GMAT Practice Question: During a certain year, 80 percent of the visitors to the Smithsonian Institution were United...
Question
During a certain year, 80 percent of the visitors to the Smithsonian Institution were United States citizens, 50 percent of the remaining visitors were Canadian or Mexican citizens, and 50 percent of the visitors who were not citizens of the United States, Canada, or Mexico were citizens of European countries. The number of United States citizens who visited the Smithsonian that year was approximately how many times the number of citizens of European countries who visited the Smithsonian that year?
- 1.6
- 4.8
- 8
- 16
- 32
Topics: word problems, percentages, ratios
Solution
Step 1
We name the total number of visitors T. We use \textbf{"80 percent of the visitors to the Smithsonian Institution were United States citizens"} to find the number of U.S. citizens and the number of remaining visitors.
U = 0.8\times T N = T - U
Step 2
We then use \textbf{"50 percent of the remaining visitors were Canadian or Mexican citizens"} to find the number of Canadian or Mexican citizens and the number of visitors left.
M = 0.5\times N R = N - M
Step 3
We use \textbf{"50 percent of the visitors who were not citizens of the United States, Canada, or Mexico were citizens of European countries"} to find the number of European visitors in terms of T.
N = T - U = T - 0.8\times T = 0.2\times T R = N - M = 0.2\times T - 0.1\times T = 0.1\times T E = 0.5\times R = 0.5\times (0.1\times T) = 0.05\times T
Step 4
We compare the number of U.S. citizens to European citizens by forming a ratio.
\frac{U}{E} = \frac{0.8\times T}{0.05\times T} = \frac{0.8}{0.05} = 16
Answer
D
