The number of elements in the set $\{n\in N:10\le n\le 100and{3}^n-3isamultipleof7\}$ is __

$3^n-3=7kk\in I$

$3^n=7k+3$

Now 

3=3(mod7)

$3^2=2$ (mod7)

$3^3=-1$ (mod7)

$3^6=1$ (mod7)

$3^7=3$(mod7)

Since $3^{13}=3$ (mod7)……….

N can be 13,19,….97

n=15