It is currently 13 Dec 2017, 05:23

# Decision(s) Day!:

CHAT Rooms | Ross R1 | Kellogg R1 | Darden R1 | Tepper R1

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 26 Nov 2009
Posts: 17

Kudos [?]: 115 [9], given: 0

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

### Show Tags

24 Dec 2009, 08:38
9
KUDOS
75
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

74% (01:09) correct 26% (01:13) wrong based on 1301 sessions

### HideShow timer Statistics

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. $$3y + 4.5z$$
[Reveal] Spoiler: OA

Kudos [?]: 115 [9], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 42579

Kudos [?]: 135467 [31], given: 12695

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

### Show Tags

24 Dec 2009, 09:23
31
KUDOS
Expert's post
40
This post was
BOOKMARKED
JimmyWorld wrote:
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

OA is
[Reveal] Spoiler:
A

Milk concentration in mix would be $$1\%x+2\%y+3\%z$$ and on the other hand we are told that in (x+y+z) there is 1.5% of milk. Hence:

$$1\%x+2\%y+3\%z=1.5\%(x+y+z)$$;

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

$$0.5x=0.5y+1.5z$$;

$$x=y+3z$$.

Hope it's clear.
_________________

Kudos [?]: 135467 [31], given: 12695

Senior Manager
Status: mba here i come!
Joined: 07 Aug 2011
Posts: 261

Kudos [?]: 1260 [11], given: 48

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

### Show Tags

15 Jan 2012, 08:46
11
KUDOS
1
This post was
BOOKMARKED
$$\frac{x+2y+3z}{x+y+z} = \frac{3}{2}$$

$$x = y+3z$$
_________________

press +1 Kudos to appreciate posts

Kudos [?]: 1260 [11], given: 48

Director
Joined: 28 Jul 2011
Posts: 516

Kudos [?]: 312 [10], given: 16

Location: United States
GPA: 3.86
WE: Accounting (Commercial Banking)
Re: Three grades of milk are 1 percent, 2 percent and 3 percent [#permalink]

### Show Tags

15 Jan 2012, 16:00
10
KUDOS
2
This post was
BOOKMARKED
Its A, just put the words into equation

x+2Y+3Z=1.5(X+2Y+3Z)

X=Y+3Z

Hope it clarifies

+1 Kudos if it helps
_________________

Kudos [?]: 312 [10], given: 16

Manager
Joined: 10 Jan 2010
Posts: 181

Kudos [?]: 31 [0], given: 7

Location: Germany
Concentration: Strategy, General Management
Schools: IE '15 (M)
GPA: 3
WE: Consulting (Telecommunications)
Re: Three grades of milk are 1 percent, 2 percent and 3 percent [#permalink]

### Show Tags

22 Jan 2012, 07:04

Kudos [?]: 31 [0], given: 7

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7792

Kudos [?]: 18111 [14], given: 236

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

### Show Tags

22 Jan 2012, 17:56
14
KUDOS
Expert's post
3
This post was
BOOKMARKED
MSoS wrote:
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.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 18111 [14], given: 236 Senior Manager Joined: 12 Mar 2012 Posts: 351 Kudos [?]: 209 [7], given: 31 Concentration: Operations, Strategy Re: Three grades of milk are 1 percent, 2 percent and 3 percent [#permalink] ### Show Tags 22 Mar 2012, 02:16 7 This post received KUDOS 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 _________________ Practice Practice and practice...!! If my reply /analysis is helpful-->please press KUDOS If there's a loophole in my analysis--> suggest measures to make it airtight. Kudos [?]: 209 [7], given: 31 Intern Joined: 15 Jan 2012 Posts: 20 Kudos [?]: 8 [0], given: 2 GMAT 1: 760 Q50 V44 GPA: 3.85 WE: Marketing (Computer Software) Re: Three grades of milk are 1 percent, 2 percent and 3 percent [#permalink] ### Show Tags 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. Kudos [?]: 8 [0], given: 2 Intern Joined: 16 Jan 2012 Posts: 4 Kudos [?]: [0], given: 0 Re: Three grades of milk are 1 percent, 2 percent and 3 percent [#permalink] ### Show Tags 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. Kudos [?]: [0], given: 0 GMAT Tutor Joined: 20 Jul 2012 Posts: 25 Kudos [?]: 3 [1], given: 4 GMAT 1: 780 Q50 V50 Re: Three grades of milk are 1 percent, 2 percent and 3 percent [#permalink] ### Show Tags 17 Sep 2012, 16:06 1 This post received KUDOS 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!!! _________________ WWW.CLEARMOUNTAINPREP.COM Kudos [?]: 3 [1], given: 4 Senior Manager Joined: 13 Aug 2012 Posts: 457 Kudos [?]: 570 [0], given: 11 Concentration: Marketing, Finance GPA: 3.23 Re: Three grades of milk are 1 percent, 2 percent and 3 percent [#permalink] ### Show Tags 28 Sep 2012, 02:10 1%x + 2%y + 3%z = 1.5% (x+y+z) 2%y - 1.5%y + 3%z - 1.5%z = 1.5%x - 1%x 2(.5y + 1.5z = .5x) y + 3z = x Answer: A _________________ Impossible is nothing to God. Kudos [?]: 570 [0], given: 11 Intern Joined: 16 Jul 2012 Posts: 24 Kudos [?]: 13 [1], given: 3 Re: Three grades of milk are 1 percent, 2 percent and 3 percent [#permalink] ### Show Tags 22 Oct 2012, 19:01 1 This post received KUDOS (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 ______________ [Reveal] Spoiler: A is the answer _________________ Give me a Kudo if you find my post useful Awesome AWA tip - http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html Amazing CR questions - http://gmatclub.com/forum/100-amazing-cr-questions-explanations-cr-700-to-800-level-137885.html Overlapping set problems - http://gmatclub.com/forum/advanced-overlapping-sets-problems-144260.html My GMAT Story - http://gmatclub.com/forum/from-530-q43-v20-to-630-q47-v30-my-gmat-story-144980.html Kudos [?]: 13 [1], given: 3 Manager Joined: 11 Jan 2011 Posts: 68 Kudos [?]: 30 [1], given: 3 GMAT 1: 680 Q44 V39 GMAT 2: 710 Q48 V40 Re: Three grades of milk are 1 percent, 2 percent and 3 percent [#permalink] ### Show Tags 25 Jul 2013, 13:22 1 This post received KUDOS 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? Kudos [?]: 30 [1], given: 3 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7792 Kudos [?]: 18111 [1], given: 236 Location: Pune, India Re: Three grades of milk are 1 percent, 2 percent and 3 percent [#permalink] ### Show Tags 25 Jul 2013, 20:52 1 This post received KUDOS Expert's post 1 This post was BOOKMARKED 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Kudos [?]: 18111 [1], given: 236

