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Math Expert V
Joined: 02 Sep 2009
Posts: 56304
If k is a non-negative integer and 15^k is a divisor of 759,325 then  [#permalink]

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4
8 00:00

Difficulty:   45% (medium)

Question Stats: 67% (01:59) correct 33% (02:26) wrong based on 180 sessions

### HideShow timer Statistics 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.

_________________
Retired Moderator Joined: 06 Jul 2014
Posts: 1224
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40 If k is a non-negative integer and 15^k is a divisor of 759,325 then  [#permalink]

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2
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
_________________

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.
Retired Moderator B
Status: On a mountain of skulls, in the castle of pain, I sit on a throne of blood.
Joined: 30 Jul 2013
Posts: 304
Re: If k is a non-negative integer and 15^k is a divisor of 759,325 then  [#permalink]

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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

Manager  Joined: 19 Mar 2015
Posts: 62
Re: If k is a non-negative integer and 15^k is a divisor of 759,325 then  [#permalink]

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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.
Manager  B
Joined: 26 Dec 2012
Posts: 145
Location: United States
Concentration: Technology, Social Entrepreneurship
WE: Information Technology (Computer Software)
Re: If k is a non-negative integer and 15^k is a divisor of 759,325 then  [#permalink]

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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

Thanks,
Math Expert V
Joined: 02 Sep 2009
Posts: 56304
Re: If k is a non-negative integer and 15^k is a divisor of 759,325 then  [#permalink]

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1
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.

MAGOOSH OFFICIAL SOLUTION:
Attachment: 15kdivisor759325_text.PNG [ 24.1 KiB | Viewed 2649 times ]

_________________
Manager  Joined: 06 Dec 2014
Posts: 67
GMAT 1: 670 Q48 V34 Re: If k is a non-negative integer and 15^k is a divisor of 759,325 then  [#permalink]

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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 Intern  B
Joined: 28 Sep 2014
Posts: 22
Schools: HBS '19
Re: If k is a non-negative integer and 15^k is a divisor of 759,325 then  [#permalink]

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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
Non-Human User Joined: 09 Sep 2013
Posts: 11719
Re: If k is a non-negative integer and 15^k is a divisor of 759,325 then  [#permalink]

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_________________ Re: If k is a non-negative integer and 15^k is a divisor of 759,325 then   [#permalink] 23 Aug 2018, 22:16
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