23. Peter wrote a list of all the numbers that could be produced by changing one digit of the number 200. How many of the numbers in Peter's list are prime?
A 0
B 1
C 2
D 3
E 4
Solution: A
If the hundreds or tens digit of 200 is changed, but the units digit is unchanged, the resulting number is, like 200 , a multiple of 10 , and so cannot be prime. So we need only consider the 9 numbers that we can get by changing the units digit. Of these, we can see immediately that $202,204,206$ and 208 are all divisible by 2 and 205 is divisible by 5 . So none of them is prime. This just leaves 201, 203, 207 and 209. Now $201=3 \times 67,203=7 \times 29,207=3 \times 3 \times 23$ and $209=11 \times 19$. So none of them is prime. So none of the numbers in Peter's list are prime.