Harvard students sometimes get a “bum rap,” because we love both to see and proclaim their failure of school logic. We expect to see failure to some extent because we all know of at least one former ivy-league student that has failed, and we also know that many Harvard graduates appear to succeed in life. Life seems unfair, so we like the scales to be “balanced” in some ways and we like to target those who appear to “have it made.”
An apparently simple test of logic was administered to Harvard students. Why would half of them fail a simple test? The test question goes something like this: “There is a baseball bat that is known to cost $1.00 more than a baseball. The total cost for the two together is known to be $1.10. So, what is the value of the ball?” It appears to be a simple question.
In elementary algebra we can set up a pretty straight-forward equation. The ball’s value is “x” in the equation, that bat’s value is $1 and the sum of the two pieces of information is $1.10. The equation would read “$1.00 + x = $1.10.” We dutifully take the formula and subtract the $1 value from each side of the equation, ending up with the solution for x and discover its real value is 10 cents, i.e. our x= $.10.
The problem is that the test “key” states the answer is wrong and flunks us on this test along with half of the Harvard student group. The test administrator announces that the ball’s value must be 5 cents and the baseball bat’s value must be $1 plus 5 cents, i.e. $1.05. When the two values are summed, the total is that $1.10 we started with. Therefore, the ball value is a nickel.
But what about other “logic”? The deciding issue as to which answer is correct relates to semantics. We can “play” with the ten cent factors a variety of ways because that ten cents may be a total of 1+9, 2+8, 3+7, 4+6, or 5+5, but it is only the last total that will meet the factor requirements if the value is not 10 cents.
There are extraneous real-world components to this question of true value as well. Alternatively, depending on the state in which the purchase takes place, the ball could just as easily cost a whopping zero, because the bat’s purchase had to be accompanied by “sales tax,” at a 10% level, i.e., $1.10.
So, instead of “poor failing Harvard students,” they could be right on at least two options not considered by those constructing this simple test. So, do we fail the students or do we fail the testers for failing to recognize that there are “multiple answers” to another dumb test?