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A weekend training program had 75 participants, each assigned to exactly one of two tracks: the morning track or the afternoon track, with at least one participant assigned to each track. If 30 of the 75 participants registered for the data-visualization session, what percentage of the afternoon-track participants did not register for the data-visualization session?
(1) Of the morning-track participants, \(\frac{2}{5}\) registered for the data-visualization session.
(2) Among the afternoon-track participants, the number who registered for the data-visualization session was \(\frac{2}{3}\) of the number who did not register for it.
(1) Of the morning-track participants, \(\frac{2}{5}\) registered for the data-visualization session.
(2) Among the afternoon-track participants, the number who registered for the data-visualization session was \(\frac{2}{3}\) of the number who did not register for it.
07 Aug 2026, 10:22
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Official Solution:
A weekend training program had 75 participants, each assigned to exactly one of two tracks: the morning track or the afternoon track, with at least one participant assigned to each track. If 30 of the 75 participants registered for the data-visualization session, what percentage of the afternoon-track participants did not register for the data-visualization session?
Of the 75 participants, 30 registered for the data-visualization session, so the overall fraction who registered was:
\(\frac{30}{75} = \frac{2}{5}\)
The question asks what percentage of the afternoon-track participants did not register.
(1) Of the morning-track participants, \(\frac{2}{5}\) registered for the data-visualization session.
The overall fraction who registered was \(\frac{2}{5}\). Statement (1) says that the fraction of morning-track participants who registered was also \(\frac{2}{5}\).
Since the overall fraction is a weighted average of the morning-track fraction and the afternoon-track fraction, the afternoon-track fraction who registered must also be \(\frac{2}{5}\). So the fraction of afternoon-track participants who did not register was:
\(1 - \frac{2}{5} = \frac{3}{5}\)
Sufficient.
(2) Among the afternoon-track participants, the number who registered for the data-visualization session was \(\frac{2}{3}\) of the number who did not register for it.
So among afternoon-track participants:
registered : did not register \(= 2:3\)
Therefore, the fraction who did not register was:
\(\frac{3}{2 + 3} = \frac{3}{5}\)
Sufficient.
Answer: D
A weekend training program had 75 participants, each assigned to exactly one of two tracks: the morning track or the afternoon track, with at least one participant assigned to each track. If 30 of the 75 participants registered for the data-visualization session, what percentage of the afternoon-track participants did not register for the data-visualization session?
Of the 75 participants, 30 registered for the data-visualization session, so the overall fraction who registered was:
\(\frac{30}{75} = \frac{2}{5}\)
The question asks what percentage of the afternoon-track participants did not register.
(1) Of the morning-track participants, \(\frac{2}{5}\) registered for the data-visualization session.
The overall fraction who registered was \(\frac{2}{5}\). Statement (1) says that the fraction of morning-track participants who registered was also \(\frac{2}{5}\).
Since the overall fraction is a weighted average of the morning-track fraction and the afternoon-track fraction, the afternoon-track fraction who registered must also be \(\frac{2}{5}\). So the fraction of afternoon-track participants who did not register was:
\(1 - \frac{2}{5} = \frac{3}{5}\)
Sufficient.
(2) Among the afternoon-track participants, the number who registered for the data-visualization session was \(\frac{2}{3}\) of the number who did not register for it.
So among afternoon-track participants:
registered : did not register \(= 2:3\)
Therefore, the fraction who did not register was:
\(\frac{3}{2 + 3} = \frac{3}{5}\)
Sufficient.
Answer: D
