If n is a positive integer, is ( 1/10 )^n < .01 ?

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If n is a positive integer, is ( 1/10 )^n < .01 ? [#permalink]

19 Jul 2011, 08:26

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If n is a positive integer, is (\frac{1}{10})^n < .01?

1. n > 2
2. (\frac{1}{10})^(n-1) < .1

[Reveal] Spoiler: OA

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Re: og.166 (exponent) [#permalink]

19 Jul 2011, 08:29

In statement 2, why isn't the [m] feature putting the entire (n-1) as an exponent?
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Re: og.166 (exponent) [#permalink]

19 Jul 2011, 08:42

Please correct me if I am wrong.

The question is asking: 100 < 10^n?

(1) Clearly sufficient.
(2) Is where I get stuck.

(1/10)^(n-1) < 1/10
1^(n-1)/10^(n-1) < 1/10
1^n . 1^-1 / 10^n . 10^-1 < 1/10
(1^n/10^n)(10) < 1/10

Hold on....

Since n > 0
(1^n/10^n)(10) < 1/10
10/10^n < 1/10 <<<<<< for this to remain true, N > 2
N=3 works for the above.

n => 3 also works for the original question.

hmmm.....does this sound right guys?
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Re: og.166 (exponent) [#permalink]

19 Jul 2011, 11:37

386390 wrote:

If n is a positive integer, is (\frac{1}{10})^n < .01?

1. n > 2
2. (\frac{1}{10})^(n-1) < .1

from the question (1/10)^n < 0.01 ;
it can be written as (10)^(-n) < (10)^(-2)
hence it will be sufficient to check if n > 2

from state-1: it clearly gives the criteria; hence sufficient
from state-2: (1/10)^(n-1) < 0.1
Or 10^(1-n) < 10^(-1)
or n-1>1
or n>2

hence sufficient.

D

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Re: og.166 (exponent) [#permalink]

19 Jul 2011, 11:45

D if its (1/10)^(n-1).....
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Re: og.166 (exponent) [#permalink]

19 Jul 2011, 11:54

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Answer is D.

Data Sufficiency Question Type: YES or NO. If either of the statements give us the answer "yes" or "no" then the statements will be sufficient.

Statement 1: n>2. if n = 2.1, you can answer the question, in this case, the answer is "YES" therefore sufficient.

Statement 2: Rearrange the equation:
10* \frac{1}{10} * (n-1) < 0.1 * 10 ---> Multiply both sides by 10.

n-1 < 1

n < 2 ---> If n = 1, then the answer is NO but it still answers the question. Therefore this statement is SUFFICIENT.

Hence D.
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Re: og.166 (exponent) [#permalink]

22 Jul 2011, 21:37

Here is a video explanation to this problem:

http://www.gmatquantum.com/list-of-vide ... ds166.html

Dabral
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Re: og.166 (exponent) [#permalink] 22 Jul 2011, 21:37

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If n is a positive integer, is ( 1/10 )^n < .01 ?

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If n is a positive integer, is ( 1/10 )^n < .01 ?

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