If c and d are integers, d is divisible by 30, and cd is divisible by 20, c must be divisible by which of the following?

a) 2
b) 4
c) 5
d) 6
e) 10

To determine which integer c must be divisible by, we need to consider the factors of both 30 and 20.

First, let's look at the factors of 30: 1, 2, 3, 5, 6, 10, 15, and 30.

Since we know d is divisible by 30 and cd is divisible by 20, we can infer that c must also be divisible by 20 for cd to be divisible by 20.

Now let's look at the factors of 20: 1, 2, 4, 5, 10, and 20.

From the factors of 30 and 20, the only common factor is 2. Therefore, c must be divisible by 2.

Hence, the correct answer is a) 2.