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05 Aug 2026, 22:22
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At a one-day music workshop, some registered participants attended the morning session, and some attended the afternoon session. If 40% of the registered participants did not attend the morning session, what percent of the registered participants attended the afternoon session?
(1) Of the registered participants who attended the morning session, \(\frac{1}{4}\) attended the afternoon session.
(2) The number of registered participants who attended the morning session but did not attend the afternoon session was 3 times the number of registered participants who attended neither session.
(1) Of the registered participants who attended the morning session, \(\frac{1}{4}\) attended the afternoon session.
(2) The number of registered participants who attended the morning session but did not attend the afternoon session was 3 times the number of registered participants who attended neither session.
05 Aug 2026, 22:22
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Official Solution:
At a one-day music workshop, some registered participants attended the morning session, and some attended the afternoon session. If 40% of the registered participants did not attend the morning session, what percent of the registered participants attended the afternoon session?
Assume there are 100 registered participants. Since \(40\%\) did not attend the morning session, 40 participants did not attend the morning session and 60 participants attended the morning session. So, \(\{\text{Morning}\} = 60\).
\(\{\text{Total}\} = \{\text{Morning}\} + \{\text{Afternoon}\} - \{\text{Both}\} + \{\text{Neither}\}\)
\(100 = 60 + \{\text{Afternoon}\} - \{\text{Both}\} + \{\text{Neither}\}\)
\(40 = \{\text{Afternoon}\} - \{\text{Both}\} + \{\text{Neither}\}\)
The question asks for \(\{\text{Afternoon}\}\).
(1) Of the registered participants who attended the morning session, 1 out of every 4 attended the afternoon session.
Since 60 participants attended the morning session:
\(\{\text{Both}\} = \frac{1}{4} * 60 = 15\)
So:
\(40 = \{\text{Afternoon}\} - 15 + \{\text{Neither}\}\)
\(55 = \{\text{Afternoon}\} + \{\text{Neither}\}\)
This is not enough to determine \(\{\text{Afternoon}\}\).
Not sufficient.
(2) The number of registered participants who attended the morning session but did not attend the afternoon session was 3 times the number of registered participants who attended neither session.
This tells us:
\(\{\text{Morning}\} - \{\text{Both}\} = 3 * \{\text{Neither}\}\)
\(60 - \{\text{Both}\} = 3 * \{\text{Neither}\}\)
This is not enough to determine \(\{\text{Afternoon}\}\).
Not sufficient.
(1)+(2) From statement (1), \(\{\text{Both}\} = 15\). So, from statement (2):
\(60 - \{\text{Both}\} = 3 * \{\text{Neither}\}\)
\(60 - 15 = 3 * \{\text{Neither}\}\)
\(\{\text{Neither}\} = 15\)
Now use the equation from statement (1):
\(55 = \{\text{Afternoon}\} + \{\text{Neither}\}\)
\(55 = \{\text{Afternoon}\} + 15\)
\(\{\text{Afternoon}\} = 40\)
So \(40\%\) of the registered participants attended the afternoon session.
Sufficient.
Answer: C
At a one-day music workshop, some registered participants attended the morning session, and some attended the afternoon session. If 40% of the registered participants did not attend the morning session, what percent of the registered participants attended the afternoon session?
Assume there are 100 registered participants. Since \(40\%\) did not attend the morning session, 40 participants did not attend the morning session and 60 participants attended the morning session. So, \(\{\text{Morning}\} = 60\).
\(\{\text{Total}\} = \{\text{Morning}\} + \{\text{Afternoon}\} - \{\text{Both}\} + \{\text{Neither}\}\)
\(100 = 60 + \{\text{Afternoon}\} - \{\text{Both}\} + \{\text{Neither}\}\)
\(40 = \{\text{Afternoon}\} - \{\text{Both}\} + \{\text{Neither}\}\)
The question asks for \(\{\text{Afternoon}\}\).
(1) Of the registered participants who attended the morning session, 1 out of every 4 attended the afternoon session.
Since 60 participants attended the morning session:
\(\{\text{Both}\} = \frac{1}{4} * 60 = 15\)
So:
\(40 = \{\text{Afternoon}\} - 15 + \{\text{Neither}\}\)
\(55 = \{\text{Afternoon}\} + \{\text{Neither}\}\)
This is not enough to determine \(\{\text{Afternoon}\}\).
Not sufficient.
(2) The number of registered participants who attended the morning session but did not attend the afternoon session was 3 times the number of registered participants who attended neither session.
This tells us:
\(\{\text{Morning}\} - \{\text{Both}\} = 3 * \{\text{Neither}\}\)
\(60 - \{\text{Both}\} = 3 * \{\text{Neither}\}\)
This is not enough to determine \(\{\text{Afternoon}\}\).
Not sufficient.
(1)+(2) From statement (1), \(\{\text{Both}\} = 15\). So, from statement (2):
\(60 - \{\text{Both}\} = 3 * \{\text{Neither}\}\)
\(60 - 15 = 3 * \{\text{Neither}\}\)
\(\{\text{Neither}\} = 15\)
Now use the equation from statement (1):
\(55 = \{\text{Afternoon}\} + \{\text{Neither}\}\)
\(55 = \{\text{Afternoon}\} + 15\)
\(\{\text{Afternoon}\} = 40\)
So \(40\%\) of the registered participants attended the afternoon session.
Sufficient.
Answer: C
