Three grades of milk are 1 percent, 2 percent and 3 percent : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 09 Dec 2016, 15:02

### 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: 14
Followers: 1

Kudos [?]: 68 [8] , given: 0

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

### Show Tags

24 Dec 2009, 08:38
8
KUDOS
41
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

72% (02:17) correct 28% (01:07) wrong based on 818 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. (y +z) / 4
C. 2y + 3z
D. 3y + z
E. 3y + 4.5z
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 35932
Followers: 6860

Kudos [?]: 90096 [16] , given: 10413

Re: GMAT Prep VIC Problem [#permalink]

### Show Tags

24 Dec 2009, 09:23
16
KUDOS
Expert's post
20
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.
_________________
Senior Manager
Status: mba here i come!
Joined: 07 Aug 2011
Posts: 270
Followers: 42

Kudos [?]: 1043 [8] , given: 48

Re: GMAT Practice Test 1 PS: Ratio [#permalink]

### Show Tags

15 Jan 2012, 08:46
8
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

Director
Joined: 28 Jul 2011
Posts: 563
Location: United States
GPA: 3.86
WE: Accounting (Commercial Banking)
Followers: 3

Kudos [?]: 202 [9] , given: 16

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

### Show Tags

15 Jan 2012, 16:00
9
KUDOS
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
_________________

Manager
Joined: 10 Jan 2010
Posts: 192
Location: Germany
Concentration: Strategy, General Management
Schools: IE '15 (M)
GMAT 1: Q V
GPA: 3
WE: Consulting (Telecommunications)
Followers: 2

Kudos [?]: 28 [0], given: 7

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

### Show Tags

22 Jan 2012, 07:04
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7076
Location: Pune, India
Followers: 2089

Kudos [?]: 13304 [11] , given: 222

### Show Tags

22 Jan 2012, 17:56
11
KUDOS
Expert's post
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 Senior Manager Joined: 12 Mar 2012 Posts: 369 Concentration: Operations, Strategy Followers: 2 Kudos [?]: 160 [6] , given: 31 Re: GMAT prep question 1 [#permalink] ### Show Tags 22 Mar 2012, 02:16 6 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. Intern Joined: 15 Jan 2012 Posts: 20 GMAT 1: 760 Q50 V44 GPA: 3.85 WE: Marketing (Computer Software) Followers: 0 Kudos [?]: 8 [0], given: 2 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. Intern Joined: 16 Jan 2012 Posts: 4 Followers: 0 Kudos [?]: 0 [0], given: 0 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. GMAT Tutor Joined: 20 Jul 2012 Posts: 25 GMAT 1: 780 Q50 V50 Followers: 2 Kudos [?]: 2 [1] , given: 4 help need! hard weighted average question [#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 Senior Manager Joined: 13 Aug 2012 Posts: 464 Concentration: Marketing, Finance GMAT 1: Q V0 GPA: 3.23 Followers: 25 Kudos [?]: 417 [0], given: 11 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. Intern Joined: 16 Jul 2012 Posts: 25 Followers: 0 Kudos [?]: 11 [0], given: 3 Re: Three grades of milk are 1 percent, 2 percent, and 3 percent [#permalink] ### Show Tags 22 Oct 2012, 19:01 (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 Manager Joined: 11 Jan 2011 Posts: 69 GMAT 1: 680 Q44 V39 GMAT 2: 710 Q48 V40 Followers: 0 Kudos [?]: 17 [1] , given: 3 Re: GMAT Practice Test 1 PS: Ratio [#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? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7076 Location: Pune, India Followers: 2089 Kudos [?]: 13304 [1] , given: 222 Re: GMAT Practice Test 1 PS: Ratio [#permalink] ### Show Tags 25 Jul 2013, 20:52 1 This post received KUDOS Expert's post 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

Intern
Joined: 18 Jun 2013
Posts: 11
Followers: 0

Kudos [?]: 2 [0], given: 3

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

### Show Tags

12 Jan 2014, 08:51
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
Senior Manager
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 310
Location: India
GMAT 1: 780 Q51 V46
Followers: 64

Kudos [?]: 255 [0], given: 5

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
_________________

Check out our essay writing workshop here:

Quick tips for your GMAT Preparation

For 5 common traps on CR check here :
http://gmatonline.crackverbal.com/p/gmat-critical-reasoning

For sentence correction videos check here -
http://gmatonline.crackverbal.com/p/gmat-sentence-correction

Learn all PS and DS strategies here-
http://gmatonline.crackverbal.com/p/mastering-quant-on-gmat

Check out 5 common challenges on RC -

Current Student
Joined: 06 Sep 2013
Posts: 2035
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 60

Kudos [?]: 582 [0], given: 355

Three grades of milk are 1 percent, 2 percent and 3 percent fat [#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
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7076
Location: Pune, India
Followers: 2089

Kudos [?]: 13304 [2] , given: 222

### Show Tags

29 Jan 2014, 20:22
2
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

Manager
Joined: 23 Jan 2012
Posts: 78
Followers: 1

Kudos [?]: 11 [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.
Math Expert
Joined: 02 Sep 2009
Posts: 35932
Followers: 6860

Kudos [?]: 90096 [0], given: 10413

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

### Show Tags

27 Oct 2014, 05:20
Expert's post
5
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.
_________________
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  [ 24 posts ]

Similar topics Replies Last post
Similar
Topics:
1 What Percent of 10 is 10 Percent of 1? 5 06 Nov 2016, 14:56
7 If mn ≠ 0 and 25 percent of n equals 37(1/2) percent of m, what is the 7 15 Jun 2016, 00:25
1 What percent of 15 is 15 percent of 1? 4 22 May 2016, 13:39
5 percent1 7 26 Oct 2010, 21:49
21 Three grades of milk are 1 percent, 2 percent and 3 percent 15 01 Jan 2007, 06:58
Display posts from previous: Sort by