Bunuel wrote:
If P represents the product of the first 15 positive integers, then P is not a multiple of:
A. 99
B. 84
C. 72
D. 65
E. 57
Let’s look at the answer choices.
Since 99 = 9 x 11, both of which are included in the product of the first 15 integers, we see that P is a multiple of 99.
Similarly, since 84 = 42 x 2 = 21 x 4 = 7 x 3 x 4, we see that P is a multiple of 84.
Since 72 = 36 x 2 = 6 x 3 x 2 x 2 = 6 x 3 x 4, we see that P is a multiple of 72.
Since 65 = 5 x 13, we see that P is a multiple of 65.
Since 57 = 19 x 3, and since the product of the first 15 integers does not have a prime factor of 19, P cannot be a multiple of 57.
Answer: E
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90% (00:44) correct 
