Is r^x < 100?

Is \(r^x<100\) ?


(1) \(r∗\sqrt[3]{x}>100\)

if x = 1/8
=> \(r∗\sqrt[3]{\frac{1}{8}}>100\)
=> \(r*\frac{1}{2} > 100\)
=> r > 200
\(r^x<100\)
=>\(300^{\frac{1}{8}}<100\) True

if x = 8
=> r > 50
\(r^x<100\)
=>\(51^{8}<100\) False
So here we don't have max and min of x and r, so we cannot calculate value of \(r^x<100\)
Insufficient

(2) x>1
Here we dont know value of r
Insufficient

1+2
\(r∗\sqrt[3]{x}>100\) and x>1

for x =8>1 => \(r∗\sqrt[3]{x}>100\)
=> \(r∗\sqrt[3]{8}>100\)
=> r >50
so \(r^x<100\)
=> \(51^8<100\) False

for x=100000000
\(r∗\sqrt[3]{x}>100\)
=> \(r∗\sqrt[3]{100000000}>100\)
=> r* 1000>100
=> r >1/10
so \(r^x<100\)
=> \(1^{1000000000}<100\) True

So here there is no max limit on x. Hence insufficient

Answer: E