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Is 3^(x+2)/9 >1 ? (1) 9^x > 1 (2) x > 0

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metallicafan
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Is 3^(x+2)/9 >1 ? (1) 9^x > 1 (2) x > 0 [#permalink] New post   26 Jun 2012, 12:25
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Is \(\frac{3^{(x+2)}}{9} >1\) ?


(1) \(9^x > 1\)

(2) \(x > 0\)


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I solved it. For example, in clue (1), I did this:
\(9^x > 1\)
\(9^x > 9^0\)
Then, \(x > 0\), SUFFICIENT.

However, I would like to know whether there is a more conceptual approach. Specifically, whether in which cases x can be positive or negative.

Source: https://www.gmathacks.com
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D
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Bunuel
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Re: Is 3^(x+2)/9 >1 ? (1) 9^x > 1 (2) x > 0 [#permalink] New post   26 Jun 2012, 12:35
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Is 3^(x+2)/9 >1 ?

Is \(\frac{3^{x+2}}{9} >1\)? --> is \(\frac{3^{x+2}}{3^2} >1\)? --> is \(3^x>1\)? --> is \(x>0\)?

Or: is \(\frac{3^{x+2}}{9} >1\)? --> is \(3^{x+2}>3^2\)? --> is \(x+2>2\)? --> is \(x>0\)?

(1) 9^x > 1 --> \(x>0\). Sufficient.
(2) x > 0. Directly answers the question. Sufficient.

Answer: D.

Hope it's clear.
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Re: Is 3^(x+2)/9 >1 ? (1) 9^x > 1 (2) x > 0 [#permalink] New post   26 Jun 2012, 12:49
I am getting A as the answer.

Question is 3^x+2/9 = 3^x*9/9 = 3^x

From Option A
9^x>1 means 3^2x>1..
(3^x)2>1 . so 3^x has to be positive as it can never be negative for positive values or negative values of x.
so 3^x is always greater than 1
So we can answer this question.
But with statement B.. if x>0 then it can be 0.00001 also. so 3^0.0001 is less than 1 and with higher value like 2 we get value greater than 1. so not possible to answer with B. So answer is A


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Re: Is 3^(x+2)/9 >1 ? (1) 9^x > 1 (2) x > 0 [#permalink] New post   26 Jun 2012, 12:55
Expert Reply
akalyan wrote:
I am getting A as the answer.

Question is 3^x+2/9 = 3^x*9/9 = 3^x

From Option A
9^x>1 means 3^2x>1..
(3^x)2>1 . so 3^x has to be positive as it can never be negative for positive values or negative values of x.
so 3^x is always greater than 1
So we can answer this question.
But with statement B.. if x>0 then it can be 0.00001 also. so 3^0.0001 is less than 1 and with higher value like 2 we get value greater than 1. so not possible to answer with B. So answer is A


With


The red part is not correct: \(3^{0.0001}\approx{1.000109867}>1\).

Generally \(3^x>1\) to hold true \(x\) must be more than zero, hence \(3^x>1\) simply means that \(x>0\).

For more on number theory and exponents check: math-number-theory-88376.html

DS questions on exponents: search.php?search_id=tag&tag_id=39
PS questions on exponents: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

Hope it helps.
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Re: Is 3^(x+2)/9 >1 ? (1) 9^x > 1 (2) x > 0 [#permalink] New post   26 Jun 2012, 15:53
akalyan wrote:
I am getting A as the answer.

Question is 3^x+2/9 = 3^x*9/9 = 3^x

From Option A
9^x>1 means 3^2x>1..
(3^x)2>1 . so 3^x has to be positive as it can never be negative for positive values or negative values of x.
so 3^x is always greater than 1
So we can answer this question.
But with statement B.. if x>0 then it can be 0.00001 also. so 3^0.0001 is less than 1 and with higher value like 2 we get value greater than 1. so not possible to answer with B. So answer is A


With

hey akalyan try taking log with base 3 to the question and you will easily reach at Is x>0 ?

Note everywhere in this answer wherever I write log it means log with base 3

Question is
3^(x+2)/9>1
Taking log both sides we get
log(3^(x+2)/9) > log 1
---> log(3^x+2) - log9>0
---->x+2 -2 >0
----> x>0
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Re: Is 3^(x+2)/9 >1 ? (1) 9^x > 1 (2) x > 0 [#permalink] New post   26 Jun 2012, 21:54
Thanks for correcting me bunuel.

Yes taking log is also good way to solve this problem manimani.
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Re: Is 3^(x+2)/9 >1 ? (1) 9^x > 1 (2) x > 0 [#permalink] New post   27 Jun 2012, 08:44
Hi Bunuel,

I would like to know whether you have a link with theory about exponents with inequalities.

For example, we cannot say inmediately that because \(a^x > a^y\) , then \(x > y\), right?

Because \(a\) could be a fraction.

Please, if you have theory about that specific point, please post it.
Thanks!
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Re: Is 3^(x+2)/9 >1 ? (1) 9^x > 1 (2) x > 0 [#permalink] New post   22 Oct 2013, 05:45
This was so cool you guys! I got it wrong and at first I didn't understand any of the explanations, but once I followed them and wrote them down, I got it!! Thanks! ....As you can probably guess, I'm new here. I promise not to be so annoying, once I get the hang of this.... :(
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Re: Is 3^(x+2)/9 >1 ? (1) 9^x > 1 (2) x > 0 [#permalink] New post   13 Nov 2018, 11:49
Is the answer A or B ?


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Re: Is 3^(x+2)/9 >1 ? (1) 9^x > 1 (2) x > 0 [#permalink] New post   13 Nov 2018, 11:53
Expert Reply
aepmk wrote:
Is the answer A or B ?


Sent from my iPhone using GMAT Club Forum


You can check the OA of a question under the spoiler in the first post. The OA for this question is D. Solutions are given above.
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Re: Is 3^(x+2)/9 >1 ? (1) 9^x > 1 (2) x > 0 [#permalink]
13 Nov 2018, 11:53
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Bunuel
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