PSAT Math Multiple-Choice Question 505: Answer and Explanation

Question: 505

Gail’s homemade iced tea is a combination of green tea and raspberry purée. If the green tea and raspberry purée are in a ratio of 23 : 7, and a pitcher of iced tea can hold 900 mL, what is the amount of green tea, in mL, that Gail needs to make a pitcher of iced tea?

• A. 63
• B. 207
• C. 210
• D. 690

Correct Answer: D

Explanation:

D

The question asks for the amount of green tea needed to make a pitcher of iced tea. Since the question asks for a specific value and the answers contain numbers in increasing order, plug in the answers. Begin by labeling the answers as "amount of green tea" and start with (B), 207. If there are 207 mL of green tea in a pitcher of 900 mL, the remaining amount is the volume of raspberry purée. This means there are 900 – 207 = 693 mL of raspberry purée. The ratio of green tea to raspberry purée becomes 207 : 693, which reduces to 23 : 77. The ratio is supposed to be 23 : 7, so this does not work. Eliminate (B). A much larger volume of green tea is needed, so try (D) next. If there are 690 mL of green tea in a pitcher of 900 mL, there are 900 – 690 = 210 mL of raspberry purée. The ratio of green tea to raspberry purée becomes 690 : 210, which reduces to 23 : 7. Since this is the given ratio, stop here. The correct answer is (D).