [#permalink]
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11 Mar 2011, 05:15
This problem is relatively easy once you break it up the way it's supposed to be broken up...
they basically say X lbs +Y lbs = 300 lbs
Now, equate the protein levels together:
0.10 X + 0.15 Y = 38
Solve



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Re: A rabbit on a controlled diet is fed daily 300 grams of a [#permalink]
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07 Nov 2011, 03:47
just calculation:
0.1*X+0.15*(300X)=38 X=140



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Re: A rabbit on a controlled diet is fed daily 300 grams of a [#permalink]
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06 Jun 2014, 02:27
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Hi Bunuel, Pls could you update the OA here? The answer is quite obvious but the stats are skewed for lack of OA. Thanks!



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Re: A rabbit on a controlled diet is fed daily 300 grams of a [#permalink]
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06 Jun 2014, 02:41



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Re: A rabbit on a controlled diet is fed daily 300 grams of a [#permalink]
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17 Aug 2015, 01:40
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we can solve by testing answers lets start with B... let qty of X be 140 gms. so Y will be 160 gms. proteins from X = 14 gms proteins from Y = 24 gms add both, we get 38gms.
so X must be 140 gms.



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Re: A rabbit on a controlled diet is fed daily 300 grams of a [#permalink]
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30 sec reasoning out: 38/300  is a bit less than a 13% protein content. Hence 13% is closer to 15%Y than to 10%X  this means that there is just sligthly more Y component because should those 2 be equal the protein content would have been sharply 12.5% which is not the case. Immediately we kick out 3 answer choices >= 150 and are left with A and B. A is too low for the aboe slight deviation  so B is much closer to truth.
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A rabbit on a controlled diet is fed daily 300 grams of a [#permalink]
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01 Feb 2016, 23:53
shasadou wrote: 30 sec reasoning out: 38/300  is a bit less than a 13% protein content. Hence 13% is closer to 15%Y than to 10%X  this means that there is just sligthly more Y component because should those 2 be equal the protein content would have been sharply 12.5% which is not the case.
Immediately we kick out 3 answer choices >= 150 and are left with A and B. A is too low for the aboe slight deviation  so B is much closer to truth. Hi, this weighted approach,if mastered, can actually make a difference in your Quant score.. Good approach and you should try this in almost all Q that asks for an average in a mixture, or for a quantity, when an average is given.. +1 kudos
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Re: A rabbit on a controlled diet is fed daily 300 grams of a [#permalink]
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I am going through word problem types of questions because I think i bombed this type of q in my last gmat both timewise and accuracy wise. And what i see from OG about 30% of all questions comprise the word problem type. During these 2 days I solved numerous word problems and here are my observations:  very time consuming because the intuitive approach is to apply algebra and form equations, on average easy question take almost the same time as hard ones  given my incline to make silly mistakes in algebraic calculations I should rely more on reasoning out the easy questions  majority of easy word problems employ weighted average or mean concepts which can be done by reasoning much faster than by doing algebra  ultimately this will save at least 30 secs on each such question 
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