A GMAT aspirant appears for a certain number of tests. His average sco

This is a fun and fairly difficult weighted averages problem!

If we ignore the first 10 tests, here's the situation:

10 tests with an average of 700, remaining tests with an unknown average
new average = original average + 10

If we ignore the last 10 tests, here's the situation:

10 tests with an average of 600, remaining tests with an unknown average
new average = original average - 10

In other words, "swapping out" ten tests with an average of 700, for ten tests with an average of 600, effectively reduces the student's average by 20 points: from 10 points above the original value, to 10 points below the original value.

So, reducing the score on the extra 10 tests by 100 points, only reduces the overall average by 20 points. Therefore, the extra 10 tests must only represent 20/100 = 1/5 of the total, since changing their value only changes the overall average by 1/5 as much. That gives us a total of 5(10) = 50 tests.

However, 50 isn't the answer! The answer is actually 50+10 = 60. That's because we're asked about how many tests there were when all of the tests were included. When we did our reasoning, we only thought about what would happen if we removed ten of the tests, and ignored the situation where all of the tests were included at the same time. So, we need to put the remaining 10 tests back in.