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

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Intern
Joined: 01 Jul 2015
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Re: Three grades of milk are 1 percent, 2 percent and 3 percent [#permalink]

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04 Oct 2015, 04:53
Have anybody tried to solve this problem by Allegation method?

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Manager
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Posts: 102

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

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05 Feb 2016, 19:26
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Hi VeritasPrepKarishma

I learnt the method to solve mixture problems from your blog and i applied the same method here. Now not sure if that is correct way or not, but i got the answer. Can you please confirm if what I did was correct?

__________|_________|__________
1% 1.5% 2% 3%
x Y z

==> x(1.5-1) = y(2..0 - 1.5) + z(3.0-1.5)
==> x/2 = y/2 + 3z/2
==> x = y + 3z

VeritasPrepKarishma wrote:
NvrEvrGvUp wrote:
MBAhereIcome wrote:
$$\frac{x+2y+3z}{x+y+z} = \frac{3}{2}$$

$$x = y+3z$$

This is essentially viewing this problem as a weighted average correct?

The mixture divided by the sum of weights?

Yes, it is just the weighted average of the fat concentration.

Kudos [?]: 16 [1], given: 6

SVP
Joined: 08 Jul 2010
Posts: 1914

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Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: Three grades of milk are 1 percent, 2 percent and 3 percent [#permalink]

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29 Aug 2016, 09:17
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

Please find the solution as attached
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File comment: www.GMATinsight.com

Sol3.jpg [ 44.4 KiB | Viewed 1045 times ]

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

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30 Aug 2016, 00:33
1
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Expert's post
neeraj609 wrote:
Hi VeritasPrepKarishma

I learnt the method to solve mixture problems from your blog and i applied the same method here. Now not sure if that is correct way or not, but i got the answer. Can you please confirm if what I did was correct?

__________|_________|__________
1% 1.5% 2% 3%
x Y z

==> x(1.5-1) = y(2..0 - 1.5) + z(3.0-1.5)
==> x/2 = y/2 + 3z/2
==> x = y + 3z

Yes, great work! In essence, you are using 'the deviation method for mean' which is of course applicable to weighted mean too.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 18503 [1], given: 237 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7869 Kudos [?]: 18503 [1], given: 237 Location: Pune, India Re: Three grades of milk are 1 percent, 2 percent and 3 percent [#permalink] ### Show Tags 02 Feb 2017, 22:56 1 This post received KUDOS Expert's post 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 Responding to a pm: Quote: I solved it by :- x+2y++3z/x+y+z = but i am not getting how did we get 3/2 on the left hand side . could you please elaborate the same What is the weighted average concept? It says Cavg = (C1*w1 + C2*w2 + C3*w3)/(w1 + w2 + w3) You are given that the average percentage when you mix them all is 1.5 (i.e. 3/2 in fractions) So, 1.5 = (x + 2y + 3z)/(x + y + z) 3/2 = (x + 2y + 3z)/(x + y + z) Now isolate x. Check another method here: https://gmatclub.com/forum/three-grades ... l#p1032710 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Manager
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Location: United States (CA)
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Re: Three grades of milk are 1 percent, 2 percent and 3 percent [#permalink]

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25 Jun 2017, 17:00
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

x + 2y + 3z = 1.5(x+y+z)

x + 2y + 3z = 1.5x + 1.5y + 1.5z

x + 0.5y + 1.5z = 1.5x

0.5y + 1.5z = 0.5x

y + 3z = x

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

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24 Nov 2017, 11:46
I tried to solve the problem with numbers.. can someone point out what's wrong with my logic?

400 gallons of X = 4 grams of fat
100 gallons of Y = 2 grams of fat
100 gallons of Z = 3 grams of fat

4+2+3 / 400+100+100 = 1.5% fat

So answer choices A and D work for me??

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Intern
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Location: Ireland
Concentration: Healthcare, Finance
Three grades of milk are 1 percent, 2 percent and 3 percent [#permalink]

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24 Nov 2017, 12:51
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. $$\frac{y +z}{4}$$

C. $$2y + 3z$$

D. $$3y + z$$

E. $$3y + 4.5z$$

$$\frac{x}{100} + \frac{2y}{100} + \frac{3z}{100} = \frac{15*(x + y + z)}{1000}$$
$$x + 2y + 3z = \frac{15*(x + y + z)}{10}$$
$$0.5y + 1.5z = 0.5x$$
$$y + 3z = x$$

Kudos [?]: 3 [0], given: 79

Three grades of milk are 1 percent, 2 percent and 3 percent   [#permalink] 24 Nov 2017, 12:51

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