If n = 3^8 - 2^8, which of the following is NOT a factor of n?
A) 97
B) 65
C) 35
D) 13
E) 5
OA: C
From the OG 13 PS 117. The explanation is lengthy - any shorter suggestions?
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I'm not sure how the OG solution looks, but I'd solve this by recognizing that we have a difference of squares here.granite wrote:If n = 3^8 - 2^8, which of the following is NOT a factor of n?
A) 97
B) 65
C) 35
D) 13
E) 5
OA: C
So, 3^8 - 2^8 = (3^4 + 2^4)(3^4 - 2^4)
.....................= (3^4 + 2^4)(3^2 + 2^2)(3^2 - 2^2)
.....................= (3^4 + 2^4)(3^2 + 2^2)(3 + 2)(3 - 2)
.....................= (97)(13)(5)(1)
We can see that C is the correct answer.
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
