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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
75% (01:57) correct
25%
(02:00)
wrong
based on 63
sessions
History
Date
Time
Result
Not Attempted Yet
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.
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
(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.
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
10 May 2025, 15:15
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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
General Discussion
05 May 2025, 23:48
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Bunuel
The number of people who attended
Only DC = d
Only Marvell = m
Both = b
d + m+ b = 120
Statement 1
(1) 60% of the people who attended the DC panel also attended the Marvel panel.
\(\frac{6}{10}(d + b) = b\)
From this statement we will get a multiplicative relationship between d and b. However, to solve the equation we also need m. Hence, from Statement 1, we cannot find the value of d, b and m. Eliminate A, and D.
Statement 2
(2) 75% of the people who attended the Marvel panel also attended the DC panel.
\(\frac{3}{4}(m + b) = b\)
From this statement we will get a multiplicative relationship between m and b. However, to solve the equation we also need d. Hence, from Statement 2, we cannot find the value of d, b and m. Eliminate B.
Combined
Combined we have a relationship between d, b, and m. Hence, the equation d + m+ b = 120, has only one unknown which can be solved. Once we have one value, the others can also be derived throught the multiplicative relationship established in Statement 1, and Statement 2.
Option C
