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If k is a non-negative integer and 15^k is a divisor of 759,325 then

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If k is a non-negative integer and 15^k is a divisor of 759,325 then  [#permalink]

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New post 02 Apr 2015, 05:20
3
7
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

72% (01:32) correct 28% (02:21) wrong based on 155 sessions

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If k is a non-negative integer and 15^k is a divisor of 759,325 then  [#permalink]

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New post Updated on: 02 Apr 2015, 07:51
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2
Bunuel wrote:
If k is a 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


Kudos for a correct solution.


At first we should understand whether 759325 divisible by 15.
15 is equal to 3 * 5 so 759325 should be divisible on these integers
759325 is divisible by 5 because of last digit 5
but not divisible by 3 because sum of its digits doesn't divisible by 3: 7 + 5 + 9 + 3 + 2 + 5 = 31 and 31 doesn't divisible by 3

so 759325 can be divisible by 15^k only if k = 0 and 15^k = 1
so 3^k - k^3 = 1 - 0 = 1
answer is B
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Originally posted by Harley1980 on 02 Apr 2015, 05:31.
Last edited by Harley1980 on 02 Apr 2015, 07:51, edited 1 time in total.
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Re: If k is a non-negative integer and 15^k is a divisor of 759,325 then  [#permalink]

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New post 02 Apr 2015, 05:37
Bunuel wrote:
If k is a 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


Kudos for a correct solution.


7+5+9+3+2+5=31=4
Therefore, 759,325 is not divisble by 15.
Hence, k=0

3^k - k^3 =1-0=1

Answer: B
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Re: If k is a non-negative integer and 15^k is a divisor of 759,325 then  [#permalink]

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New post 02 Apr 2015, 06:03
Good question. I thought the question was incorrect, because I didn't see any way how 15^k could be a divisor of 759,325.
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Re: If k is a non-negative integer and 15^k is a divisor of 759,325 then  [#permalink]

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New post 02 Apr 2015, 12:00
759325 is divisible by 5 & 25 but not by 3; so 759325 to be divisible by 15^k; it should be divisible by 3 as well, but its not. so k=0
put this value to 3^k-k^3=3^0-0^k=1-0=1

Hence answer is B

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Re: If k is a non-negative integer and 15^k is a divisor of 759,325 then  [#permalink]

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New post 06 Apr 2015, 06:52
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Re: If k is a non-negative integer and 15^k is a divisor of 759,325 then  [#permalink]

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New post 13 Apr 2015, 02:10
759325 = 5*5*30373

that means for 759325 to be a multiple of 15^k, then

(5*5*30373)/(3^k*5^k) has to be an integer.

That means k can be maximum 2(As we have 5^2 in numerator).... So try k=0,1,and 2 in 3^k-k^3... The only option that matches is 1. B answer.


Is this method correct or just a fluke???I'm not too sure...
Requesting some help.
Thanks :)
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Re: If k is a non-negative integer and 15^k is a divisor of 759,325 then  [#permalink]

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New post 13 Apr 2015, 02:21
Bunuel wrote:
If k is a 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


Kudos for a correct solution.



This is a PS question so everything that divides the number 759325 will hold true for give equation.

As we know 1 divides any number. Thus 15^0=1 therefore k=0

3^k-k^3
=3^0-0^3
=1-0 =1
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Re: If k is a non-negative integer and 15^k is a divisor of 759,325 then  [#permalink]

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