At a medical convention attended only by pediatricians and general surgeons, 40 percent of the 250 pediatricians in attendance were male, and 60 percent of the general surgeons were male. How many people were at the convention?
(1) The ratio of male pediatricians to female general surgeons was 2 to 3.
(2) There were exactly 150 female general surgeons in attendance.
OA D
Source: Princeton Review
At a medical convention attended only by pediatricians and general surgeons, 40 percent of the 250 pediatricians in
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Given that:
Male pediatricians = 40% of 250 = 100
Total pediatricians = 250
Male surgeons = 60% of s = 0.6s
Female surgeons = 40% of s = 0.4s
Female pediatricians = 60% of 250 = 150
Target question => How many people were at the convention?
Statement 1: The ratio of male pediatricians to female general surgeons was 2 to 3.
$$\frac{male\ pediatrician}{female\ pediatrician}=\frac{2}{3}$$
$$\frac{100}{0.4s}=\frac{2}{3}$$
$$300=0.8s$$
$$s=\frac{300}{0.8}=375$$
Total people at the convention = 375 + 250 = 625.
Therefore, statement 1 is SUFFICIENT.
Statement 2: There were exactly 150 female general surgeons in attendance.
0.4s = 150
$$s=\frac{150}{0.4}=375$$
Total people at the convention = 375 + 250 = 625.
Statement 2 is also SUFFICIENT.
Therefore, since each statement alone is SUFFICIENT, option D is the correct answer.
Male pediatricians = 40% of 250 = 100
Total pediatricians = 250
Male surgeons = 60% of s = 0.6s
Female surgeons = 40% of s = 0.4s
Female pediatricians = 60% of 250 = 150
Target question => How many people were at the convention?
Statement 1: The ratio of male pediatricians to female general surgeons was 2 to 3.
$$\frac{male\ pediatrician}{female\ pediatrician}=\frac{2}{3}$$
$$\frac{100}{0.4s}=\frac{2}{3}$$
$$300=0.8s$$
$$s=\frac{300}{0.8}=375$$
Total people at the convention = 375 + 250 = 625.
Therefore, statement 1 is SUFFICIENT.
Statement 2: There were exactly 150 female general surgeons in attendance.
0.4s = 150
$$s=\frac{150}{0.4}=375$$
Total people at the convention = 375 + 250 = 625.
Statement 2 is also SUFFICIENT.
Therefore, since each statement alone is SUFFICIENT, option D is the correct answer.