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Which one of the following numbers is the greatest positive

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Which one of the following numbers is the greatest positive [#permalink] New post 12 May 2013, 09:38
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Which one of the following numbers is the greatest positive integer x such that 3^x is a factor of 27^5?

(A) 5
(B) 8
(C) 10
(D) 15
(E) 19


[Reveal] Spoiler:
the answer is 15 but all it says is 27^5= (3^3)^5 = 3^15 so 15 is the answer..

Can anyone explain this better? Also am i posting in the right area when i have questions like this?
[Reveal] Spoiler: OA

Last edited by Bunuel on 13 May 2013, 02:51, edited 1 time in total.
Moved to PS forum, renamed the topic and edited the question.
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Re: help please! i don't understand this. [#permalink] New post 12 May 2013, 09:44
basker561 wrote:
I'm new to this site so i'm probably posting in the wrong area. but i have a question that my book gave a horrible explanation on how to solve..

Which one of the following numbers is the greatest positive integer x such that 3^x is a factor of 27^5?

the answer is 15 but all it says is 27^5= (3^3)^5 = 3^15 so 15 is the answer..

Can anyone explain this better? Also am i posting in the right area when i have questions like this?


Hi Basker!

For the above question, as the solution states \(27^5 = 3^15\)
Now \(3^x\) being a factor of\(3^15\) i.e \(3^x\) is to divide \(3^15\) with 0 remainder. If the question simply stated the possible range of x, the answer would be {0...15} The greatest value of the set is 15 and if x > 15, then it wouldn't be a factor anymore, it would become a multiple!

Hope this helps!

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Re: Which one of the following numbers is the greatest positive [#permalink] New post 08 Jun 2015, 13:50
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Re: Which one of the following numbers is the greatest positive [#permalink] New post 10 Jun 2015, 20:30
Expert's post
Hi All,

While this question is a couple of years old, it DOES showcase a particular Exponent-rule 'concept' that you're almost certain to face on the Official GMAT: re-writing a "base" when dealing with exponents...

Any time the 'base value' is a positive integer that is not 1 and is not prime, it has the potential to be rewritten...

Here, we're dealing with 27^5....

27 = (3)(3)(3) = 3^3, so we can re-write that base as...

(3^3)^5

Here, we have a 'power to a power', which means we can multiply the two exponent values....

(3)(5) = 15

So...(3^3)^5 = 3^15

This is just one of several Exponent rules that you need to know for Test Day. While you're not going to be tested on every rule, having the overall knowledge and the ability to manipulate the numbers will help you to pick up the handful of Exponent rule questions you'll face on the GMAT.

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Re: Which one of the following numbers is the greatest positive [#permalink] New post 14 Aug 2015, 13:09
Please tag Divisibility/Factors/Multiples
thank you
basker561 wrote:
Which one of the following numbers is the greatest positive integer x such that 3^x is a factor of 27^5?

(A) 5
(B) 8
(C) 10
(D) 15
(E) 19


[Reveal] Spoiler:
the answer is 15 but all it says is 27^5= (3^3)^5 = 3^15 so 15 is the answer..

Can anyone explain this better? Also am i posting in the right area when i have questions like this?

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Re: Which one of the following numbers is the greatest positive [#permalink] New post 14 Aug 2015, 22:17
basker561 wrote:
Which one of the following numbers is the greatest positive integer x such that 3^x is a factor of 27^5?

(A) 5
(B) 8
(C) 10
(D) 15
(E) 19


[Reveal] Spoiler:
the answer is 15 but all it says is 27^5= (3^3)^5 = 3^15 so 15 is the answer..

Can anyone explain this better? Also am i posting in the right area when i have questions like this?

27 = 3*3*3= 3^3
27^5 =(3^3)^5
=3^15
we have to find the greatest positive integer value for x
when x=15, it divides exactly once and that is the least positive integer value of the quotient
therefore, the correct option is D
Re: Which one of the following numbers is the greatest positive   [#permalink] 14 Aug 2015, 22:17
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