In the figure above, circular region A represents all integers from 10 to 100, inclusive; circular region B represents all integers that are multiples of 3; and circular region C represents all squares of integers. How many numbers are represented by the shaded region?
- a) 24
- b) 25
- c) 26
- d) 27
- e) 28
Here's my train of thought: All we need to know is this set of numbers is from 10-100 (which I'm assuming does include 10 and 100?) and is multiples of 3. Instead of listing out every multiple of 3, I can have the largest multiple of 3 less than or equal to 100, which is 99, subtract the smallest multiple of 3 more than or equal to 10, which is 12. 99 - 12 = 87 Then to find the number of times 3 fits into 87, divide 87 by 3. 87 / 3 = 29 Agh! 29 is not one of the answer options provided!
Assuming what I've done so far is correct, now I'm thinking that for some reason 1 has to be subtracted from 29 29 - 1 = 28 to get 28, which is one of the options provided and also is the correct answer.
But why would I need to subtract 1 from 29? (Or is that not the right way to find the answer?)