BTGmoderatorDC wrote: ↑Tue Jun 02, 2020 7:35 pm
If p is a positive integer, is p^2 divisible by 96?
(1) p is a multiple of 8.
(2) p^2 is a multiple of 12.
OA
C
Source: Manhattan Prep
Let's take each statement one by one.
(1) p is a multiple of 8.
Say p = 8m, where m = a positive integer
Thus, p^2 = 64m^2.
Case 1: Say m = 1, then p^2 = 64. We see that p^2 = 64 is not divisible by 96.
Case 2: Say m = 3, then p^2 = 64*9 = 96*6. We see that p^2 = 96*6 is divisible by 96.
No unique answer. Insufficient.
(2) p^2 is a multiple of 12.
Say p^2 = 12n, where n = a positive integer
Case 1: Say n = 1, then p^2 = 12. We see that p^2 = 12 is not divisible by 96.
Case 2: Say n = 8, then p^2 = 96. We see that p^2 = 96 is divisible by 96.
No unique answer. Insufficient.
(1) and (2) together
From (1), we know that p^2 is divisible by 64 and from (2), we know that p^2 is divisible by 12; thus, we conclude that p^2 is divisible by the LCM of 64 & 12 or p^2 is divisible by 192 (LCM of 64 & 12). Since 192 is divisible by 96, the answer is yes. Sufficient
The correct answer:
C
Hope this helps!
-Jay
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