A1. Let $n$ be a two-digit natural number. If we add the next three consecutive natural numbers following $n$, we get a two-digit number with the same digits as $n$. How many positive divisors does the number $n$ have?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
A1. Let $n=\overline{a b}=10 a+b$. Then $(n+1)+(n+2)+(n+3)=\overline{b a}=10 b+a$. It follows that $10 b+a=3 n+6=30 a+3 b+6$ or $29 a=7 b-6$. Since $a$ and $b$ are digits, $29 a \leq 7 \cdot 9-6=57$, from which it follows that $a=1$. Therefore, $7 b=35$ or $b=5$ and thus $n=15$. The number $n$ has 4 positive divisors, which are $1,3,5$ and 15.