Question 76
Alessandro, Daniele and Manuela discuss a two-digit natural number $n$. Each makes two statements, but since they are all rather weak at mathematics, each makes one true and one false statement.
Alessandro says: “$n$ is even. It is also a multiple of 3.”
Daniele replies: “Yes, $n$ is a multiple of 3. Also, its units digit is 5.”
Finally, Manuela says: “$n$ is a multiple of 5. The sum of its digits is 12.”
How many values can $n$ have?
(A) No such $n$ exists.
(B) 1
(C) 2
(D) 3
(E) 4
Alessandro says: “$n$ is even. It is also a multiple of 3.”
Daniele replies: “Yes, $n$ is a multiple of 3. Also, its units digit is 5.”
Finally, Manuela says: “$n$ is a multiple of 5. The sum of its digits is 12.”
How many values can $n$ have?
(A) No such $n$ exists.
(B) 1
(C) 2
(D) 3
(E) 4