Sergio took four exams. He received good scores on three exams, but failed one. The teacher allows her student's to drop their lowest score. When Sergio does this, his average increases from 70 to 80. What was Sergio's failing exam score?

For 4 perfect exam scores Sergio would have had 400 total points, as it was he ended up with 70% of those points or

0.7*400 = 280 points

By dropping a test grade Sergio reduced the number of possible points to 300 and his grade improved to 80%

0.8*300 = 240 points

The difference between the two is the score (in points) Sergio received that lowered his original average

280 - 240 = 40 points

Assuming the test was out of a possible 100 points that means he got a 40% on that test.