BTGmoderatorDC wrote:If a = 15! + 13, which of the following are factors of a?
I. 13
II. 14
III. 26
A. I only
B. I and II only
C. I and III only
D. I, II, and III only
E. None of the above
MULTIPLE OF X + MULTIPLE OF X = MULTIPLE OF X.
MULTIPLE OF X + NON-MULTIPLE OF X = NON-MULTIPLE OF X.
Since the prime-factorization of 15! includes 13, we get:
a = 15! + 13 = multiple of 13 + multiple of 13 = multiple of 13.
Since
a is a multiple of 13, option I is a factor of
a.
Eliminate any answer that does not include option I.
Eliminate E.
Since the prime-factorization of 15! includes 2*7=14, we get:
a = 15! + 13 = multiple of 14 + non-multiple of 14 = non-multiple of 14.
Since
a is not a multiple of 14, option II is a NOT factor of
a.
Eliminate any remaining answer that includes option II.
Eliminate B and D.
Since the prime-factorization of 15! includes 2*13=26, we get:
a = 15! + 13 = multiple of 26 + non-multiple of 26 = non-multiple of 26.
Since
a is not a multiple of 26, option III is a NOT factor of
a.
Eliminate any remaining answer that includes option III.
Eliminate C.
The correct answer is
A.
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