7. A certain two-digit number is a multiple of 2, adding 1 makes it a multiple of 3, adding 2 makes it a multiple of 4, and adding 3 makes it a multiple of 5. What is this two-digit number? $\qquad$ .
【Key Points】Number Theory, Remainder Problems
【Difficulty】Recognizable
【Answer】 62
【Analysis】From the question, we know that this number is a multiple of 2, and when divided by $3, 4, 5$, it leaves a remainder of 2. The smallest such number is 2. Since this number is a two-digit number, $2+[3, 4, 5]=62$.