What is the largest integer n such that 3^n

Question

What is the largest integer n such that 3^n < 0.001?

A. −13
B. −9
C. −7
D. 0
E. 3

RMD007 · Accepted Answer

Consider this pattern:

3^-1 = \frac{1}{3} = 0.3.. 
 3^-2 = \frac{1}{9} = 0.1.. 
 3^-3 = \frac{1}{27} = 0.03.. 
 3^-4 = \frac{1}{81} = 0.01..

With this pattern:
 3^-5 ~ 0.003 
 3^-6 ~ 0.001

3^-7 < 0.001

broall · Answer

It's clearly that n<0 $3^n<10^{-3} \implies \frac{1}{3^{|n|}}<\frac{1}{10^3} \implies 3^{|n|}>10^3 >9^3 = 3^6 \implies |n| \geq 7 \implies n \leq -7$ The answer is C

prashantrchawla · Answer

My answer is C. 
Multiplying both side by 1000. 
3^n *1000 < 1. 
By looking at answer choice only we can eliminate two options i.e. 0 and 3. 
Taking value n=-7 itself value just less than 0.001. i.e. 0.0004. As the value goes high i.e. 9 and 13 it will be far less than 0.001. 
Hope my answer is right.

umg · Answer

Substitution of options:

(D) when n = 0,

3^n = 3^0 = 1 > 0.001    X

(C) when n = -7,
3^(-7) =  (1/3)^7  = (1/9)*(1/9)*(1/9)*(1/3) = (1/243)*(1/9) = (1/2187)

1/2187 < 1/1000  Answer

dineshril · Answer

Given 3^n<0.001 => Multiplying & dividing RHS by 1000 we have => 3^n<\frac{1}{1000} => OR 1000<\frac{1}{3^n} => OR 1000<3^{-n} Therefore 'n' should be -ve so that the power of 3^{-n} becomes +ve Thus => if n=-6 then 3^{-(-6)}=3^6=729 => if n=-7 then 3^{-(-7)}=3^7=2187 SUFFICIENT => if n=-8 then 3^{-(-8)}=3^8=6561 Since 'n' is -ve largest integer value of 'n' that satisfy 1000<3^{-n} is n=-7 Option "C" Thanks Dinesh

CEdward · Answer

Plug in. Start with n = 0.

3^0 = 1 ----> Eliminate D and E.
3^7 = 1/729 ---> Winner

Answer is C.

luisdicampo · Answer

Deconstructing the Question

We must find the largest integer   n   such that

3^n < 0.001

Note that

0.001 = 10^{-3}

If  n  were positive, then  3^n  would be greater than  1 , so the inequality cannot hold.

Therefore  n  must be negative.

Step-by-step

Test nearby powers.

3^{-6} = \frac{1}{3^6}

3^6 = 729

3^{-6} \approx 0.00137

This is greater than  0.001 , so it does not satisfy the condition.

Now test

3^{-7} = \frac{1}{3^7}

3^7 = 2187

3^{-7} \approx 0.000457

This value is less than  0.001 , so the condition is satisfied.

Since  3^{-6}  is already greater than  0.001 , the largest integer that works is

-7

Answer C: -7

What is the largest integer n such that 3^n < 0.001?

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GMAT Problem Solving (PS) Questions

What is the largest integer n such that 3^n < 0.001?

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