Let x be a positive integer such that 7x + 96 is divisible by x. How many values of x are possible?
Let x be a positive integer such that 7x + 96 is divisible by x. How many values of x are possible?
10
11
12
Infinitely many
Solution
Since $7x$ is always divisible by $x$, $7x + 96$ is divisible by $x$ if and only if $x$ divides 96. The number of positive divisors of $96 = 2^5 \times 3$ is $(5+1)(1+1) = 12$. So 12 values of $x$ are possible.