Max@Math Revolution wrote:[GMAT math practice question]
If n is a positive integer, is 3^4+3^{n+4} divisible by 5?
1) n is an even integer.
2) 3^8 +3^{n+8} is divisible by 5.
3� + 3^(n+4) = 3� + (3^n)(3�) = 3�(1 + 3^n) =
3�(3^n + 1).
The expression in blue will be divisible by 5 only if (3^n + 1) is a multiple of 5.
Question stem, rephrased:
Is (3^n + 1) a multiple of 5?
Statement 1:
Case 1: n=2, with the result that 3^n + 1 = 3² + 1 = 10.
In this case, the answer to the rephrased question stem is YES.
Case 2: n=4, with the result that 3^n + 1 = 3� + 1 = 82
In this case, the answer to the rephrased question stem is NO.
INSUFFICIENT.
Statement 2:
3� + 3^(n+8) = 3� + (3^n)(3�) = 3�(1 + 3^n) =
3�(3^n + 1).
For the expression in red to be divisible by 5, (3^n + 1) must be a multiple of 5.
Thus, the answer to the rephrased question stem is YES.
SUFFICIENT.
The correct answer is
B.
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