PSAT Math Multiple-Choice Question 633: Answer and Explanation

Question: 633

Whole milk has 3.5% fat content. If you used equal amounts of 1% and 2% milk, how many total gallons of the combined milk would you use to equal the fat content in exactly 1 gallon of whole milk?

• A.
• B.
• C.
• D.

Correct Answer: D

Explanation:

(D) A gallon of whole milk would have 3.5% of a gallon of fat, or 0.035 gallons. If we mix 1% milk and 2% milk in equal parts, we will essentially have 1.5% milk since the fat content will be the average of the two fat contents.

Therefore, the whole milk has times the amount of fat of the 1% and 2% mixture. You would need 2.333 times the amount of milk of the mixture to have the same quantity of fat as in 1 gallon of whole milk. Because 0.333 can be represented as , the answer is choice (D).

Alternatively, take the combined average of the lower-fat milks:

Then using x as the number of gallons needed of the combined milks, you can set up this equation:

1.5x = 3.5

Then solve for x to get .