We received these questions and published them in our paper. We published the answers as were given to us by the test maker. We’ve since had a reader question the answers. I was an 8th grader a hundred or so years ago and always hated these kinds of problems, so I’m not the person to make a definitive call. For this I turn to my fellow dopers and ask…
Ms. Osborne asks each student in her class to draw a rectangle with integer side lengths and a perimeter of 50 units. All of her students calculate the area of the rectangle they draw. What is the difference between the largest and smallest possible areas of the rectangles?
a. 76
b. 120
c. 128
d. 132
e. 136
For how many positive integer values of n are both n/3 and 3n three-digit whole numbers?
a. 12
b. 21
c. 27
d. 33
e. 34
Answers (that we were given as correct) will follow after I see some responses. (Didn’t think I was going to let you cheat did you?)
Damn you, Desert Nomad. You are right in 3., and I was wrong. This is what I get for trying to be first and doing hasty calculation in head without checking results.
Ok, thanks very much. Most of you ARE smarter than 8th graders - even if you have a hard time discerning the letter answer required from the actual numerical answer…
It’s funny - I see these types of problems and my eyes just glaze over. I typically am one of those weird people who actually likes taking quizzes/tests. I looked forward to the “fill in the ovals” in school. But, there’s just something about this type of math problem. But after reading your responses and seeing the logic of how you worked it out - yes, they were easy. Thanks for taking the trouble to think out loud.
Now, the issue - - I’ve tracked down that the writer mistyped the first answer - should have been “d” as noted above, but she became momentarily dyslexic and typed “b”. My fault (as editor) for not doublechecking first.
Second answer is listed in the test answer booklet, garnered directly from the teacher administering the test, as “c”. This is clearly incorrect and should have been “a”. Apparently in the answer booklet itself (which I didn’t have prior to publication, but the writer did) is also a verbal explanation of how to arrive at the correct solution and within that paragraph, they conclude the answer is 12. Unfortunately, that does not correspond to the answer ‘c’. So, now the question is, how were the kids graded? We’re checking into that with the teacher.
This is from a standardized test, too, so the implications go beyond this particular classroom. Hopefully there’s an easy explanation and it won’t effect the rest of the entire math-test-taking world…
I found the first one easier than the second. I was trying to remember how to graph inequalities, and then how to interpret the intersections of two inequalities graphed together. Then I gave up.
Me too. Guess we both failed the reading comprehension part.
I hated both of those questions. They are too “mathy” and not at all the sort of thing one would do in real life. If I was a kid I’d be bored in a class that taught those sorts of questions. At the very least have something like “you have 50 feet of fringe. What is the largest and smallest quilt you could make from 1 foot squares.”
Except it doesn’t, as demonstrated by the correct answers in spoiler boxes.
Question 3 is a particularly nasty question, and it really tests the reader’s reading comprehension and logical reasoning more than it does any particular learned math skill.
Unless you’re quibbling that it should be “for how many values of x are x and 9x both 3-digit numbers”, or that it doesn’t explicitly say that the numbers must be positive, I don’t see what is wrong with Sublight’s assertion. Set n = 3x and substitute into the original question, it’s equivalent.
And I enjoyed the questions. Which I guess is what separates the pure mathematicians from the applied mathematicians. The pure mathematicians know that 2 + 3 = 5. The applied mathematicians know that $2 + $3 = $5.
Yikes; I find this a bit scary. There’s no way anyone should give a standardized/multiple-choice test unless they’re absolutely sure that each question has exactly oe correct answer and that that’s the answer given in the answer key.
These types of questions would be fair game for the SAT (for which I tutor)-I’d probably peg them at a 3 or 4 difficulty (out of 5). Those who chose the wrong answer for #3 did what many of my students do-didn’t read the question carefully enough (the word “integer” is the first thing you look for in such questions).
The first one was easy, the second one I had to read carefully to realize that N was not meant to be the three digit number, but both {X, Y} where X = (n/3) and Y = (3n).
