Marbles Brainteaser

This brainteaser comes from 256.com:

Five youngsters entered a contest to guess how many marbles were in a bowl. Alice guessed 45, Betty guessed 39, Chuck guessed 49, Dan guessed 50, and Ed guessed 47. One was off by 6, one by 5, one by 2, and one by 4. One was right.

Who was right?

A. Alice
B. Betty
C. Chuck
D. Dan
E. Ed

(Scroll down for answer)





An explanation from Moana:
A. Alice was right. You can do this easily by testing each number to see which one was right, but there are some easy ways to narrow it down. Firstly, the range of the numbers is 11, so the correct answer HAS to be one of the middle numbers - if it were the largest or smallest, the wrong answers would be off by much more than 6. In fact, since one answer is off by 6 and one off by 5 (two numbers which add up to the range of the set), the right number HAS to either be 44 or 45, since those are the only two numbers which are 5 and 6 off from the high and low guesses. And since nobody guessed 44, it HAS to be 45.