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Mixture of milk

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Mixture of milk

by rohit_gmat » Thu Oct 20, 2011 9:32 am
Three grades of milk: 1%, 2%, and 3% fat by volume. x gallons of 1%, y gallons of 2%, and z gallons of 3% are mixed to give x + y + z gallons of 1.5%. What is x in terms of y and z?
a. y + 3z
b. (y + z)/4
c. 2y + 3z
d. 3y + z
e. 3y + 4z


totally lost :( plz help.
can this solved by plugging in numbers? how do we pick numbers for this one?
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by Anurag@Gurome » Thu Oct 20, 2011 9:36 am
rohit_gmat wrote:Three grades of milk: 1%, 2%, and 3% fat by volume. x gallons of 1%, y gallons of 2%, and z gallons of 3% are mixed to give x + y + z gallons of 1.5%. What is x in terms of y and z?
Form the question we can write the following equation,
--> 1*x + 2*y + 3*z = 1.5*(x + y + z)
--> x + 2y + 3z = 1.5x + 1.5y + 1.5z
--> 0.5x = 0.5y + 1.5z
--> x = y + 3z

The correct answer is A.
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by rohit_gmat » Thu Oct 20, 2011 9:51 am
thanks !! the algebraic way looks much clearer...!!!
is there any way to solve this with plugging in numbers?
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by shankar.ashwin » Thu Oct 20, 2011 10:21 am
You could substitute numbers as well. Notice the resultant is between 1 and 2. So mixing an equal amount of 1% and 2% milk would yield an 1.5% milk.

Hence substitute
X=1
Y=1
Z=0.

You can see X=Y here and Z is 0.

From the answer choices you can see only A satisfies this. X=Y+3Z -> X=Y + 3(0)
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by neelgandham » Thu Oct 20, 2011 1:06 pm
GMAT Prep question isn't it ?

(1/100)*x + (2/100)*y + (3/100)*z = (1.5/100)*(x+y+z)

=> x = y + 3z

@Anurag - Is there another way(other than algebra/substitution) of solving this? like say using ratios ?
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by GMATGuruNY » Thu Oct 20, 2011 7:57 pm
I posted a non-algebraic solution here:

https://www.beatthegmat.com/mixturess-t91444.html
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by neelgandham » Fri Oct 21, 2011 2:21 am
GMATGuruNY wrote:I posted a non-algebraic solution here:

https://www.beatthegmat.com/mixturess-t91444.html
Thanks GMATGuru - Is there another way(other than algebra/substitution) of solving this? like say using ratios ? The solution provided by you is more of a substitution method, isn't it?
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by GMATGuruNY » Fri Oct 21, 2011 5:18 am
neelgandham wrote:
GMATGuruNY wrote:I posted a non-algebraic solution here:

https://www.beatthegmat.com/mixturess-t91444.html
Thanks GMATGuru - Is there another way(other than algebra/substitution) of solving this? like say using ratios ? The solution provided by you is more of a substitution method, isn't it?
More than one ratio will yield the desired mixture. Check my post at the bottom of the following thread:

https://www.beatthegmat.com/allegation-t69552.html

To solve a mixture problem with 3 ingredients, I would use algebra or plug in numbers.
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