If square ABCD has area 25, and the area of the larger shaded square is 9 times the area of the smaller shaded square, what is the length of one side of the smaller shaded square?
A. 3/4
B. 5/4
C. 6/5
D. 4/3
E. 5/3
We can plug in the answers, which represent the length of one side of the smaller square.
On the GMAT, the answers likely would be listed in ascending order: 3/4, 6/5, 5/4, 4/3, 5/3.
Middle answer choice: 5/4
Since side of ABCD = 5, side of the larger shaded square = 5 - 5/4 = 15/4.
The denominators of the two lengths (5/4 and 15/4) are the same.
To compare the areas of the two squares, we need to compare only the squares of the numerators:
Bigger area:smaller area = (15^2)/(5^2) = (15/5)^2 = 9.
Success!
The correct answer is
B.
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