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

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

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-is-a-positive-integer-is-1-10-n-129176.html
[Reveal] Spoiler: OA

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

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

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

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

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19 Jul 2011, 11:45
D if its (1/10)^(n-1).....
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Kaustubh

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

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19 Jul 2011, 11:54
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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: If n is a positive integer, is ( 1/10 )^n < .01 ? [#permalink]

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

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12 Mar 2016, 06:58
Hi,

I agree that D is the correct answer. But isn't it true that in DS, the two statements never give contradict answers to the question given in the stem? Here statement (1) gives a definite YES while statement (2) gives a definite NO to the question.

Can I expect to see such contradiction in the real test?

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

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12 Mar 2016, 07:11
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Expert's post
truongynhi wrote:
Hi,

I agree that D is the correct answer. But isn't it true that in DS, the two statements never give contradict answers to the question given in the stem? Here statement (1) gives a definite YES while statement (2) gives a definite NO to the question.

Can I expect to see such contradiction in the real test?

Thank you!

Hi,

The actual GMAT will never give you contradictory answers for the two statements..

But having said that this Q too gives you 'YES' in both cases..
You are actually deriving and then reaching what is directly given in I..

1. n > 2

2. $$(\frac{1}{10})^{(n−1)}<.1$$
so $${(\frac{1}{10})^n}/{\frac{1}{10}^{1}}<.1$$..
$${(\frac{1}{10})^n}<.1*{\frac{1}{10}$$
=>$${(\frac{1}{10})^n}<.01$$..
so n>2.. same as Statement I
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Re: If n is a positive integer, is ( 1/10 )^n < .01 ? [#permalink]

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12 Mar 2016, 08:45
OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-is-a-positive-integer-is-1-10-n-129176.html
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Re: If n is a positive integer, is ( 1/10 )^n < .01 ?   [#permalink] 12 Mar 2016, 08:45
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