In the sequence of tiles shown below, the missing tile indicated by the question mark should be:
Show Hint
Hint:
Count the dots in the tiles you can already see (2, 3, then a gap, then 7, 11) and check whether these numbers share a special property, such as all being prime, rather than following a simple addition pattern.
Step 1: List the totals you can already see.
Counting the dots tile by tile gives 2, 3, a missing value, 7, 11.
Step 2: Test whether these follow simple addition or multiplication.
The gaps between the visible numbers are not constant: from 2 to 3 is a jump of 1, but from 7 to 11 is a jump of 4, so there is no single fixed common difference. It is not a doubling pattern either, since 3 times 2 equals 6, not 7. Both a constant-difference rule and a constant-ratio rule fail here.
Step 3: Check each visible number for prime factors instead.
2 has no factors besides 1 and itself. 3 has no factors besides 1 and itself. 7 has no factors besides 1 and itself. 11 has no factors besides 1 and itself. Every visible number in the row is prime, and none of them is composite.
Step 4: Find the prime that belongs between 3 and 7.
Listing primes in order gives $2, 3, 5, 7, 11, 13, \ldots$. The only prime sitting between 3 and 7 in this list is 5, so the missing tile must carry 5 dots.
Step 5: Confirm against the answer choices.
Checking each option for primality: 4 is composite (2 times 2), 5 is prime, 6 is composite (2 times 3), 8 is composite (2 times 2 times 2). Only option (B) is prime and matches the required value.
Final Answer:
The sequence of dot counts is exactly the list of prime numbers 2, 3, 5, 7, 11, so the missing tile has 5 dots.
\[ \boxed{\text{Option (B)}} \]
