Digital PSAT Math Practice Question 270: Answer and Explanation

Question: 270

A polling company surveys 1,000 randomly selected senior citizens in the state of Connecticut. The senior citizens surveyed are representative of the typical demographics of senior citizens in the state. There are approximately 3.6 million residents in Connecticut, and approximately 14% of these residents are senior citizens. If 23% of the survey respondents indicated they planned on supporting a new tax regulation, what is the best estimate for how many senior citizens in the state as a whole would support the tax regulation?

• A. 83,000
• B. 98,000
• C. 116,000
• D. 828,000

Correct Answer: C

Explanation:

(C) First, you need to know how many senior citizens there are in the state of Connecticut. If 14% of 3.6 million are seniors, then 3,600,000(0.14) = 504,000 are senior citizens. This also could have been done using a proportion, recognizing that 3.6 million is 100% of the population.

Next, you know that 23% of the survey respondents said that they would support the new tax regulation. Since the question says that those surveyed are representative of the population, it follows that 23% of the senior population would also support the tax regulation. Find 23% of 504,000 by using a proportion (although you could just as easily multiply 504,000 by 0.23 to find the answer).

Next, cross-multiply:

Dividing by 100 tells you that x = 115,920. This most closely matches choice (C).