Question

Which of the following numbers will completely divide $(3^{25}+3^{26}+3^{27}+3^{28})$?

• A. $11$
• B. $16$
• C. $25$
• D. $30$

Answer 1

Answer: (D)

$30$

$(3^{25}+3^{26}+3^{27}+3^{28})=3^{25}\times (1+3+3^2+3^3)=3^{25}\times 40$
$=3^{24}\times 3\times 4\times 10$
$=(3^{24}\times 4\times 30)$, which is divisible by $30$.