Hello Everyone,

Please help me in answering this question from GMATPrep:

3 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?

1. y+3z

2. (y+z)/4

3. 2y+3z

4. 3y+z

5. 3y+4.5z

## 3 grades of milk

##### This topic has expert replies

- GMATGuruNY
- GMAT Instructor
**Posts:**15539**Joined:**Tue May 25, 2010 12:04 pm**Location:**New York, NY**Thanked**: 13060 times**Followed by:**1906 members**GMAT Score:**790

The desired grade -- 1.5% -- is equal to the AVERAGE of x=1% and y=2%: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

(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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Followed here and elsewhere by over 1900 test-takers.

I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.

My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.

I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].

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### GMAT/MBA Expert

- Brent@GMATPrepNow
- GMAT Instructor
**Posts:**16207**Joined:**Mon Dec 08, 2008 6:26 pm**Location:**Vancouver, BC**Thanked**: 5254 times**Followed by:**1268 members**GMAT Score:**770

Let's start with a "word equation" and slowly turn it into an algebraic expression:Three grades of milk: 1%, 2%, and 3% fat by volume. X gallons of 1%, y gallons of 2%, and z gallons of 3% are mixed to give x + y + z gallons of 1.5%. What is x in terms of y and z?

a. y + 3z

b. (y + z)/4

c. 2y + 3z

d. 3y + z

e. 3y + 4z

Total fat in mixture = 1.5% of (x+y+z)

(1% of x) + (2% of y) + (3% of z) = 0.015(x+y+z)

Rewrite as: 0.01x + 0.02y + 0.03z = 0.015x + 0.015y + 0.015z

Multiply both sides by 100: 1x + 2y + 3z = 1.5x + 1.5y + 1.5z

Rearrange and simplify: 0.5y + 1.5z = 0.5x

Multiply both sides by 2 to get: y + 3z = x

Answer = A

Cheers,

Brent