Ian has three pets: Barnum the cat, Bailey the cat, and Daisy the dog, each of whom is older than $1.$ If the product

Ian has three pets: Barnum the cat, Bailey the cat, and Daisy the dog, each of whom is older than $1.$ If the product of their ages is $x,$ and the product of $x$ and $361$ is $361,361,$ how old is Ian's dog Daisy?

(1) Daisy is not yet $10$ years old.

(2) The sum of the digits of Barnum's age is even.

Answer: A

Source: Veritas Prep

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