Step 1: Count the dots in every visible tile. Tile 1 has 2 dots, tile 2 has 3 dots, tile 4 has 7 dots (3 dots in the top row, 1 dot in the middle, 3 dots in the bottom row), and tile 5 has 11 dots (4 dots in the top row, 3 dots in the middle row, 4 dots in the bottom row). The third tile, marked with "?", is missing.
Step 2: Write the known counts in order. The sequence of dot counts, with the missing term as \(x\), is \(2, 3, x, 7, 11\).
Step 3: Identify the number pattern. Look at the known terms 2, 3, 7 and 11. Every one of these numbers is prime (a number greater than 1 whose only positive factors are 1 and itself), and they appear in increasing order: the 1st prime is 2, the 2nd prime is 3, the 4th prime is 7, and the 5th prime is 11. For the sequence to be the list of primes in order, the 3rd term must be the 3rd prime number.
Step 4: Find the 3rd prime number. The primes in increasing order are \(2, 3, 5, 7, 11, 13, \ldots\). The 3rd prime is 5, and it fits exactly between 3 (the 2nd prime) and 7 (the 4th prime), so \(x = 5\).
Step 5: Match with the given options. A tile with 5 dots arranged as 2 dots on top, 1 in the centre and 2 at the bottom (the standard five pattern, like the "5" face of a die) is option (B). Option (A) shows 4 dots, option (C) shows 6 dots, and option (D) shows 8 dots, none of which equals 5, so only option (B) completes the prime number sequence \(2, 3, 5, 7, 11\).
