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Which one of the following numbers is the greatest positive

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Joined: 24 Apr 2013
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Which one of the following numbers is the greatest positive  [#permalink]

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Updated on: 05 Jul 2019, 03:36
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5% (low)

Question Stats:

89% (00:42) correct 11% (00:45) wrong based on 73 sessions

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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

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?

Source: Nova GMAT
Difficulty Level: 500

Originally posted by basker561 on 12 May 2013, 10:38.
Last edited by SajjadAhmad on 05 Jul 2019, 03:36, edited 2 times in total.
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Re: Which one of the following numbers is the greatest positive  [#permalink]

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12 May 2013, 10:44
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?

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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Arpan
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Re: Which one of the following numbers is the greatest positive  [#permalink]

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10 Jun 2015, 21:30
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.

GMAT assassins aren't born, they're made,
Rich
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Re: Which one of the following numbers is the greatest positive  [#permalink]

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14 Aug 2015, 14:09
thank you
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

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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Joined: 10 Jun 2015
Posts: 110
Re: Which one of the following numbers is the greatest positive  [#permalink]

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14 Aug 2015, 23:17
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

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
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Re: Which one of the following numbers is the greatest positive  [#permalink]

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20 Nov 2019, 11:42
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Re: Which one of the following numbers is the greatest positive   [#permalink] 20 Nov 2019, 11:42
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