No need to solve for X

Jay Tea over at Wizbang linked to a Boston Globe story about the math question that stumped the most students on the Massachusetts Comprehensive Assesssment System (MCAS) test. Here it is:

Of the people in attendance at a recent baseball game, one-third had grandstand tickets, one-fourth had bleacher tickets, and the remaining 11,250 people in attendance had other tickets. What was the total number of people in attendance at the game?
A) 27,000
B) 20,000
C) 16,000
D) 18,000

Jay provides an extended answer and writes that he had the solution in “30-40 seconds.” Not to brag, but I had it in about one. One-third plus one-fourth makes up more than half of the baseball fans, so the remaining 11,250 comprises less than half. If that share is less than half, the total is more than double 11,250 making (A) the only reasonable answer.

Is that so hard? Still, with paper, pencil and calculator at hand, half of all Massachusetts students missed the question. Considering that random guessing would produce a 25% success rate, the 50% level is a little startling. What would Danica say?

As I like to say, there are three kinds of people in the world: those who can count and those who can’t.