Intern
Joined: 18 Jun 2013
Posts: 10

Kudos [?]: 4 [1], given: 3

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

### Show Tags

12 Jan 2014, 08:51
1
KUDOS
1
This post was
BOOKMARKED
I approached it as a residuals problem

Since 1% fat = -0.5% from average
2% fat = 0.5% from average
3% fat = 1.5% from average

When added together, they have to create a 0 'residual' from 1.5% average:

-0.5x + 0.5y + 1.5z = 0
0.5y + 1.5z = 0.5x

[Reveal] Spoiler:
y + 3z = x --> A

Kudos [?]: 4 [1], given: 3

Director
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 515

Kudos [?]: 612 [0], given: 6

Location: India
GMAT 1: 780 Q51 V46
Re: Three grades of milk are 1 percent, 2 percent and 3 percent [#permalink]

### Show Tags

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

Using weighted average:

(x) (1) + (y) (2) + (z)(3) = (1.5) (x + y + z)

x + 2y + 3z = 1.5x + 1.5y + 1.5z
0.5y + 1.5z = 0.5x

Removing 0.5 overall:

y +3z = x
_________________

Join Free 4 part MBA Through GMAT Video Training Series here -
https://gmat.crackverbal.com/mba-through-gmat-video-2018

Enroll for our GMAT Trial Course here -
http://gmatonline.crackverbal.com/

Kudos [?]: 612 [0], given: 6

Current Student
Joined: 06 Sep 2013
Posts: 1966

Kudos [?]: 759 [0], given: 355

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

### Show Tags

29 Jan 2014, 14:33
I solved this by using differentials

1% - x
2% - y
3% - z

So then x+y+z is also given as 1.5%, which is in fact the weighted average

Let's just play with nice numbers here

10% - x
20% - y
30% - z

x + y + z = 15%

So -5x+5y+15z = 0

X = Y + 3Z

A

Kudos [?]: 759 [0], given: 355

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7792

Kudos [?]: 18111 [3], given: 236

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

### Show Tags

29 Jan 2014, 20:22
3
KUDOS
Expert's post
Impenetrable wrote:
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.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 18111 [3], given: 236

Manager
Joined: 23 Jan 2012
Posts: 75

Kudos [?]: 16 [0], given: 40

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

### Show Tags

26 Oct 2014, 09:13
Bunuel - Where can I find challenging mixture problems/weighted avg problems to practice? Can you please help?

Thanks.

Kudos [?]: 16 [0], given: 40

Math Expert
Joined: 02 Sep 2009
Posts: 42579

Kudos [?]: 135467 [0], given: 12695

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

### Show Tags

27 Oct 2014, 05:20
Expert's post
8
This post was
BOOKMARKED
p2bhokie wrote:
Bunuel - Where can I find challenging mixture problems/weighted avg problems to practice? Can you please help?

Thanks.

Check our Questions Bank: viewforumtags.php

All DS Mixture Problems to practice: search.php?search_id=tag&tag_id=43
All PS Mixture Problems to practice: search.php?search_id=tag&tag_id=114

GMAT PS Question Directory by Topic & Difficulty: gmat-ps-question-directory-by-topic-difficulty-127957.html
GMAT DS Question Directory by Topic & Difficulty: ds-question-directory-by-topic-difficulty-128728.html

Hope this helps.
_________________

Kudos [?]: 135467 [0], given: 12695

Re: Three grades of milk are 1 percent, 2 percent and 3 percent   [#permalink] 27 Oct 2014, 05:20

Go to page    1   2    Next  [ 28 posts ]

Display posts from previous: Sort by