1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

AMC test question

  1. Feb 1, 2005 #1
    This is not exatly homework, but it seems the best place to post it.

    Let A, M, and C be digits with:

    (100A+10M+C)(A+M+C) = 2005

    A. 1 B. 2 C. 3 D. 4 E. 5

    maybe some one can help me out on this, was one of the test questions i did not know how to do. :blushing:
     
  2. jcsd
  3. Feb 1, 2005 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    I don't see other solution than
    [tex] A=4;M=0;C=1 [/tex]

    Daniel.
     
  4. Feb 1, 2005 #3
    Use the fact that 2005 is written in decimal notation, which is incidently convenient with respect to how the left-hand side is written. Remember how decimal notation is defined. Any ideas ?
     
  5. Feb 1, 2005 #4
    wow, i didnt notice that, hmmm, thxs. :smile:
     
  6. Feb 1, 2005 #5

    t!m

    User Avatar

    Yeah dex is right. If you look at the range of answers, assuming A, M, and C are all going to be in that range, then 2005 only divides evenly by 5, leaving 401. Quick glance yields 4, 0, and 1.
     
  7. Feb 1, 2005 #6
    how about this one:

    Three circles of radius [itex]s[/itex] are drawn in the first quadrant of the xy-plane. The first circle is tangent to both axes, the second is tangent to the first circle and the x-axis, and the third is tangent to the first circle and the y-axis. A circle of radius [itex] r > s [/itex] is tangent to both axes and to the second and third circles. What is [itex] r/s [/itex]?

    A. 5 B. 6 C.8 D. 9 E. 10
     
  8. Feb 1, 2005 #7
    That is a better method. :smile:
     
  9. Feb 1, 2005 #8

    t!m

    User Avatar

    cdhotfire: Here's how I did it.

    I drew a line from the center of the large circle to the center of the top small circle (tangent to the first circle and the y-axis) and used that as the hypotenuse for a right triangle with sides (r-3s), (r-s), and (r+s). This makes more sense if you're looking at the diagram. In which case, (r-s)^2 + (r-3s)^2 = (r+s)^2. I just tried each answer, and found r=9, s=1 (r/s=9) to be the one which works. If you're confused, I'll see if I can work up a diagram.
     
  10. Feb 2, 2005 #9
    thxs man, that really helped me out. :). How about the star one:

    In the five-sided star shown, the letters A, B, C, D and E are replaced by the numbers 3, 5, 6, 7 and 9, although not necessarily in that order. The sums of the numbers at the ends of the line segments [itex]\lin{AB},\lin{BC},\lin{CD},\lin{DE}[/itex] and [itex]\lin{EA}[/itex] form an arithmetic sequence, although not necessarily in that order. What is the middle term of the arithmetic sequence?

    [​IMG]

    A. 9 B. 10 C. 11 D. 12 E. 13
     
  11. Feb 2, 2005 #10

    t!m

    User Avatar

    Put down the nine arbitrarily. Connect it to the two smallest, 3 and 5. Then to make the 3 connected to the two largest, connect it to 7 in addition to 9. Put the 5 in the remaining spot and you have 10, 11, 12, 13, and 14, with 12 being the middle term.
     
  12. Feb 2, 2005 #11
    o i see, i didnt understand the question. :rolleyes: , thxs though. :smile:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: AMC test question
  1. Test Questions (Replies: 2)

  2. Test Question (Replies: 4)

  3. TEST question (Replies: 8)

  4. Test Question (Replies: 1)

  5. Test question (Replies: 5)

Loading...