sanaa.rizwan wrote:if n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is
a.6
b.12
c.24
d.36
e.48
n² must be divisible by 72.
Since n² is the square of an integer, the value of n² must be a perfect square: 1, 4, 9, 16, 25, 36, 64, 81, 100, 121, 144...
In the list above, the smallest value divisible by 72 is 144.
If n² = 144, then n = 12.
This is the MINIMUM value of n.
Since n=12 is not divisible by 24, 36, or 48, eliminate C, D and E.
Since n cannot be any smaller than 12, it must be divisible by answer choice
B (12).
The correct answer is
B.
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