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SAT math: is this a valid question?

  1. Aug 31, 2004 #1
    The College Board's website contains a "SAT question of the day" feature. As I'm going to be taking my SAT I's (as well as three SAT II tests, lucky me) in the near future, I check it on a regular basis in conjunction with the rest of my studies.

    Today's question seems completely crazy, though. I'd link to it, but the link would change by tomorrow, so I'll just copy it here:

    It was accompanied by this image.

    The LEAST number of trees one would need in order to arrange 4 trees on each line of the plan above is


    Would you be able to confidently answer this question using only the information presented above? Give it a try before reading on.

    The correct answer is apparently 10, and here's the reasoning they use:

    Since a point that is located where two lines intersect is considered to lie on both of those lines, you want to put trees on as many intersection points of the lines in the figure as possible in order to minimize the number of trees needed. There are 10 points where two lines intersect. With a tree in each of these 10 locations, there are then 4 trees on each line of the figure. Thus, the least number of trees needed is 10.

    Based on this, I think they're talking about actual, real-life trees, and that pattern is supposed to be drawn in soil from a bird's-eye perspective. I could be mistaken, though.

    If that is correct, I feel that it is not at all reasonable to expect someone to be able to answer this question with the provided information. The word "tree" has mathematical connotations that come to mind long before I'd ever think of arranging literal flora in an abstract pattern.

    So, my question is this: Is the question, in your opinion, a valid one for this sort of test (and therefore answerable using only the information provided), or is it sufficiently flawed to be inappropriate?
  2. jcsd
  3. Aug 31, 2004 #2


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    Actually, I thought of 'real life' trees immediately.
    The only other tree I know of is a graph without any loops, but if you use that notion, the question doesn't make any sense. So it seems obvious to me.
  4. Aug 31, 2004 #3


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    I thought it was fine. But then again, I've seen a few problems formulated in terms of (floral) trees, and placing them in arrangements with certain properties was one of the more common themes.

    I don't think there are any ambiguities here: you don't place mathematical trees onto lines, and plans are generally drawn from above.
  5. Aug 31, 2004 #4


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    If a problem ever doesn't make any sense, just try to change your perspective. Don't follow down one path of thinking blindingly. (I've lost a quite a few questions because of this...)
  6. Aug 31, 2004 #5
    Mathematical trees aren't on the SAT I anyway.
  7. Sep 1, 2004 #6


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    On the SAT, a tree is a member of family plantae, a big thing with a hard, brown cylindrical base and a softer, green head.
  8. Sep 1, 2004 #7
    You certainly can form trees out of the figure, and the question "what is the least number of trees you'd have to stack on top of the figure so that each line is occupied by at least four trees" is a question that can be legitimately answered, it's just complicated.

    I realize that it's important to try different ways of looking at a problem instead of getting stuck on just one, but that doesn't change the fact that the way this problem is worded leaves it readily open to more than one interpretation. That could be easily avoided by replacing the word "trees" with something like "pebbles".
  9. Sep 1, 2004 #8


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    Scholastic Aptitude Tests are intended to measure how well a student has retained knowledge that he could reasonably be expected to have been exposed to in high school.

    Generally, the simplest, most common interpretation of a test question will get you better results than finding the most creative answer - even when the more creative answer might display more knowledge.

    You don't get to explain your answers. They're scanned and read into a computer and the computer grades them. Trying to impress a computer is about as effective as saluting a telephone pole - they don't even know the concept exists.
  10. Sep 1, 2004 #9
    Sat scorees range too
    my PSAT I got an 80/80 which predicts 800 on SAT 1 math
    then i got 710 it was just random stuff-- for example I didn't know how many days were in a month which was needed to insert into a basic function
    all in all
    sat math is real easy
  11. Sep 1, 2004 #10
    Thanks for clearing that up, Bob! I thought telephone poles were sentient, but now that you point it out, it all "clicks" for me.
  12. Sep 2, 2004 #11


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    Sorry, that probably didn't come across that well.

    The point is that to give the answer you gave, you had to be looking for the answer that would show the highest degree of knowledge. The tests don't work that way. They're very straight forward and there's only one acceptable answer - as opposed to the possibility of constructing a test to award so many points for answer a, so many points for answer b, etc., which might actually look for the type of answer you gave.
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