2. Given that $A$ is a two-digit number, the remainder when $A^{2}$ is divided by 15 is 1, then the number of $A$ that satisfies the condition is $($ )



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Answer: 24
Explanation: $A^{2} \div 15$ leaves a remainder of 1, then by enumerating $A \div 14$ with remainders 0 and 14, we get $A \div 15$ leaves remainders of $1, 4, 11, 14$. For a remainder of 1, there are $16, 31, 46, 61, 76, 91$, a total of 6; for a remainder of 4, there are also 6, for a remainder of 11, there are $11, 26, 41, 56, 71, 86$, a total of 6, and for a remainder of 14, there are also 6, making a total of $6 \times 4 = 24$ (numbers).