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A rabbit on a controlled diet is fed daily 300 grams of a

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A rabbit on a controlled diet is fed daily 300 grams of a [#permalink]

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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
[Reveal] Spoiler: OA

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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New post 26 Jul 2007, 09:52
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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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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(300-x) = 38

solve for x, x = 140
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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= (15-12.66)/(12.66-10)=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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New post 26 Jul 2007, 11:16
D

Assume x grams is of mixture A and 300-x is of mixture B
Eqn is:

(300-x)*.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 = 300-y

so 0.1(300-y) + 0.15y = 38
30-0.1y + 0.15y = 38
0.05y = 8
y = 160 grams

then x = 140 grams.

Ans B
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New post 27 Jul 2007, 05:35
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.

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Re: Mixture Problem. Please explain [#permalink]

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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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New post 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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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=300-y
x=300-160
x=140
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Re: Mixture Problem. Please explain [#permalink]

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New post 24 Sep 2010, 03:21
let x= mixture A ,, then 300-x is Mixture B

.0.1 x + (300-x)0.15=38

after the solving the equation ,,x=140
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Re: Mixture Problem. Please explain [#permalink]

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New post 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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New post 07 Nov 2011, 03:47
just calculation:

0.1*X+0.15*(300-X)=38
X=140
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New post 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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New post 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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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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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..
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Re: A rabbit on a controlled diet is fed daily 300 grams of a [#permalink]

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New post 02 Feb 2016, 00:14
I am going through word problem types of questions because I think i bombed this type of q in my last gmat both time-wise 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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