Three Grades of milk are 1 percent, 2 percent and 3 percent

Expert replies

GMAT/MBA Expert

lunarpower: GMAT Instructor; Posts: 3380; Joined: Mon Mar 03, 2008 1:20 amFollowed by: 1535 members; Thanked: 2256 times; GMAT Score:800

by lunarpower » Sat Jul 12, 2008 2:02 am

courtesy of user 'karenmeow'

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 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

1. y+ 3z
2. y+z/4
3. 2y+3z
4. 3y + z
5. 3y + 4.5z

Ron has been teaching various standardized tests for 20 years.

--

Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions Ã Ron en franÃ§ais
Voit esittÃ¤Ã¤ kysymyksiÃ¤ Ron:lle myÃ¶s suomeksi

--

Quand on se sent bien dans un vÃªtement, tout peut arriver. Un bon vÃªtement, c'est un passeport pour le bonheur.

Yves Saint-Laurent

--

Learn more about ron

Like this post

Source: Beat The GMAT — Problem Solving | Sat Jul 12, 2008 2:02 am

GMAT/MBA Expert

lunarpower: GMAT Instructor; Posts: 3380; Joined: Mon Mar 03, 2008 1:20 amFollowed by: 1535 members; Thanked: 2256 times; GMAT Score:800

by lunarpower » Sat Jul 12, 2008 2:03 am

the easiest way to do this is to pick numbers. in fact, you can pick numbers on ALL problems whose question prompts feature the words "in terms of", because such problems, by definition, work with any given values of those variables.

let's pick easy numbers: y = 2, z = 4. (these aren't totally random. the choice for y is essentially random, but z has been deliberately chosen so that #2 and #5 will be integers.)

then we have:
x gallons of 1% = 0.01x gallons of fat
2 gallons of 2% = 0.02(2) = 0.04 gallons of fat
4 gallons of 3% = 0.03(4) = 0.12 gallons of fat
total fat = 0.01x + 0.04 + 0.12 = (0.01x + 0.16) gallons
total volume = x + 2 + 4 = (x + 6) gallons

so:
(0.01x + 0.16)/(x + 6) = 0.015
multiply by 100 ----- (x + 16)/(x + 6) = 1.5
multiply through by (x + 6) ----- x + 16 = 1.5x + 9
7 = 0.5x
14 = x

check the answer choices with y = 2, z = 4:
a: 14
b: 3
c: 16
d: 10
e: 24

a wins

Like this post

N.O: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Fri Aug 08, 2008 2:12 pm; Location: Palo Alto, CA; Thanked: 12 times

by N.O » Wed Oct 08, 2008 12:26 pm

Not sure whether the post above (picking a number) is necessarily the best and most efficient solution. Here is a general solution - no picking numbers where any mistakes could happen.

The general formula that we can write as soon as we read:

0.01x+0.02y+0.03z=0.015(x+y+z) /lets multiply everything by 1000 to make things easier

[Exp of the formula above:
0.01x+0.02y+0.03z===adding up all those milks with different fat
0.015(x+y+z)==total amount with mixed fat (1.5%)]

10x+20y+30z=15x+15y+15z --> 5x=5y+15z or x=y+3z --> Ans A.

Like this post

VP_Jim: GMAT Instructor; Posts: 1223; Joined: Thu May 01, 2008 3:29 pmFollowed by: 15 members; Location: Los Angeles, CA; Thanked: 185 times

by VP_Jim » Wed Oct 08, 2008 7:35 pm

I'm going to side with Ron on this one - sure, you might be able to solve it using algebra. But, picking numbers is foolproof once you get the hang of it, and it's a universal strategy for any problem that says "in terms of" and some problems that don't.

The best GMAT strategies are those that turn complex equations into simple math, and that are applicable to many problems. Plugging in numbers is one of those strategies.

Good question, Ron.

Jim S. | GMAT Instructor | Veritas Prep

Like this post

mjjking: Master | Next Rank: 500 Posts; Posts: 353; Joined: Sat Jan 20, 2007 1:29 am; Location: Italy; Thanked: 7 times; GMAT Score:720

by mjjking » Thu Apr 02, 2009 11:45 pm

it took 8 minutes in the gmatprep to figure this problem out but Isolved it!

Ron, very good explanation, thanks!

Beat The GMAT - 1st priority
Enter a top MBA program - 2nd priority
Loving my wife: MOST IMPORTANT OF ALL!

REAL THING 1 (AUG 2007): 680 (Q43, V40)
REAL THING 2 (APR 2009): 720 (Q47, V41)

Like this post

heymrdj: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Mon Mar 30, 2009 3:37 am; Location: Toronto, ON; Thanked: 1 times

by heymrdj » Fri Jul 03, 2009 7:00 pm

what level would you say this question is? 600? 700? Mid-700+?

