### Instruction: Let   $$x = 64 + 96 + 128 + 160 + 288 + 352 + 3232.$$ Which of the following statements are true?

A. $x$ is a multiple of $4$.
B. $x$ is a multiple of $8$.
C. $x$ is a multiple of $16$.
D. $x$ is a multiple of $32$.

Answer as a list of letters in alphabetical order, separated by commas.  For example, if you think A and C are the true statements, then answer ``A,C" (without the quote marks).### Response: So we have $x = 64 + 96 + 128 + 160 + 288 + 352 + 3232$.
64, 96, 128, 160, 288, and 352 are all multiples of 32.
3232 is also a multiple of 32 since $3232 = 32*101$.
So $x$ is a multiple of 32 since $x = 32(2+3+4+5+9+11+101)$.
And since $x$ is a multiple of 32, $x$ is also a multiple of 16, 8, and 4.
So all four statements are true.