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If k is an integer and 0.01 < 1/3^k < 0.1, then what is the
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04 May 2022, 05:38
04 May 2022, 05:38
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If k is an integer and \(0.01<\frac{1}{3^k}<0.1\), then what is the product of all possible value of k ?
A. -12
B. 0
C. 6
D. 12
E. 24
A. -12
B. 0
C. 6
D. 12
E. 24
Part of the project: GRE Quantitative Comparison & Problem Solving Challenge
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
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Re: If k is an integer and 0.01 < 1/3^k < 0.1, then what is the
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04 May 2022, 06:06
04 May 2022, 06:06
1
Carcass wrote:
If k is an integer and \(0.01<\frac{1}{3^k}<0.1\), then what is the product of all possible value of k ?
A. -12
B. 0
C. 6
D. 12
E. 24
A. -12
B. 0
C. 6
D. 12
E. 24
Given: \(0.01<\frac{1}{3^k}<0.1\)
Rewrite as follows: \(\frac{1}{100}<\frac{1}{3^k}<\frac{1}{10}\)
At this point we can see that it must be the case that \(10 < 3^k < 100\)
Since \(k\) must be an integer, we can see that there are two possible solutions that satisfy the inequality \(10 < 3^k < 100\).
They are: \(k = 3\) and \(k = 4\)
So the product of the solutions \(= (3)(4) = 12\)
Answer: D
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Re: If k is an integer and 0.01 < 1/3^k < 0.1, then what is the
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24 Mar 2023, 07:56
24 Mar 2023, 07:56
1
Expert Reply
Carcass wrote:
If k is an integer and \(0.01<\frac{1}{3^k}<0.1\), then what is the product of all possible value of k ?
A. -12
B. 0
C. 6
D. 12
E. 24
A. -12
B. 0
C. 6
D. 12
E. 24
Rewriting the given inequality, we have:
1/100 < 1/3^k < 1/10
We see that k can be 3 and 4. Thus, the product is 12.
Answer: D
