1. Decode the Main Clues
Before looking at the statements, let's figure out what we already know from the prompt:
Total = 54: Everyone signed up for Photography, Ceramics, or both. This means 0 people signed up for neither.
18 did not take Photography: Since nobody is taking neither class, these 18 people must be taking Ceramics only.
So, our starting board looks like this:
Ceramics only = 18
Photography only = ?
Both = ?
Total = 54
Now, let's look at the statements to see if we can find the "Both" group.
2. Check Statement (1)
"Of the 54 participants, 12 did not sign up for ceramics."
If they didn't sign up for ceramics, they must be taking Photography only.
Now we have the missing pieces:
Photography only (12) + Ceramics only (18) + Both = 54 total.
30 + Both = 54, which means Both = 24.
Statement (1) is sufficient.
3. Check Statement (2)
"Of the 54 participants, 42 signed up for ceramics."
The "Total Ceramics" group is made up of two types of people: those taking Ceramics only and those taking Both.
We already know 18 people are taking Ceramics only.
Ceramics only (18) + Both = Total Ceramics (42).
18 + Both = 42, which means Both = 24.
Statement (2) is sufficient.
Since we can solve the problem using either clue completely on its own, each statement alone is enough to get the answer!