## Thursday, January 23, 2014

### 4: Percent Increase

On the Praxis Exam I took some years ago, there was a question that ran something like this:

The parking lot at the college was a square 100 yards on a side. The lot was increased by paving enough land to make a new square with a side that was 400% bigger. The size of the new lot was what percent of the old lot?
a)  400%
b)  800%
c)  1200%
d)  1600%

So ... what's wrong with this question and those answers?

1. There are two things here .. area comparison and the OF versus MORE THAN issue. 400% bigger means 5x as large.
Area is thus 25x as large, or 2500% of the the old lot.
The 400 % answer is there to entice the gullible.
The 800% answer is there because 400% + 400% is 800%
The 1200% answer is just wrong.
The 1600% answer is there because everyone will feel clever about not falling into the "length or area comparison" trap.
But the correct answer just isn't there.
It would have been (d) if the question read "That size of the new lot is what percent bigger than the old lot."

2. The correct answer isn't there.

3. So true ... this was on the test, written in this way. I told the test administrator that there was an error and she gave me one of "those" looks -- you know the kind: "Really? Well, don't you think you're so smart?" She didn't say it with her outer voice, but I could hear it, so I wrote down the particulars and gave it to her.

It only took them about three months to send me the letter acknowledging the mistake. I doubt they corrected any of the exams for other people, though.

1. I took a practice ASVAB before enlisting - it had an unfactorable quadratic equation but all the choices were integers. The recruiters were a little embarrassed when I showed them the error.

4. It would have been (d) if the question read "That size of the new lot is what percent bigger than the old lot."

That's not right either, is it? I assume we are taking "percent bigger than" to mean the same thing in question and answer. The original lot is 100*100 = 10000 yd^2. The new lot has sides which are 400% larger than the original lot, so its sides are 500 yd each, and the area is 500*500 = 250000 yd^2. The new lot is 240000 yd^2 larger than the original lot, meaning 240000/10000 = 2400% larger. Funny that the completely wrong answer (1200%) seems related, but not for a reason I'd expect.