If x is a positive integer with fewer than 3 digits, what is the probability Q that x*(x + 1) is a multiple of either 4 or 5?  Pick one.
A) 4/99
B) 2/25
C) 8/99
D) 49/100
E) 86/99
Interesting question! Also one that we should be able to answer very quickly be keeping an eye on our best friends, the answer choices.   We know that x belongs to the set {1, 2, 3, ... , 99}. We want to know the probability Q that x(x+1) is a multiple of either 4 or 5.   When will this happen? If either x OR (x+1) is a multiple of 4 or 5.   Since 4*5 is 20, let's look at the first 20 numbers to get a rough idea of how often this happens.   Out of the numbers from 1 to 20:   4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 20   So, 14 out of the first 20 numbers match our criteria. Since:   probability = (# of desired outcomes)/(total # of possibilities), we guesstimate the answer to be 14/20. Since (86/99) is the only answer greater than 1/2, we go with (86/99).
<result>E</result>
If x is a positive integer with fewer than 3 digits, what is the probability Q that x*(x + 1) is a multiple of either 4 or 5?