Answer: a logical conclusion based on the two statements is D. Hannah's math grade has improved.
Explanation:
Hi, a logical conclusion based on the two statements is option D. Hannah's math grade has improved.
The second statement says : Hannah has been doing her homework.
So, it can´t be option b, because it states that she had no homework this week.
The first statement says : "If Hannah does her homework, then her math grade will improve".
So, options C and A can´t be logical conclusions neither, because we don't know the quantity of homework that Hannah had this week, and her math grade had improved.
Feel free to ask for more if it´s necessary or if you did not understand something.