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For how many values of integer n is 0.01 < 3-n+1 < 0.1?

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For how many values of integer n is 0.01 < 3-n+1 < 0.1?  [#permalink]

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New post 14 Mar 2019, 05:16
3
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

64% (01:48) correct 36% (01:46) wrong based on 47 sessions

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For how many values of integer n is \(0.01 < 3^{-n+1} < 0.1\)?

A. 0
B. 1
C. 2
D. 3
E. 4
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Re: For how many values of integer n is 0.01 < 3-n+1 < 0.1?  [#permalink]

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New post 14 Mar 2019, 06:25
2
1
kiran120680 wrote:
For how many values of integer n is 0.01 < 3-n+1 < 0.1?

A. 0
B. 1
C. 2
D. 3
E. 4


I'm guessing that there's meant to be an exponent in the inequality, since if not, the answer is clearly zero. I'm guessing the inequality is meant to read:

\(0.01 < 3^{-n+1} < 0.1\)

So we just want to know how many different integer powers of 3 lie between 0.01 and 0.1, and by inspection, 3^(-3) = 1/27 and 3^(-4) = 1/81 are between 1/10 and 1/100, but these are the only two possibilities.
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Re: For how many values of integer n is 0.01 < 3-n+1 < 0.1?  [#permalink]

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New post 15 Mar 2019, 05:44
0.01<3^-n+1<0.1
= 1/100 < 3^ -n+1< 1/10

= 1 <100/3^ n+1<10 Here n can take two integers value 3 and 4; Hence, Answer is C
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Re: For how many values of integer n is 0.01 < 3-n+1 < 0.1?  [#permalink]

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New post 22 Nov 2019, 23:34
1
10^-2 < 3^-n+1 < 10^-1

= 10^2 > 3^n+1 > 10

Possible for values 2 & 3 => 2 values.

Ans C
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Re: For how many values of integer n is 0.01 < 3-n+1 < 0.1?   [#permalink] 22 Nov 2019, 23:34
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