Question in the attachment.

[eitijan]

Question in the attachment.
How to solve this question?
Source: GmatPrep

[GMATGuruNY]

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.

[Brent@GMATPrepNow]

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

Let's start with a "word equation" and slowly turn it into an algebraic expression:

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

[[email protected]]

Hi eitijan,

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

[eitijan]

Thank you for detailed explanation.
I formed a correct equation.
But such questions are good and easy to solve by plugging so I tried doing it but could not.
@Mitch Hunt : How you inferred that x=y, I could not understand . Could you please elaborate?

[[email protected]]

Hi eitijan,

You mentioned that you tried solving this question "by plugging" (re: TESTing VALUES), so there's something here worth noting: in many cases, when a question uses the phrase "in terms of", it is NOT a good question to TEST VALUES on (so approaching the prompt algebraically is recommended).

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

[eitijan]

Hi Rich

My understanding was completely the other way.
Which type of questions are the good target to solve by plugging?
As per GMATTutor, questions with in terms are a good target to solve by plugging.

[Matt@VeritasPrep]

Hi Rich

My understanding was completely the other way.
Which type of questions are the good target to solve by plugging?
As per GMATTutor, questions with in terms are a good target to solve by plugging.

Usually the best candidate is a word problem in which all the answer choices are variables. In those cases, you can usually pick values for each letter, then check the answers to see which matches your number.