Medical residents at Lakewood Hospital are choosing their individual specialties. Among them, 40% choose cardiology, 16% choose oncology, 34% choose endocrinology, and the remaining x% choose hematology. Once the doctors pick their first specialty, they are then each asked to choose a second specialty from the previous four options in case their original specialty is already filled. They may not pick their original specialty again. 20% of those who originally picked cardiology choose oncology as their second choice. If no other field chooses oncology as their second choice, and the hospital boasts 200 medical residents, then what is the total number of residents who named oncology as either their first or second choice, in terms of x ?
A. 8x - 128
B. 8x - 144
C. x2 + 24x - 188
D. x2 - 24x + 188
Answer:D
Medical residents at Lakewood Hospital are choosing their individual specialties. Among them, 40% choose cardiology, 16% choose oncology, 34% choose endocrinology, and the remaining x% choose hematology. Once the doctors pick their first specialty, they are then each asked to choose a second specialty from the previous four options in case their original specialty is already filled. They may not pick their original specialty again. 20% of those who originally picked cardiology choose oncology as their second choice. If no other field chooses oncology as their second choice, and the hospital boasts 200 medical residents, then what is the total number of residents who named oncology as either their first or second choice, in terms of x ?
A. 8x - 128 B. 8x - 144 C. x2 + 24x - 188 D. x2 - 24x + 188
Explanation: D 16% of the 200 medical residents named oncology as their first choice: (200) or (0.16)(200) = 32 residents. 40% of the 200 medical residents named cardiology as their first choice: (200) or (0.4)(200) = 80 residents. Of these 80 residents, 20% chose oncology as their second choice: (80) or (0.2)(80) = 16 residents. The total number of residents who named oncology as either their first or second choice was therefore 32 + 16 = 48 residents. To find the value of x, you need to subtract the percentages given in the question from the total, 100%: 100 - 40 - 16 - 34 = x = 10%. Now, plug x = 10 into the answer choices in order to determine which one matches your target of 48 residents. Only (D) works: x2 - 24x + 188 = 100 - 24(10) + 188 = 100 - 240 + 188 = 48.