A

Statement 1:
She began the job at 8.15 am. Time elapsed till noon - 3hr 45 min. By this time she had completed half the job. So time taken to complete the job is a further 3 hr 45 min. So job was finished at 3.45 pm

Statement 2:
We do not know when she started, so we cannot calculate the end time.
Thus 1 alone is sufficient but 2 alone is not sufficient. Hence answer is A.

Hi!

thank you for posting questions on beatthegmat,com, Sanju09.

(1) She started the job at 8:15 a.m. and at noon of the same day she had worked exactly half of the time that it took her to do the whole job.

12 h - 8 h - 15 min = 3 h 45 min

3 h 45 min it is half of her working time

full period of time is twice as much as 3 h 45 min. It is 7 h 30 min

she had finished job at 3:45 p.m.

this statement ALONE is SUFFICIENT so answer should be A or D

(2) She was finished exactly 7.5 hours after she had started.

we can't answer the question because we don't know when she started the job

so it is INSUFFICIENT

IMO A

hope it helps!