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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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Math Expert
Joined: 02 Sep 2009
Posts: 52938
If n is an integer, what is the least value of n such that 1/3^n < 0.0  [#permalink]

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24 Jun 2017, 06:36
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35% (medium)

Question Stats:

58% (00:57) correct 42% (00:55) wrong based on 110 sessions

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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

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

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24 Jun 2017, 06:50
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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Re: If n is an integer, what is the least value of n such that 1/3^n < 0.0  [#permalink]

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25 Jun 2017, 12:25
1
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

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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]

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25 Jun 2017, 23:15
Imo D
When n=5 we have 3^5 = 243
1/243=0.00411 which is less than 0.01
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If n is an integer, what is the least value of n such that 1/3^n < 0.0  [#permalink]

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25 Jun 2017, 23:28
2
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]

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18 Jan 2019, 07:30
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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] 18 Jan 2019, 07:30
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