PSAT Math Multiple-Choice Question 230: Answer and Explanation

Question: 230

The United States Senate has two voting members for each of the 50 states. The 113th Congress had a 4:1 male-to-female ratio in the Senate. Forty-five of the male senators were Republican. Only 20 percent of the female senators were Republican. How many senators in the 113th Congress were Republican?

• A. 20
• B. 49
• C. 55
• D. 65

Correct Answer: B

Explanation:

B

Difficulty: Medium

Category: Problem Solving and Data Analysis/Rates, Ratios, Proportions, and Percentages

Getting to the Answer: Break the question into short steps. Step 1: Find the number of female senators. Step 2: Use that number to find the number of female Republican senators. Step 3: Find the total number of Republican senators.

Each of the 50 states gets 2 voting members in the Senate, so there are 50 × 2 = 100 senators. The ratio of males to females in the 113th Congress was 4:1, so 4 parts male plus 1 part female equals a total of 100 senators. Write this as 4 x + x = 100, where x represents one part and therefore the number of females. Next, simplify and solve the equation to find that x = 20 female senators. To find the number of female senators that were Republican, multiply 20% (or 0.20) times 20 to get 4. Finally, add to get 45 male plus 4 female = 49 Republican senators in the 113th Congress, (B).