Question

Find the units digit of $(12{)}^{3^x}+(18{)}^{3x}(x\in N)$.

• A. 2
• B. 8
• C. 0
• D. 1

Answer 1

Answer: (C)

For all $x\in N$,
$(12{)}^{3^x}$ ends in either 8 or 2 and $(18{)}^{3^x}$ ends in either 2 or 8
If $(12{)}^{3^x}$ ends in 8 , then $(18{)}^{3^x}$ ends in 2 .
If $(12{)}^{3^{\ast }}$ ends in 2 , then $(18{)}^{3^{\ast }}$ ends in 8 .
$\therefore (12{)}^{3^x}+(18{)}^{3^x}$ ends in 0 only.