If n is an integer, what is the least value of n such that 1/3^n

Question

If n is an integer, what is the least value of n such that  \frac{1}{3^n} < 0.01  ?

(A) 2 
(B) 3 
(C) 4 
(D) 5 
(E) 6

Source:   Nova GMAT  
Difficulty Level:   600

Luckisnoexcuse · Answer

1/3^n = 1/100

for n=4 1/3^n will be 1/81
for n=5 it will be 1/243
Least value of n will be 5 for which equation holds
hence D

hermitnisant · Answer

to make 1/3^n < 1/100 we will take a value of 3^n that is more than 100

3^4 = 81 not sufficient 
3^5 = 243 sufficient

so n=5 .. answer D

arvind910619 · Answer

Imo D
When n=5 we have 3^5 = 243 
1/243=0.00411 which is less than 0.01

sashiim20 · Answer

\frac{1}{3^n} < 0.01

3^n >\frac{1}{0.01}

3^n >\frac{1}{10^{(-2)}}

3^n > 10^{2}

3^n > 100

3^4 = 81  ,  3^5 = 243

3^5 > 100

Since  3^n  should be greater than  100 . Therefore  3 ^n = 3^5. n = 5  . Answer (D)...

chetan2u · Answer

\frac{1}{3^n} < 0.01  
 \frac{1}{3^n} < \frac{1}{100}  
Since both  3^n  and 100 are positive, we can cross multiply.

100<3^n........3^4=81 \ \ \ and \ \ \ 3^5=243 
 3^4<100<3^5

Least value is 5.

D

If n is an integer, what is the least value of n such that 1/3^n < 0.0