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At a community art festival, 54 participants signed up for photography, ceramics, or both. If 18 of these participants did not sign up for photography, how many participants signed up for both photography and ceramics?
(1) Of the 54 participants, 12 did not sign up for ceramics.
(2) Of the 54 participants, 42 signed up for ceramics.
(1) Of the 54 participants, 12 did not sign up for ceramics.
(2) Of the 54 participants, 42 signed up for ceramics.
07 Aug 2026, 10:09
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Official Solution:
At a community art festival, 54 participants signed up for photography, ceramics, or both. If 18 of these participants did not sign up for photography, how many participants signed up for both photography and ceramics?
Since all 54 participants signed up for photography, ceramics, or both, any participant who did not sign up for photography must have signed up for ceramics only.
So the 18 participants who did not sign up for photography signed up for ceramics only.
The question asks for the number of participants who signed up for both photography and ceramics.
(1) Of the 54 participants, 12 did not sign up for ceramics.
Since all participants signed up for at least one of the two activities, these 12 participants signed up for photography only.
Therefore:
Both \(=\) Total \(-\) Ceramics only \(-\) Photography only \(= 54 - 18 - 12 = 24\)
Sufficient.
(2) Of the 54 participants, 42 signed up for ceramics.
Of these 42 participants, 18 signed up for ceramics only.
Therefore:
Both \(= 42 - 18 = 24\)
Sufficient.
Answer: D
At a community art festival, 54 participants signed up for photography, ceramics, or both. If 18 of these participants did not sign up for photography, how many participants signed up for both photography and ceramics?
Since all 54 participants signed up for photography, ceramics, or both, any participant who did not sign up for photography must have signed up for ceramics only.
So the 18 participants who did not sign up for photography signed up for ceramics only.
The question asks for the number of participants who signed up for both photography and ceramics.
(1) Of the 54 participants, 12 did not sign up for ceramics.
Since all participants signed up for at least one of the two activities, these 12 participants signed up for photography only.
Therefore:
Both \(=\) Total \(-\) Ceramics only \(-\) Photography only \(= 54 - 18 - 12 = 24\)
Sufficient.
(2) Of the 54 participants, 42 signed up for ceramics.
Of these 42 participants, 18 signed up for ceramics only.
Therefore:
Both \(= 42 - 18 = 24\)
Sufficient.
Answer: D
