Mixture of milk

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rohit_gmat: Master | Next Rank: 500 Posts; Posts: 158; Joined: Wed Jun 16, 2010 8:21 amFollowed by: 1 member; Thanked: 13 times

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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Source: Beat The GMAT — Problem Solving | Thu Oct 20, 2011 9:32 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

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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rohit_gmat: Master | Next Rank: 500 Posts; Posts: 158; Joined: Wed Jun 16, 2010 8:21 amFollowed by: 1 member; Thanked: 13 times

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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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

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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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

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 ?

Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

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?

Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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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