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For how many values of integer n is 0.01 < 3-n+1 < 0.1?
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14 Mar 2019, 05:16
14 Mar 2019, 05:16
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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
A. 0
B. 1
C. 2
D. 3
E. 4
GMAT Tutor
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Posts: 4127
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Q51 V47
Re: For how many values of integer n is 0.01 < 3-n+1 < 0.1?
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14 Mar 2019, 06:25
14 Mar 2019, 06:25
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Expert Reply
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
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?
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15 Mar 2019, 05:44
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
= 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
