Bunuel wrote:
Which of the following values times 12 is not a multiple of 64?
I. \(6^6\)
II. \(12^2\)
III. \(30^3\)
A. I only
B. II only
C. III only
D. I and III only
E. I, II and III
Since 12 = 2^2 x 3^1 and since 64 = 2^6, we see that, in order for the product of 12 and a number to be divisible by 64, the number needs to have at least 4 twos. Thus, the product of 12 and either 6^6 or 12^2 will be divisible by 64 but 30^3 will not.
Answer: C
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