Statement X: The percentage of drop-outs (from Registration stage to posting CV’s) had decreased from 2004 to 2005 for Managerial category
Statement Y: The percentage of drop-outs was higher for Technical than for Managerial category in 2005

Statement X:

Percentage of drop-outs for Managerial category in 2004 = $$\ \frac{\ 19236\ -\ 15389}{19236}\times\ 100\ \approx\ 20\%$$

Percentage of drop-outs for Managerial category in 2005 = $$\ \frac{\ 45292\ -\ 40763}{45292}\times\ 100\ \approx\ 10\%$$

Therefore, percentage of drop-outs from 2004 to 2005 has decreased. Statement X is true.

Statement Y:

Percentage of drop-outs for Managerial category in 2005 = $$\ \frac{\ 45292\ -\ 40763}{45292}\times\ 100\ \approx\ 10\%$$

Percentage of drop-outs for Technical category in 2005 = $$\ \frac{\ 63298\ -\ 60133}{63298}\times\ 100\ \approx\ 5\%$$

Percentage of drop-out is lower for Technical category.

Statement Y is false

Answer is option A.