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02 Apr 2021, 03:30
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
71% (02:05) correct
29%
(02:19)
wrong
based on 275
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\(k = 2^n + 7\), where n is an integer greater than 1. If k is divisible by 9, which of the following MUST be divisible by 9?
A. \(2^n - 8\)
B. \(2^n - 2\)
C. \(2^n\)
D. \(2^n + 4\)
E. \(2^n + 5\)
A. \(2^n - 8\)
B. \(2^n - 2\)
C. \(2^n\)
D. \(2^n + 4\)
E. \(2^n + 5\)
05 Apr 2021, 10:21
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Bunuel
N>1, If we know that (2^n+7)/9 = integer we also know that (2^n+7) + 9 = 2^n + 16, also is divisible by 9 , or (2^n+7) - 9 = 2^n - 2.
Examples: 18/9 = 2 , (18+9)/9 = 3, or (18-9)/9 = 1.
B is the answer.
General Discussion
02 Apr 2021, 03:37
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Bunuel
A quick Approach:
\(k = 2^n + 7\) and k is divisible by 9
An easy value of n for which k is divisible by 9 is n=1
@n = 1, \(k = 2^1 + 7 = 9\) i.e. Divisible by 9
Now, let's check options
A. \(2^n - 8 = 2^1-8 = -6\) NO
B. \(2^n - 2 = 2^1 - 2 = 0\) YES
C. \(2^n = 2^1 = 2\) NO
D. \(2^n + 4 = 2^1 + 4 = 6\) NO
E. \(2^n + 5 = 2^1 + 5 = 7\) NO
ANswer: Option B
