BTGmoderatorRO wrote:If k is an non-negative integer and $$^{15^k}$$ is a divisor of 759,325 then $$^{3^k}$$ − $$^{k^3}$$ =
A. 0
B. 1
C. 37
D. 118
E. 513
Since 15 = 3 x 5, we see that both 3 and 5 must evenly divide into 759,325. Since 759,325 ends in "5," we know it is evenly divisible by 5.
Recall the shortcut to determine if a number is evenly divisible by 3: Add the digits of the number; if that sum is evenly divisible by 3, then the number itself is divisible by 3. For 759,325,the sum of the digits is 7 + 5 + 9 + 3 + 2 + 5 = 29; we see that 3 can't evenly divide into 759,325. Thus, k can't be a positive integer, so k = 0.
Thus, 3^0 - 0^3 = 1 - 0 = 1.
Answer: B
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