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Three grades of milk are 1 percent, 2 percent and 3 percent [#permalink]

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24 Dec 2009, 08:38

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Three grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?

I got this problem wrong on the GMAT Prep and don't really understand it.

Three grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?

A. y + 3z B. (y +z) / 4 C. 2y + 3z D. 3y + z E. 3y + 4.5z

Hi, would someone please so kind and explain the question:

Three grades of milk are 1 percent, 2 percent, and 3 percent fat by volume. If x gallons of the q percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x + y + z gallons of a 1.5 percent grade, what is x in terms of y and z?

(a) y + 3z (b) (y+z)/4 (c) 2y +3z (d) 3y + z (e) 3y + 4.5z

Thanks a lot...

A quick approach:

The question asks you for x in terms of y and z. Whatever values x, y and z can take, this relation should hold. Since we mix 1%, 2% and 3% milk and get 1.5% milk, one way of mixing them could be that 1% and 2% are mixed in equal quantities (to give 1.5% milk) and 3% milk is not added at all. Which means x = 1, y = 1 and z = 0 should satisfy the relation between x, y and z. The only relation that satisfies these values is (A).

Note: If multiple options satisfied these values, you could take another set of values e.g. x = 3, y = 0 and z = 1 and check out of the shortlisted options.
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Re: Three grades of milk are 1 percent, 2 percent and 3 percent [#permalink]

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22 Mar 2012, 02:16

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imadkho wrote:

Three grades of milk are 1 percent, 2 percent, and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of 1.5 percent grade, what is x in terms of y and z ? A- y+3z B- (y+z)/4 C- 2y +3z D- 3y+z E-3y+4.5z

0.01x+0.02y+0.03z=0.015(x+y+z) => x=y+3z

hence A
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Re: Three grades of milk are 1 percent, 2 percent and 3 percent [#permalink]

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10 May 2012, 10:33

Hi all, I think I have seen a problem like this somewhere, but in DS form

If (1) is x= y + 3z and (2) gives you the y:z ratio Is the second one sufficient? I somehow feel that it should be, but can't find the reasoning for that.What can we do here? pick numbers? Or is it exessive info and thus is sufficient? sorry, I can't quote the exact second choice.

Re: Three grades of milk are 1 percent, 2 percent and 3 percent [#permalink]

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12 May 2012, 22:29

Yep this one would have seemed more obtuse to me until I realized that the percentages were meant to be for the fat content in milk. Combining the various milk types we got a 1.5% of fat content in the resulting mixture. Got the same answer y+3z.

Re: Three grades of milk are 1 percent, 2 percent and 3 percent [#permalink]

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17 Sep 2012, 16:06

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three grades of milk are 1 percent 2 percent and 3 percent fat by volume. if x gallons of the 1 percent y gallons of the 2 percent and z gallons of the 3 percent are mixed to give x +y+z gallons of a 1.5 percent grade, what is x in terms of y and z? Thanks in advance!!!
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Re: Three grades of milk are 1 percent, 2 percent and 3 percent [#permalink]

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22 Oct 2012, 19:01

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(x/100)+ (2y/100)+(3z/100) = 1.5 (x+y+z)/100 - > cancel out 100 on each side. x+2y+3z = 1.5x+1.5y+1.5z -> bring x to one side of = sign .5x=.5y+1.5x -> multiply by 2 on both side x=y+3z ______________

Re: Three grades of milk are 1 percent, 2 percent and 3 percent [#permalink]

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12 Jan 2014, 23:27

JimmyWorld wrote:

Three grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?

A. y + 3z B. (y +z) / 4 C. 2y + 3z D. 3y + z E. 3y + 4.5z

Three grades of milk are 1%, 2% and 3% fat by volume. If x gallons of 1%, y gallons of 2% and z gallons of 3% are mixed together to give x+y+z gallons of a 1.5%, what is x in terms of y and z?

y+3z (y+z)/4 2y+3z 3y+z 3y+4.5z

My idea was:

(x+2y+3z)/(x+y+z) = 1.5 from here on I have no idea how to get x to one side...

Cheers, Lars

If you develop a knack for playing with numbers, you will rarely need to make equations for ratios/percent/mixture/average problems.

What I thought here was that milk of 1% (volume x), 2% (volume y) and 3% (volume z) have to be mixed to give 1.5%. An easy way I can see immediately is that I don't take any 3% milk and mix 1% and 2% in equal quantities to get 1.5%. i.e. If z = 0, x = y If we put z = 0, only option (A) gives x = y hence it is the answer.
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