Like this post

real2008: Legendary Member; Posts: 527; Joined: Thu May 01, 2008 12:06 am; Thanked: 7 times

by real2008 » Sun Jul 05, 2009 9:41 am

heymrdj wrote:what level would you say this question is? 600? 700? Mid-700+?

probably 500

Like this post

ghacker: Master | Next Rank: 500 Posts; Posts: 148; Joined: Wed Jun 03, 2009 8:04 pmFollowed by: 1 member; Thanked: 18 times

by ghacker » Sun Jul 05, 2009 12:48 pm

This is a very easy question

I thinks its in the most lowest level ( say level 100---- if their is such a one )

"TThree 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 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 "

First thing is to read the question properly

Then u understand that the % is a buff it has no bearing on the result
so forget about the % and focus on the numbers

2.0 The numbers are 1 ,2, 3 and 1.5 ----> If you look at the numbers
you see that they are multiples of 0.5 that is

1 = 0.5*2 ; 2 = 0.5*4 ; 3 = 0.5*6 and 1.5 = 0.5*3

So know u can for get about the 1,2,3,and 1.5 , and concentrate on the
2,3,4and 6

So now you see that the answer is

X = Y+3Z

Last edited by ghacker on Sun Jul 05, 2009 1:16 pm, edited 5 times in total.

Like this post

ghacker: Master | Next Rank: 500 Posts; Posts: 148; Joined: Wed Jun 03, 2009 8:04 pmFollowed by: 1 member; Thanked: 18 times

by ghacker » Sun Jul 05, 2009 12:51 pm

VP_Jim wrote:I'm going to side with Ron on this one - sure, you might be able to solve it using algebra. But, picking numbers is foolproof once you get the hang of it, and it's a universal strategy for any problem that says "in terms of" and some problems that don't.

The best GMAT strategies are those that turn complex equations into simple math, and that are applicable to many problems. Plugging in numbers is one of those strategies.

Good question, Ron.

I agree with
"The best GMAT strategies are those that turn complex equations into simple math "

But question is what is simple maths ???? Is it writing inefficient equations or is it using common sense and logic ??? I think the second one is better than the first

Like this post

doclkk: Master | Next Rank: 500 Posts; Posts: 180; Joined: Tue Apr 07, 2009 3:46 pmFollowed by: 2 members; Thanked: 5 times

by doclkk » Fri Jul 24, 2009 7:43 am

ghacker wrote:This is a very easy question

I thinks its in the most lowest level ( say level 100---- if their is such a one )

"TThree 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 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 "

First thing is to read the question properly

Then u understand that the % is a buff it has no bearing on the result
so forget about the % and focus on the numbers

2.0 The numbers are 1 ,2, 3 and 1.5 ----> If you look at the numbers
you see that they are multiples of 0.5 that is

1 = 0.5*2 ; 2 = 0.5*4 ; 3 = 0.5*6 and 1.5 = 0.5*3

So know u can for get about the 1,2,3,and 1.5 , and concentrate on the
2,3,4and 6

So now you see that the answer is

X = Y+3Z

I've read your method and I was hoping that you could elaborate a bit more on it for those of us who went to public school.

So you get 2,3,4 and 6 - then what?

Like this post

Thouraya: Master | Next Rank: 500 Posts; Posts: 112; Joined: Wed Jan 20, 2010 5:46 am; Thanked: 1 times

by Thouraya » Sun Jul 18, 2010 11:28 pm

Hey Ron,

I didn't understand the part: (0.01x + 0.16)/(x + 6) = 0.015
How did we set up this equation? why isn't x+6 the numerator instead? and how did we know that this over this means the 1.5%?

Thank you!

Like this post

gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Sun Jul 18, 2010 11:46 pm

N.O wrote:Not sure whether the post above (picking a number) is necessarily the best and most efficient solution. Here is a general solution - no picking numbers where any mistakes could happen.

The general formula that we can write as soon as we read:

0.01x+0.02y+0.03z=0.015(x+y+z) /lets multiply everything by 1000 to make things easier

[Exp of the formula above:
0.01x+0.02y+0.03z===adding up all those milks with different fat
0.015(x+y+z)==total amount with mixed fat (1.5%)]

10x+20y+30z=15x+15y+15z --> 5x=5y+15z or x=y+3z --> Ans A.

Dont convert 1% into 1/100..

1X+2Y+3Z= 1.5X+1.5Y+1.5Z

0.5X= 0.5Y +1.5Z

X= Y+3Z

R&D on GMAT algorithm:

https://www.beatthegmat.com/r-d-on-gmat- ... tml#305739

Like this post

amirp: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Sun Dec 20, 2009 2:02 pm; Thanked: 3 times

by amirp » Wed Sep 29, 2010 11:32 am

I did this a bit different, you might find my way helpful.

so I picked the following numbers to get the average of 1.5 for the final solution.

x=2
y=2
z=0

This would give us the average of 1.5 for our final solution since its the middle of X and Y

now do back solving. we want our end result to be x=2

a) 2+3(0) = 2
b) (2+0)/4 = 1/2
c) 2(2) + 3(0) = 4
d) 3(2) + 0 = 6
e) 3(2) + 4.5(0) = 6

and the only solution that gives us 2 is the choice A.

I do understand that picking 0 for Z is a bit risky, and thats why you have to check all solutions, but since only A was correct, there is no need to pick another set of values.

hope this helps.

Like this post

[email protected]: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Wed Nov 10, 2010 7:49 am

by [email protected] » Thu Nov 11, 2010 1:56 am

I understand your solution but this is how i was doing it and for some reason i am getting a wrong answer. Can someone point out to me why i am wrong.

For every 1 unit of Z i would need to add 3 units of X to keep the ratio 1.5 and for every unit of y i would have to add equal amount of x.
converting it to equations,
3x=z
x=y
4x=y+z and hence answer is b.

Like this post

[email protected]: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Wed Nov 10, 2010 7:49 am

by [email protected] » Thu Nov 11, 2010 1:56 am

Like this post

Post new topic Post Reply

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review