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If x is an integer and 4^x < 100, what is x?

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venkygct
 Post subject: If x is an integer and 4^x < 100, what is x?
 Post Posted: Tue Feb 09, 2010 8:45 pm 
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Students


Posts: 4
If x is an integer and 4^x < 100, what is x?

(1) 4^(x + 1) – 4^(x – 1) > 100
(2) 4^(x + 1) + 4^x > 100
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venkygct
 Post subject: Re: If x is an integer and 4^x < 100, what is x?
 Post Posted: Tue Feb 09, 2010 8:49 pm 
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Students


Posts: 4
please ignore this question. MGMAT explaination is very clear
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Ben Ku
 Post subject: Re: If x is an integer and 4^x < 100, what is x?
 Post Posted: Wed Feb 24, 2010 11:30 pm 
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ManhattanGMAT Staff


Posts: 824
Please ask if there are additional questions about this problem. Thanks!

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Ben Ku
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ManhattanGMAT
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yousuf_azim
 Post subject: Re: If x is an integer and 4^x < 100, what is x?
 Post Posted: Sun Sep 04, 2011 2:12 am 
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Students


Posts: 45
Dears,

What is the ans?

BR

yousuf azim
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mithunsam
 Post subject: Re: If x is an integer and 4^x < 100, what is x?
 Post Posted: Sun Sep 04, 2011 11:19 am 
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Course Students


Posts: 76
Let us try...

From the question, we have 4^x < 100. That means x could be any -ve value or any of 0, 1, 2, or 3.

Statement 1
4^(x + 1) – 4^(x – 1) > 100
4^(x - 1) [4^2 - 1] > 100
15 * 4^(x-1) > 100
For this statement to be true, (x-1) should be > 2. In other words, x should be > 3. But, from the question, we know that x cannot be > 3. Therefore, x = 3. Sufficient.

Statement 2
4^(x + 1) + 4^x > 100
4^x(4 + 1) > 100
5 * 4^x > 100
For this statement to be true, x should be > 3. But, from the question, we know that x cannot be > 3. Therefore, x = 3. Sufficient.

So, it looks like D is the correct Answer.
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jnelson0612
 Post subject: Re: If x is an integer and 4^x < 100, what is x?
 Post Posted: Mon Oct 10, 2011 9:24 pm 
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ManhattanGMAT Staff


Posts: 1618
mithunsam, as always, you are awesome!

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Jamie Nelson
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