Math question

Discussion in 'High School' started by krysmorgsu, Aug 15, 2011.

  1. krysmorgsu

    krysmorgsu Cohort

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    Aug 15, 2011

    Hello! I know this is not the usual type of post, but I need some help for an SAT type math question for a student I tutor. I was hoping that some of the Math teachers on here would help me, since I really can't figure out what is wrong with the student's solution.

    Here's the problem: Andrew has 50 small boxes, 60 medium size boxes, and 70 large size boxes. He wants to arrange them in rows so that there are equal number of same size boxes in each row. How many rows will he need, to be able to arrange the boxes?
    (A) 10
    (B) 12
    (C) 15
    (D) 18
    (E) 70

    Here's the solution from the tutoring company: To find the number of rows so that there are equal number of boxes of the same size in each row, the total number of boxes must be divided with the greatest common factor (GCF) of the number of boxes of each size.
    The prime factorization of 50 = 2 5
    The prime factorization of 60 = 2 2 3 5
    The prime factorization of 70 = 2 5 7
    Thus, the GCF of 50, 60, and 70 = 10
    The number of rows of boxes = (50+60+70) /10 = 180
    180/10 = 18
    The correct answer is (D).

    Now, my student said he could take 5 small, 6 medium, and 7 large per row- which means 18 boxes per row, for 10 rows- rather than the company's solution of 18 rows with 10 boxes each. I really do not get what is wrong with his solution of A. Maybe I'm looking at it wrong, but I really cannot figure this one out. Please help!
     
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  3. Catcherman22

    Catcherman22 Companion

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    I'm not quite sure where the tutoring company gets the idea they need to divide the total number of boxes by the gcf?

    You're student has the correct answer. The tutoring company starts off correctly, but fails to realize that the gcf is the answer.. they need not do anything else with it.

    Unless something is worded incorrectly, poorly, or I'm missing something in the wording of the problem.
     
  4. krysmorgsu

    krysmorgsu Cohort

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    Thank you!!! I'm going to take it up with the company.
    T
     
  5. czacza

    czacza Multitudinous

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    Aug 15, 2011

    I'm coming up with ten rows as well.
    You can't put 50 or 60 or 70 boxes equally in 18 rows!:eek:
     
  6. Cerek

    Cerek Aficionado

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    Aug 15, 2011

    18 rows of 10 boxes is the same as 10 rows of 18 boxes. You still have a 10 x 18 matrix. It just depends on which way you look at it as to how many rows you have.

    Having said, that, I agree the correct answer should be 10 rows as well.
     
  7. Cerek

    Cerek Aficionado

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    Actually, Catcherman is right. The GCF would be the number of rows. Dividing the total number of boxes by the GCF tells you how many boxes are in each row, but since the question asks the number of rows instead of the number of boxes per row, the right answer is 10.
     
  8. czacza

    czacza Multitudinous

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    How would you put 10 boxes in each of 18 rows and still have the same number of each size box in each row?
     
  9. Cerek

    Cerek Aficionado

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    Aug 15, 2011

    Sorry, I was distracted with when I posted my first response, but what I was basically saying is that 18 rows of 10 boxes is the same as 10 rows of 18 boxes. It just depends on which side you look at.

    If you make a 10 x 18 matrix, it will look like 10 rows (or columns) from the top, but 18 rows (or columns) from the side. Either way, you still have the same number of boxes. Of course, after I looked at it again, I realized the 18 rows would NOT have boxes of each size in them. Rather, each "row" would have boxes that were all the same size. (that's what I get for posting and watching TV at the same time. LOL)

    So the correct answer IS 10 rows.
     
  10. Aliceacc

    Aliceacc Multitudinous

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    Aug 15, 2011

    Do me a favor, OP, check the wording on the question to ensure you've typed it exactly as it appeared.

    And I'm curious as to which book you got it from.
     
