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# The largest power of 3 that is a factor of

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Joined: 18 Apr 2015
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Kudos [?]: 1343 [0], given: 6316

The largest power of 3 that is a factor of [#permalink]  18 Sep 2018, 10:28
Expert's post
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Question Stats:

58% (00:46) correct 41% (00:56) wrong based on 31 sessions

 Quantity A Quantity B The largest power of 3that is a factor of $$5*3^2 + 3^2*2$$ The largest power of 3that is a factor of $$3*2 + 7*3$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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GRE Instructor
Joined: 10 Apr 2015
Posts: 1981
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Kudos [?]: 1803 [1] , given: 9

Re: The largest power of 3 that is a factor of [#permalink]  19 Sep 2018, 08:58
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Expert's post
Carcass wrote:
 Quantity A Quantity B The largest power of 3that is a factor of $$5*3^2 + 3^2*2$$ The largest power of 3that is a factor of $$3*2 + 7*3$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

QUANTITY A: (5)(3²) + (3²)(2)
Factor out the 3² to get: 3²(5 + 2)
Evaluate to get: 3²(7)
We can see that is the largest power of 3 that is a factor of (5)(3²) + (3²)(2)

QUANTITY B: (3)(2) + (7)(3)
Factor out the 3 to get: 3(2 + 7)
Evaluate to get: 3(9)
Evaluate to get: 27
Rewrite as: 3³
We can see that is the largest power of 3 that is a factor of (3)(2) + (7)(3)

3³ is greater than 3²

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

Re: The largest power of 3 that is a factor of   [#permalink] 19 Sep 2018, 08:58
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