Test 7 Section 7 - #15 (page 789)

They're asking for the number of integers from 1-100 that aren't the square of an integer, but it's going to be a lot easier and faster to count how many are the square of an integer*:

1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100 ...and we're done! (Any higher will be out of the range we care about.)

Count how many we've got. I'm counting 10.

There are 100 integers between 1 and 100 inclusive (inclusive just means "including the ends," so we are counting both 1 and 100), and only 10 of them are squares of integers. Which means 90 aren't. The answer is (E).

* This is kinda like a shaded region area problem in that way...it's easier to look for the opposite of what they ask for, and then subtract.