  11. czacza

    czacza Multitudinous

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    Aug 15, 2011

    Cerek...As a third grade teacher, I'm quite familiar with arrays. Of course 18 x 10 is the 'sideways' version of 10 x 18, but as I'm sure you teach your students, it's important to double check and make sure your answer fits the parameters of the problem. Guess the tutoring company textbook writers forgot to check this as well!:eek:
     
  12. Aliceacc

    Aliceacc Multitudinous

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    Aug 15, 2011

    OK, how's this:

    They're looking for rows of equal size, each containing ALL boxes of the same size-- one size per row.

    So 5 rows, each containg 10 small boxes,
    an additional 6 rows, each containing 10 medium boxes
    and 7 rows, each containg 10 large boxes.

    For a total of 5+6+7, or 18, rows.

    I would have phrased it as: "Andrew has 50 small boxes, 60 medium size boxes, and 70 large size boxes. He wants to arrange them in rows so that there are equal number of only thesame size boxes in each row. How many rows will he need, to be able to arrange the boxes?" or something similar
     
  13. czacza

    czacza Multitudinous

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    Aug 15, 2011

    If it's typed as it is in the textbook, however:
    He wants to arrange them in rows so that there are equal number of same size boxes in each row.
    The 'in each row' part implies for me that Andrew is going to put some of each size box in each row...I can imagine how this is confusing for the student!:dizzy:
    Similar situations arise in both LA and Math test prep materials for lower grades as well....we hash it out as a class, talk about how some problems are badly worded and I reassure them that the 'test people' probably didn't put such confusing questions on the test. In addition to teaching my students to read carefully, I also teach them text taking skills such as process of elimination for multiple choice, drawing pictures, and making a 'best guess' when absolutely necessary.:whistle:
     
  14. Aliceacc

    Aliceacc Multitudinous

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    My guess is that either the OP or the workbook publisher copied it incorrectly. That's why I asked where the question came from; I might have a different edition of the same book here.

    But I agree, Czacza-- as written, the correct answer would be 10.

    I would also like to know what question number it was. I suspect it was number 19 or 20 on a practice set. That, in and of itself, would have warned us that the obvious answer-- 10-- couldn't be correct.
     
  15. Mrs_Garland

    Mrs_Garland Rookie

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    This is how I read the problem from the beginning and I got the answer of 18 immediately.
     
  16. czacza

    czacza Multitudinous

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    But that's not what the problem says. As written, the best answer is ten rows of 18 boxes.
     
  17. Catcherman22

    Catcherman22 Companion

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    See, I thought the same thing in terms of the question being not worded correctly, however the same mistake is made in the answer. It again fails to mention that it's only the one size in each row.

    The way Alice words it make more sense with the way the solution is provided, but that's not what it's asking and it's an extremly poorly worded question.
     
  18. Aliceacc

    Aliceacc Multitudinous

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    Aug 16, 2011

    Absolutley.

    It's not unheard of to have an typo or two in an SAT review book. Looking at their explanation usually exposes the error, as I'm assuming it did here.
     
  19. krysmorgsu

    krysmorgsu Cohort

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    Aug 16, 2011

    Thank you to all who answered! I am waiting to hear back from the tutoring company with an explanation or correction. I believe it is, as Czaza said, a poorly worded question. From what I can tell, they needed to do one of three things: accept 10 as an answer, remove 10 as a possible answer (thus forcing the student to chose 18), OR reword the question. I think Alice is right: they wanted each row to only have one size box. Then it makes sense. However, worded the way it is, one can think he either wants each row to have only 1 size box OR that each row must have the same number of each size box as all of the others, which is what my student thought.

    Alice, to answer your questions:
    - the wording is correct - I literally copied and pasted the question/solution
    - this is not from any textbook. It is a tutoring company I work for, and it is one of their "homemade" problems. If it is in any review book, I am not aware of it.

    I'll post what the response is when I get it. Thank you so much for the help!! I know I'm not a math whiz, but I knew that the teachers on here wouldn't let me down! You guys are AWESOME!:2up: :atoz_love:
     
  20. Aliceacc

    Aliceacc Multitudinous

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    That makes sense Krys. ETS is usually pretty careful. Their questions can be tricky, but they don't contain these type of errors.
     

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