If k is an non-negative integer and 15^k is a divisor of 758,325 then 3^k - k^3 =
A. 0
B. 1
C. 37
D. 118
E. 513
A. 0
B. 1
C. 37
D. 118
E. 513
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Source: Beat The GMAT — Problem Solving |
Hi,
The number is 758325. As it ends with 5, it is divisible by 5.
Sum of digits is 30. So, it is divisible by 3 but not by 9.
So 15 can be a divisor but not 15^2 or higher powers.
1 is anyway a divisor of the number. so, k=0 or k=1
If k=1, 3^k - k^3 = = 3-1 =2(not in options)
if k=0, 3^k - k^3 = 1-0 = 1
Hence, B
The number is 758325. As it ends with 5, it is divisible by 5.
Sum of digits is 30. So, it is divisible by 3 but not by 9.
So 15 can be a divisor but not 15^2 or higher powers.
1 is anyway a divisor of the number. so, k=0 or k=1
If k=1, 3^k - k^3 = = 3-1 =2(not in options)
if k=0, 3^k - k^3 = 1-0 = 1
Hence, B
Cheers!
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758325 = (15^0)*758,325MBA.Aspirant wrote:If k is an non-negative integer and 15^k is a divisor of 758,325 then 3^k - k^3 =
A. 0
B. 1
C. 37
D. 118
E. 513
758325 = (15^1)*50555
Hence, possible values of k are 0 and 1
Therefore,
- If k = 0, 3^k - k^3 = 1 - 0 = 1 --> Option B
If k = 1, 3^k - k^3 = 3 - 1 = 2 --> Not an option
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15^k is divisor of 15*50555 = 15*50555If k is an non-negative integer and 15^k is a divisor of 758,325 then 3^k - k^3 =
A. 0
B. 1
C. 37
D. 118
E. 513
Thus k =0 or 1. if k=0, we get 1; if k=1; we get 2
2 is not option
Thus IMO B
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