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GMAT Quant — Applied Mathematics (Word Problems)

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?

Explanation	Calculations	Help
$We name the total number of visitors T . We use "80 percent of the visitors to the Smithsonian Institution were United States citizens" to find the number of U.S. citizens and the number of remaining visitors.$	$U = 0.8 \times T N = T - U$	Theory & Tactics Method Card FDPR4-A Click to view full details
$We then use "50 percent of the remaining visitors were Canadian or Mexican citizens" to find the number of Canadian or Mexican citizens and the number of visitors left.$	$M = 0.5 \times N R = N - M$	Theory & Tactics Method Card FDPR4-A Click to view full details
$We use "50 percent of the visitors who were not citizens of the United States, Canada, or Mexico were citizens of European countries" to find the number of European visitors in terms of T .$	$N = T - U = T - 0.8 \times T = 0.2 \times T R = N - M = 0.2 \times T - 0.1 \times T = 0.1 \times T E = 0.5 \times R = 0.5 \times (0.1 \times T) = 0.05 \times T$	Theory & Tactics Method Card FDPR4-A Click to view full details
$We compare the number of U.S. citizens to European citizens by forming a ratio.$	$\frac{U}{E} = \frac{0.8 \times T}{0.05 \times T} = \frac{0.8}{0.05} = 16$	Theory & Tactics Method Card FDPR0-K Click to view full details

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GMAT Quant — Applied Mathematics (Word Problems)

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?

Explanation	Calculations	Help
$We name the total number of visitors T . We use "80 percent of the visitors to the Smithsonian Institution were United States citizens" to find the number of U.S. citizens and the number of remaining visitors.$	$U = 0.8 \times T N = T - U$	Theory & Tactics Method Card FDPR4-A Click to view full details
$We then use "50 percent of the remaining visitors were Canadian or Mexican citizens" to find the number of Canadian or Mexican citizens and the number of visitors left.$	$M = 0.5 \times N R = N - M$	Theory & Tactics Method Card FDPR4-A Click to view full details
$We use "50 percent of the visitors who were not citizens of the United States, Canada, or Mexico were citizens of European countries" to find the number of European visitors in terms of T .$	$N = T - U = T - 0.8 \times T = 0.2 \times T R = N - M = 0.2 \times T - 0.1 \times T = 0.1 \times T E = 0.5 \times R = 0.5 \times (0.1 \times T) = 0.05 \times T$	Theory & Tactics Method Card FDPR4-A Click to view full details
$We compare the number of U.S. citizens to European citizens by forming a ratio.$	$\frac{U}{E} = \frac{0.8 \times T}{0.05 \times T} = \frac{0.8}{0.05} = 16$	Theory & Tactics Method Card FDPR0-K Click to view full details

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D