2018/008) Five distinct 2 digit numbers are in GP. Find them

As we have $2^4=16$ and $10 * 16 > 99$ hence the common ratio $< 2$

So let the common ration be $\frac{b}{a}$ where a and b are co-primes

So the numbers are $a^4, a^3b,a^2b^2,a^3b,a^4$ and we should have

$a^4 >=10=>a>= 2$ and $b^4 < 100=> b <=3$ ands hence $a=2,b=3$ and the numbers are$16,24,36,54,81$