GIVEN: n² is a multiple of 24
24 = (2)(2)(2)(3)
So, n² must have at least three 2's and one 3 in its prime factorization.
What does this tell us about n?
Since n² = (n)(n), we can conclude that n must have at least two 2's and one 3 in its prime factorization.
GIVEN: n² is a multiple of 108
108 = (2)(2)(3)(3)(3)
So, n² must have at least two 2's and three 3's in its prime factorization.
What does this tell us about n?
Since n² = (n)(n), we can conclude that n must have at least one 2 and two 3's in its prime factorization.
So, when we combine both pieces of information, we can see that n must have at least two 2's and two 3's in its prime factorization.
In other words, n = (2)(2)(3)(3)(k), where k is some positive integer
Now let's check the answer choices...
A. 12 = (2)(2)(3)
Since n = (2)(2)(3)(3)(k), we can see that n IS divisible by 12
B. 24 = (2)(2)(2)(3)
Since n = (2)(2)(3)(3)(k), we can see that n need NOT be divisible by 24
C. 36 = (2)(2)(3)(3)
Since n = (2)(2)(3)(3)(k), we can see that n IS divisible by 36
D. 72 = (2)(2)(2)(2)(3)
Since n = (2)(2)(3)(3)(k), we can see that n need NOT be divisible by 72
Answer: A,C
Cheers,
Brent
_________________
Brent Hanneson – Creator of greenlighttestprep.com
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48% (02:15) correct
