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GMAT Practice exam 2 - Mixture problem

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by lucas211 » Sat Jun 04, 2016 2:25 am
Hello BTG

I am having difficulties on how to approach this problem:
Would appreciate a little help, and if you have a couple of similar problems I can practice on.


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Thanks in advance :-)
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by GMATGuruNY » Sat Jun 04, 2016 2:37 am
3 grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of 1% grade, y gallons of 2% grade and z gallons of 3 % grade are mixed to give x+y+z gallons of 1.5% grade, what is x in terms of y & z?
1) y+3z
2) (y+z)/4
3) 2y+3z
4) 3y+2
5) 3y+4.5z
The desired grade -- 1.5% -- is equal to the AVERAGE of x=1% and y=2%:
(1% + 2%)/2 = 1.5%.
Thus, a mixture composed of equal amounts of x and y will be 1.5% grade.

Let x=2, y=2, and z=0, implying that the mixture will composed of equal amounts of x and y (2 units each).
The question stem asks for the value of x=2. This is our target.
Now plug y=2 and z=0 into the answers to see which yields our target of 2.
Only A works:
y + 3z = 2 + 3(0) = 2.

The correct answer is A.

Algebraically:

(1% of X) + (2% of Y) + (3% of Z) must be equal to (1.5% of X+Y+Z).
Thus:
x + 2y + 3x = 1.5(x + y + z)
10x + 20y + 30z = 15x + 15y + 15z.

Since the question stem asks for the value of x, solve for x:
20y + 30z = 5x + 15y + 15z
5y + 15z = 5x
y + 3z = x.

The correct answer is A.
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by lucas211 » Sat Jun 04, 2016 2:53 am
GMATGuruNY wrote:
3 grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of 1% grade, y gallons of 2% grade and z gallons of 3 % grade are mixed to give x+y+z gallons of 1.5% grade, what is x in terms of y & z?
1) y+3z
2) (y+z)/4
3) 2y+3z
4) 3y+2
5) 3y+4.5z
The desired grade -- 1.5% -- is equal to the AVERAGE of x=1% and y=2%:
(1% + 2%)/2 = 1.5%.
Thus, a mixture composed of equal amounts of x and y will be 1.5% grade.

Let x=2, y=2, and z=0, implying that the mixture will composed of equal amounts of x and y (2 units each).
The question stem asks for the value of x=2. This is our target.
Now plug y=2 and z=0 into the answers to see which yields our target of 2.
Only A works:
y + 3z = 2 + 3(0) = 2.

The correct answer is A.

Algebraically:

(1% of X) + (2% of Y) + (3% of Z) must be equal to (1.5% of X+Y+Z).
Thus:
x + 2y + 3x = 1.5(x + y + z)
10x + 20y + 30z = 15x + 15y + 15z.

Since the question stem asks for the value of x, solve for x:
20y + 30z = 5x + 15y + 15z
5y + 15z = 5x
y + 3z = x.

The correct answer is A.
Hi GMATGuru

Great explanations. Thanks a lot!
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by [email protected] » Sat Jun 04, 2016 9:18 am
Hi lucas211,

This is an "in terms of" question; these questions are usually built around 4-5 algebra steps and are fairly straight-forward "math" questions.

First, translate the equation:

[(.01x) + (.02y) + (.03z)] / {x + y + z] = .015

.01x + .02y + .03z = .015x + .015y + .015z

Let's multiply everything by 1000 to get rid of the decimals....

10x + 20y + 30z = 15x + 15y + 15z

5y + 15z = 5x

y + 3z = x

Final Answer: A

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by lucas211 » Sun Jun 05, 2016 5:18 am
[email protected] wrote:Hi lucas211,

This is an "in terms of" question; these questions are usually built around 4-5 algebra steps and are fairly straight-forward "math" questions.

First, translate the equation:

[(.01x) + (.02y) + (.03z)] / {x + y + z] = .015

.01x + .02y + .03z = .015x + .015y + .015z

Let's multiply everything by 1000 to get rid of the decimals....

10x + 20y + 30z = 15x + 15y + 15z

5y + 15z = 5x

y + 3z = x

Final Answer: A

GMAT assassins aren't born, they're made,
Rich
Hi Rich

Thank you for the explanation and the approach!

Lucas
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by Matt@VeritasPrep » Tue Jun 07, 2016 10:44 pm
It also helps to write these out before you start.

Say you have x gallons of the 1% grade. That means 1% of x, or .01x, is fat.

From there, we know the TOTAL amount of fat can be expressed as

.01x + .02y + .03z

But we're also told that it can be expressed as

.015*(x + y + z)

Since these are two ways of writing the same thing, they must be equal, and from there, the solution is cake.
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