PSAT Math Multiple-Choice Question 702: Answer and Explanation

Question: 702

A rock is made up by volume of 32% coal, which has a specific gravity (expressed in grams per cubic centimeter) of 1.20. The rock contains 29% granite with a specific gravity of 2.60. The rock also contains 39% of an unknown mineral. If the specific gravity of the entire rock is 1.4, the unknown material has what approximate specific gravity?

• A. 0.43
• B. 0.54
• C. 0.67
• D. 0.81

Correct Answer: C

Explanation:

(C) Let's imagine the total volume of this rock to be 1 cubic centimeter. Therefore, 0.32 cubic centimeters are coal, 0.29 cubic centimeters are granite, and 1 - 0.32 - 0.29 = 0.39 cubic centimeters are an unknown mineral. Using the specific gravities, we can calculate the mass of each species.

For coal:

For granite:

For the unknown:

We know that the specific gravity of the whole thing is 1.4 grams/centimeter cubed, so its mass is:

Because all of the masses together must equal 1.4, it follows that:

0.384 + 0.754 + 0.39x = 1.4

Subtract the first 2 terms from both sides:

0.39x = 0.262

Divide both sides by 0.39:

x = 0.67