Let total earnings and number of shares be \(E_x \ \ and \ \ S_x\) in year x.
So we are looking for \(\frac{\frac{E_{2010}}{S_{2010}}-\frac{E_{2000}}{S_{2000}}}{\frac{E_{2000}}{S_{2000}}}*100\)

(1) The total earnings of company x increased by 70% from 2000 to 2010
So \(E_{2010}=1.7*E_{2000}\)

\(\frac{\frac{1.7*E_{2000}}{S_{2010}}-\frac{E_{2000}}{S_{2000}}}{\frac{E_{2000}}{S_{2000}}}*100\)

(2) The total number of shares of company x increased by 30% from 2000 to 2010
So \(S_{2010}=1.3*S_{2000}\)

\(\frac{\frac{E_{2010}}{1.3*S_{2000}}-\frac{E_{2000}}{S_{2000}}}{\frac{E_{2000}}{S_{2000}}}*100=\frac{\frac{E_{2010}}{1.3}-E_{2000}}{E_{2000}}*100\)

combined
\(\frac{\frac{E_{2010}}{1.3}-E_{2000}}{E_{2000}}*100\) and \(E_{2010}=1.7*E_{2000}\)

\(\frac{\frac{1.7*E_{2000}}{1.3}-E_{2000}}{E_{2000}}=(\frac{1.7}{1.3}-1)*100=\frac{400}{13}\)%

C

What was the percent increase in the earnings per share of company x from year 2000 to 2010?

Stat1: The total earnings of company x increased by 70% from 2000 to 2010
We don't know about nos. of shares. Not sufficient

Stat2: The total number of shares of company x increased by 30% from 2000 to 2010
We don't know about earning of company x. Not sufficient

Combining both, we have nos. of shares and earning increase. So, Sufficient.

So, I think C.