Sophia did push-ups every day for 7 days. Each day after the first day, she did 5 more push-ups than the day before. In total she did 175 push-ups. How many push-ups did Sophia do on the last day?
(A) 55
(B) 35
(C) 50
(D) 45
(E) 40
Sophia did push-ups for 7 days (an odd number of days), and on each day she did an equal number of push-ups more than the day before (5 more).

Therefore, the number of push-ups that Sophia did on the middle day (day 4) is equal to the average number of push-ups that she completed each day.

Sophia did 175 push-ups in total over the 7 days, and thus on average she did $175 \div 7=25$ push-ups each day.

Therefore, on day 4 Sophia did 25 push-ups, and so on day 5 she did $25+5=30$ push-ups, on day 6 she did $30+5=35$ push-ups and on the last day she did $35+5=40$ push-ups.

(Note: We can check that $10+15+20+25+30+35+40=175$, as required.)

ANSWER: (E)