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

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

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
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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
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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.
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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.
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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!
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by heymrdj » Fri Jul 03, 2009 7:00 pm
what level would you say this question is? 600? 700? Mid-700+?
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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
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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.
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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
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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?
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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!
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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
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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.
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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.
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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.
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