Question

If n = 67 then find the unit digit of $[3^n+2^n]$

• A. 1
• B. 10
• C. 5
• D. None

Answer 1

The correct option is C 5

$n=67$
$\therefore \frac{n-1}{4}=\frac{67-1}{4}=\frac{66}{4}=16\frac{2}{4}$
$\therefore remainder=4$
$\therefore Requiredlastdigit=unitdigitin\left(3^{3+1}\right)+unitdigitof\left(2^{3+1}\right)$
$=Unitdigitin27+Unitdigitin8$
$=unitdigitin(7+8)$
$=unitdigitin\left(15\right)=5$