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If n is an integer, what is the least value of n such that 1/3^n < 0.0

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Bunuel
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If n is an integer, what is the least value of n such that 1/3^n < 0.0 [#permalink] New post   Updated on: 06 Jul 2019, 23:29
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If n is an integer, what is the least value of n such that \(\frac{1}{3^n} < 0.01\) ?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

Source: Nova GMAT
Difficulty Level: 600
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D

Originally posted by Bunuel on 24 Jun 2017, 07:36.
Last edited by Sajjad1994 on 06 Jul 2019, 23:29, edited 1 time in total.
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Re: If n is an integer, what is the least value of n such that 1/3^n < 0.0 [#permalink] New post   26 Jun 2017, 00:28
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Bunuel wrote:
If n is an integer, what is the least value of n such that \(\frac{1}{3^n} < 0.01\) ?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6


\(\frac{1}{3^n} < 0.01\)

\(3^n >\frac{1}{0.01}\)

\(3^n >\frac{1}{10^{(-2)}}\)

\(3^n > 10^{2}\)

\(3^n > 100\)

\(3^4 = 81\) , \(3^5 = 243\)

\(3^5 > 100\)

Since \(3^n\) should be greater than \(100\). Therefore \(3 ^n = 3^5. n = 5\) . Answer (D)...
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Re: If n is an integer, what is the least value of n such that 1/3^n < 0.0 [#permalink] New post   25 Jun 2017, 13:25
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to make 1/3^n < 1/100 we will take a value of 3^n that is more than 100

3^4 = 81 not sufficient
3^5 = 243 sufficient

so n=5 .. answer D
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Re: If n is an integer, what is the least value of n such that 1/3^n < 0.0 [#permalink] New post   26 Jun 2017, 00:15
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Imo D
When n=5 we have 3^5 = 243
1/243=0.00411 which is less than 0.01
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Re: If n is an integer, what is the least value of n such that 1/3^n < 0.0 [#permalink] New post   24 Jun 2017, 07:50
Bunuel wrote:
If n is an integer, what is the least value of n such that \(\frac{1}{3^n} < 0.01\) ?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6


1/3^n = 1/100

for n=4 1/3^n will be 1/81
for n=5 it will be 1/243
Least value of n will be 5 for which equation holds
hence D
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If n is an integer, what is the least value of n such that 1/3^n < 0.0 [#permalink] New post   31 Jan 2021, 00:20
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Bunuel wrote:
If n is an integer, what is the least value of n such that \(\frac{1}{3^n} < 0.01\) ?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

Source: Nova GMAT
Difficulty Level: 600



\(\frac{1}{3^n} < 0.01\)
\(\frac{1}{3^n} < \frac{1}{100}\)
Since both \(3^n\) and 100 are positive, we can cross multiply.

\(100<3^n........3^4=81 \ \ \ and \ \ \ 3^5=243\)
\(3^4<100<3^5\)

Least value is 5.

D
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If n is an integer, what is the least value of n such that 1/3^n < 0.0 [#permalink]
31 Jan 2021, 00:20
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