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# Is 3^x greater than 100?

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Math Expert
Joined: 02 Sep 2009
Posts: 58335
Is 3^x greater than 100?  [#permalink]

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23 Aug 2016, 02:45
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Difficulty:

25% (medium)

Question Stats:

76% (01:06) correct 24% (01:28) wrong based on 73 sessions

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Is 3^x greater than 100?

(1) 9x = 36
(2) 1/3^x > 0.01

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Intern
Joined: 18 Aug 2013
Posts: 12
Re: Is 3^x greater than 100?  [#permalink]

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23 Aug 2016, 04:54
(1) 9x = 36 => x = 4

3^4 = 81 is NOT greater than 100 => Sufficient

(2) (1/3^x) > 0.01

(1/3^x) > (1/100) => 3^x < 100 => Sufficient

--> Option D
CEO
Joined: 12 Sep 2015
Posts: 3990
Re: Is 3^x greater than 100?  [#permalink]

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24 Sep 2018, 13:43
1
Top Contributor
Bunuel wrote:
Is 3^x greater than 100?

(1) 9x = 36
(2) 1/(3^x) > 0.01

Target question: Is 3^x greater than 100?

Statement 1: 9x = 36
This tells us that x = 4
Once we know the value of x, we can definitely determine whether 3^x is greater than 100
Are we going to waste any time evaluating 3^4? No!
Since we COULD answer the target question with certainty, statement 1 is SUFFICIENT

ASIDE: Spoiler alert: If x = 4, then 3^x = 3^4 = 81. So, the answer to the target question is NO, 3^x is NOT greater than 100

Statement 2: 1/(3^x) > 0.01
Since 3^x is POSITIVE for all values of x, we can safely multiply both sides of the inequality by 3^x
When we do so, we get: 1 > (0.01)(3^x)
Now multiply both sides by 100 to get: 100 > 3^x
o, the answer to the target question is NO, 3^x is NOT greater than 100
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

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Re: Is 3^x greater than 100?   [#permalink] 24 Sep 2018, 13:43
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