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The largest power of 3 that is a factor of

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

61% (00:50) correct 38% (00:44) wrong based on 18 sessions
Quantity A
Quantity B
The largest power of 3
that is a factor of \(5*3^2 + 3^2*2\)
The largest power of 3
that 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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Re: The largest power of 3 that is a factor of [#permalink] New post 19 Sep 2018, 08:58
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Carcass wrote:
Quantity A
Quantity B
The largest power of 3
that is a factor of \(5*3^2 + 3^2*2\)
The largest power of 3
that 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
Answer: B

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