Statement X: The percentage increase in number of Registrations from 2004 to 2005 is higher for Managerial candidates than for Technical candidates
Statement Y: The overall Registrations have grown by more than 25%

Considering statement X,

Percentage increase for Managerial candidates= $$\ \frac{\ \left(45292-19236\right)}{19236}\cdot100=\ \ \frac{\ 26056}{19236}\cdot100=135.45\%$$

Percentage increase in Technical candidates= $$\ \frac{\ \left(63298-61205\right)}{61205}\cdot100=3.3\%$$

Therefore statement X is true.

Considering statement Y,

Total registrations in 2004= 61205+19236= 80441.

Total registrations in 2005= 63298+45292= 108690.

So, growth in the overall number of registrations= $$\ \frac{\ \left(108690-80441\right)}{80441}\cdot100=35.11\%$$, which is greater than 25%.

So, both statement X and Y are true.