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At a San Diego Comic-Con, a total of 120 people attended either the DC panel, the Marvel panel, or both. How many people attended only the DC panel?
(1) 60% of the people who attended the DC panel also attended the Marvel panel.
(2) 75% of the people who attended the Marvel panel also attended the DC panel.
(1) 60% of the people who attended the DC panel also attended the Marvel panel.
(2) 75% of the people who attended the Marvel panel also attended the DC panel.
30 Apr 2025, 10:11
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Official Solution:
At a San Diego Comic-Con, a total of 120 people attended either the DC panel, the Marvel panel, or both. How many people attended only the DC panel?
The question asks for the number of people who attended only the DC panel. That is, we are asked to find \(DC - Both\), given that \(DC + Marvel - Both = 120\).
(1) 60% of the people who attended the DC panel also attended the Marvel panel.
This implies that \(0.6* DC = Both\). We cannot solve the system of equations \(DC + Marvel - Both = 120\) and \(0.6 * DC = Both\) to determine the value of \(DC - Both\). Not sufficient.
(2) 75% of the people who attended the Marvel panel also attended the DC panel.
This implies that \(0.75 * Marvel = Both\). We cannot solve the system of equations \(DC + Marvel - Both = 120\) and \(0.75 *Marvel = Both\) to determine the value of \(DC - Both\). Not sufficient.
(1)+(2) From (1), we get that \(DC = \frac{5}{3} * Both\), and from (2), we get that \(Marvel = \frac{4}{3} * Both\). Substituting into \(DC + Marvel - Both = 120\), we get:
\(\frac{5}{3} * Both + \frac{4}{3} * Both - Both = 120\), which gives \(Both = 60\).
Then \(DC = \frac{5}{3} * 60 = 100\), so \(DC - Both = 100 - 60 = 40\). Sufficient.
Answer: C
At a San Diego Comic-Con, a total of 120 people attended either the DC panel, the Marvel panel, or both. How many people attended only the DC panel?
The question asks for the number of people who attended only the DC panel. That is, we are asked to find \(DC - Both\), given that \(DC + Marvel - Both = 120\).
(1) 60% of the people who attended the DC panel also attended the Marvel panel.
This implies that \(0.6* DC = Both\). We cannot solve the system of equations \(DC + Marvel - Both = 120\) and \(0.6 * DC = Both\) to determine the value of \(DC - Both\). Not sufficient.
(2) 75% of the people who attended the Marvel panel also attended the DC panel.
This implies that \(0.75 * Marvel = Both\). We cannot solve the system of equations \(DC + Marvel - Both = 120\) and \(0.75 *Marvel = Both\) to determine the value of \(DC - Both\). Not sufficient.
(1)+(2) From (1), we get that \(DC = \frac{5}{3} * Both\), and from (2), we get that \(Marvel = \frac{4}{3} * Both\). Substituting into \(DC + Marvel - Both = 120\), we get:
\(\frac{5}{3} * Both + \frac{4}{3} * Both - Both = 120\), which gives \(Both = 60\).
Then \(DC = \frac{5}{3} * 60 = 100\), so \(DC - Both = 100 - 60 = 40\). Sufficient.
Answer: C
