If k is an integer and 0.01

Question

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

BrentGMATPrepNow · Accepted Answer

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

ScottTargetTestPrep · Answer

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

0Lucky0 · Answer

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.

Aishyk97 · Answer

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

deepak.brijendra · Answer

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?

Bunuel · Answer

k = -4 does not satisfy 0.01 < 1/3^k < 0.1 because  \frac{1}{3^{-4} }=3^4 = 81 .

Usernamevisible · Answer

All three numbers are positive, so taking reciprocals reverses the inequality.

For example,

1/8 < 1/5 becomes 8 > 5.

Applying the same rule,

1/100 < 1/(3^k) < 1/10

becomes

100 > 3^k > 10

which is the same as

10 < 3^k < 100

This is the important step. The inequality reverses because reciprocals of positive numbers move in the opposite direction.

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

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