GRE- Quantitative Reasoning
A. Option A
B. Option B
C. Option C
D. Option D
Answer(s): B
Explanation: Since the smallest circle has a radius of 1, the middle-sized circle has a radius of
2, and, therefore, the diameter of the large circle must be 6, which makes its radius 3. The arc of
a semicircle is half the circle's circumference-- that is,
r. So the length of the boundary of
the shaded region is the sum of the arcs of the three semicircles:

QUESTION: 21

Among registered voters in a certain district, the ratio of male to female voters is 3:5. If the
district currently includes 2,400 registered voters, how many additional males must register to
make the ratio 4:5, assuming the number of female voters remains unchanged?

A. 120
B. 150
C. 240
D. 300
E. 360
Answer(s): D
Explanation: Given a 3:5 male-female ratio and a total of 2,400 voters, the number of male
voters must be of 2,400, or 900. Accordingly, female voters must account for the remaining
1,500. Determine the number of male voters needed altogether for a 4:5 male-female ratio
(assuming the number of female voters remains unchanged at 1,500) by setting up a proportion
and solving for that number:

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