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# What is the largest integer n such that 3^n < 0.001?

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What is the largest integer n such that 3^n < 0.001?  [#permalink]

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30 Nov 2016, 03:02
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72% (01:30) correct 28% (01:29) wrong based on 351 sessions

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What is the largest integer n such that 3^n < 0.001?

A. −13
B. −9
C. −7
D. 0
E. 3

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What is the largest integer n such that 3^n < 0.001?  [#permalink]

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26 Feb 2017, 01:05
6
Bunuel wrote:
What is the largest integer n such that 3^n < 0.001?

A. −13
B. −9
C. −7
D. 0
E. 3

Consider this pattern:

$$3^-1 = \frac{1}{3} = 0.3..$$
$$3^-2 = \frac{1}{9} = 0.1..$$
$$3^-3 = \frac{1}{27} = 0.03..$$
$$3^-4 = \frac{1}{81} = 0.01..$$

With this pattern:
$$3^-5 ~ 0.003$$
$$3^-6 ~ 0.001$$

$$3^-7 < 0.001$$
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Re: What is the largest integer n such that 3^n < 0.001?  [#permalink]

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30 Nov 2016, 04:02
2
2
Bunuel wrote:
What is the largest integer n such that 3^n < 0.001?

A. −13
B. −9
C. −7
D. 0
E. 3

It's clearly that $$n<0$$
$$3^n<10^{-3} \implies \frac{1}{3^{|n|}}<\frac{1}{10^3} \implies 3^{|n|}>10^3 >9^3 = 3^6 \implies |n| \geq 7 \implies n \leq -7$$

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Re: What is the largest integer n such that 3^n < 0.001?  [#permalink]

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30 Nov 2016, 04:45
Multiplying both side by 1000.
3^n *1000 < 1.
By looking at answer choice only we can eliminate two options i.e. 0 and 3.
Taking value n=-7 itself value just less than 0.001. i.e. 0.0004. As the value goes high i.e. 9 and 13 it will be far less than 0.001.
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Re: What is the largest integer n such that 3^n < 0.001?  [#permalink]

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24 Apr 2017, 06:08
2
Bunuel wrote:
What is the largest integer n such that 3^n < 0.001?

A. −13
B. −9
C. −7
D. 0
E. 3

Substitution of options:

(D) when n = 0,

$$3^n = 3^0 = 1 > 0.001$$ X

(C) when n = -7,
3^(-7) = $$(1/3)^7$$ = (1/9)*(1/9)*(1/9)*(1/3) = (1/243)*(1/9) = (1/2187)

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What is the largest integer n such that 3^n < 0.001?  [#permalink]

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18 Mar 2018, 05:58
2
Bunuel wrote:
What is the largest integer n such that 3^n < 0.001?

A. −13
B. −9
C. −7
D. 0
E. 3

Given $$3^n<0.001$$
=> Multiplying & dividing RHS by 1000 we have
=> $$3^n<\frac{1}{1000}$$
=> OR $$1000<\frac{1}{3^n}$$
=> OR $$1000<3^{-n}$$

Therefore 'n' should be -ve so that the power of $$3^{-n}$$ becomes +ve
Thus
=> if $$n=-6$$ then $$3^{-(-6)}=3^6=729$$
=> if $$n=-7$$ then $$3^{-(-7)}=3^7=2187$$ SUFFICIENT
=> if $$n=-8$$ then $$3^{-(-8)}=3^8=6561$$

Since 'n' is -ve largest integer value of 'n' that satisfy $$1000<3^{-n}$$ is $$n=-7$$

Option "C"

Thanks
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Re: What is the largest integer n such that 3^n < 0.001?  [#permalink]

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21 Jul 2019, 05:31
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Re: What is the largest integer n such that 3^n < 0.001?   [#permalink] 21 Jul 2019, 05:31
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