Question

If the greatest divisor of $30\cdot 5^{2n}+4\cdot 2^{3n}$ is $p,\forall n\in N$ and that of $2^{2n+1}-6n-2$ is $q,\forall n\in N$, then $p+q=$

• A. 26
• B. 52
• C. 104
• D. 13

Answer 1

Answer: (B)

We have, $30\cdot 5^{2n}+4\cdot 2^{3n}$
Put $n=1$
$30\times 25+4\times 8=750+32=782$
$782=2\times 23\times 17\dots (i)$
Put $x=2$
$30\times 625+4\times 64=18750+256=19006\dots (ii)$
In Eqs. (i) and (ii), we get
Greatest divisor $=2\times 17=34$
$\therefore p=34$
Now in $2^{2n+1}-6n-2$
Put $n=1$
$8-6-2=0$
Put $n=2$
$32-12-2=18$
Put $n=3$
$128-18-2=108$
$\because$ Greatest divisor $=18$
$\therefore q=18$
$\therefore p+q=34+18=52$