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If k is an integer and 0.01 < 1/3^k < 0.1, then what is the product

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Bunuel
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If k is an integer and 0.01 < 1/3^k < 0.1, then what is the product [#permalink] New post   01 Feb 2022, 04:00
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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
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D
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BrentGMATPrepNow
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Re: If k is an integer and 0.01 < 1/3^k < 0.1, then what is the product [#permalink] New post   01 Feb 2022, 09:31
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Bunuel wrote:
If k is an integer and \(0.01<\frac{1}{3^k}<0.1\), then what is the product of all possible values of k ?

A. -12
B. 0
C. 6
D. 12
E. 24

I think you mean all possible values of k.

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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ScottTargetTestPrep
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Re: If k is an integer and 0.01 < 1/3^k < 0.1, then what is the product [#permalink] New post   24 Mar 2023, 08:55
Expert Reply
Bunuel 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


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
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0Lucky0
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If k is an integer and 0.01 < 1/3^k < 0.1, then what is the product [#permalink] New post   30 Apr 2023, 06:01
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Bunuel 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

Given: \(\frac{1}{100}<\frac{1}{3^k}<\frac{1}{10}\)
Taking Reciprocal reverses the greater than/less than symbol:
\(100>3^k>10\)
So \(3^2 = 9; 3^3 = 27; 3^4 = 81; 3^5 = 243.\)
Out of these, only \( 3^3 = 27; 3^4 = 81\) lie between 10 and 100.
So k can only be 3 and 4.
3*4 = 12.
So the right answer is D.
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Aishyk97
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Re: If k is an integer and 0.01 < 1/3^k < 0.1, then what is the product [#permalink] New post   22 Jun 2023, 20:26
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Bunuel 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


Another simple way to solve this for anyone who has trouble with decimals and fractions is:

\(0.01<\frac{1}{3^k}<0.1\)

Immediately try to get rid of the decimal by multiplying by 100.
You get:

\(1<\frac{100}{3^k}<10\)
So k has to be positive

if k = 1 then \(\frac{100}{3^1} = 33\) (NO)

if k = 2 then \(\frac{100}{3^2} = 11 \) (NO)

if k = 3 then \(\frac{100}{3^3} = 3. \) (YES)

if k = 4 then \(\frac{100}{3^4} = 1. \) (YES)

Only k = 3 and k = 4 is possible. So 3*4 = 12
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deepak.brijendra
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Re: If k is an integer and 0.01 < 1/3^k < 0.1, then what is the product [#permalink] New post   11 Jul 2023, 12:59
Hi
Since K is integer thus it can be +ve and -Ve both. In that Case K can be 3,4 and -4 as well so the desired answer should be -48.

Can you explain where am I missing?
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Bunuel
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Re: If k is an integer and 0.01 < 1/3^k < 0.1, then what is the product [#permalink] New post   11 Jul 2023, 13:56
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deepak.brijendra wrote:
Hi
Since K is integer thus it can be +ve and -Ve both. In that Case K can be 3,4 and -4 as well so the desired answer should be -48.

Can you explain where am I missing?


k = -4 does not satisfy 0.01 < 1/3^k < 0.1 because \(\frac{1}{3^{-4} }=3^4 = 81\).
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Re: If k is an integer and 0.01 < 1/3^k < 0.1, then what is the product [#permalink]
11 Jul 2023, 13:56
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