shasadou wrote:
If n is the product of the first 10 prime numbers, which of the following is an integer?
I. \(\frac{n}{7}\)
II. \(\frac{n}{4}\)
III. \(\frac{n}{143}\)
A. I only
B. I and II only
C. I and III only
D. III only
E. I, II, and III
Looking at each Roman numeral, we see that II is n/2^2 and III is n/(11 x 13).
Since 7 is included in the product of the first 10 prime numbers as well as 11 x 13, while 2^2 is not, only 7 and 143 will divide n.
Answer: C
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