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Math Help - Need help with problems!

  1. #1
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    Need help with problems!

    Q1. John tells the truth on Monday, Tuesday, Wednesday and Thursday. He lies on all other days. Dieter tells the truth on Monday, Friday, Saturday and Sunday. He lies on all other days. One day, they both sayd: "Yesterday I lied". The day they said that was:
    A) Monday
    B) Wednesday
    C) Thursday
    D) Friday
    E) Saturday

    I seriously have no clue to solve this one..all my friends dunno either..

    Q2. A rectangular sheet of cardboard is folded in half to form a smaller rectangle. The smaller rectangle is similar to the original rectangle. What is the ratio of the length to the width of the small rectange?
    A) 2 : 1
    B) 3 : 2
    C) root 3 : 1
    D) (1+ root 5) : 2
    E) root 2 : 1

    (Diagram) ------->
    |----------|----------| |----------|
    |----------|----------| |----------|
    |----------|----------| |----------|
    |----------|----------| |----------|
    |----------|----------| |----------|
    |----------|----------| |----------|
    |----------|----------| |----------|
    |----------|----------| |----------|
    Original Rectange Smaller (folded) rectange

    I guessed that it would be 2:1, but I'm seriously not sure because im really bad at geometry...

    Also, could you please tell me how you solved it..that would be greatly appreciated.

    Thank you in advance =).
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  2. #2
    MHF Contributor Quick's Avatar
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    Your teacher's not so nice...

    Quote Originally Posted by thedarktemplar
    Q1. John tells the truth on Monday, Tuesday, Wednesday and Thursday. He lies on all other days. Dieter tells the truth on Monday, Friday, Saturday and Sunday. He lies on all other days. One day, they both sayd: "Yesterday I lied". The day they said that was:
    A) Monday
    B) Wednesday
    C) Thursday
    D) Friday
    E) Saturday

    I seriously have no clue to solve this one..all my friends dunno either..
    This is a trick question, the answer is Friday because on Friday Dieter would tell the truth and say "Yesterday I lied", while John would lie and say "Yesterday I lied"
    no other day would work, the way to do this problem though is to write it out like this...note:Lied means he would sya "Yesterday I lied" and Honest means "Yesterday I told the truth"
    Code:
          |Sunday|Monday|Tuesday|Wednesday|Thursday|Friday| Saturday|
    John  | Lied | Lied |Honest | Honest  | Honest | Lied |  Honest |
    Dieter|Honest|Honest| Lied  | Honest  | Lied   | Lied |  Honest |
    Last edited by Quick; July 21st 2006 at 03:24 AM.
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  3. #3
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    Ahhh.. i c now.. quite tricky question lol.. required people to think deeply i think. Many thanks.
    Anyone wanna help me with Q2.?- Im really bad at geometry =\
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by thedarktemplar

    Q2. A rectangular sheet of cardboard is folded in half to form a smaller rectangle. The smaller rectangle is similar to the original rectangle. What is the ratio of the length to the width of the small rectange?
    A) 2 : 1
    B) 3 : 2
    C) root 3 : 1
    D) (1+ root 5) : 2
    E) root 2 : 1

    (Diagram) ------->
    |----------|----------| |----------|
    |----------|----------| |----------|
    |----------|----------| |----------|
    |----------|----------| |----------|
    |----------|----------| |----------|
    |----------|----------| |----------|
    |----------|----------| |----------|
    |----------|----------| |----------|
    Original Rectange Smaller (folded) rectange

    I guessed that it would be 2:1, but I'm seriously not sure because im really bad at geometry...

    Also, could you please tell me how you solved it..that would be greatly appreciated.

    Suppose the rectangle is a units long by b units wide. Then when folded
    it is b units long by a/2 units wide. These are similar so:

    a/b=b/(a/2),

    so:

    a^2=2b^2,

    or:

    a=sqrt(2)b.

    So the answer is (e) (someone is not reading what he is writting these days
    , this has been edited to the correct form)

    RonL
    Last edited by CaptainBlack; July 21st 2006 at 11:26 PM.
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  5. #5
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    wow u guys are smart.. thanks a bunch!
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  6. #6
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by CaptainBlack
    Suppose the rectangle is a units long by b units wide. Then when folded
    it is b units long by a/2 units wide. These are similar so:

    a/b=b/(2a), this is wrong it should be a/b=b/(a/2) this is now
    corrected in the earlier post


    so:

    2a^2=b^2,

    or:

    sqrt(2)a=b.

    So the answer is (c) should have been (e) as that is the one with the sqrt(2) in it

    Red text edited in to this by CaptainBlack to reflect needed corrections to earlier post

    RonL
    I got that too, but than I realized that the smaller rectangle is equal to b/(2a) and therefore you have to do this:
    \sqrt2a=b\longrightarrow\sqrt2=\frac{b}{a}<br />
\longrightarrow<br />
\frac{\sqrt2}{2}=\frac{b}{2a}
    and I couldn't figure out how to simplify from there...
    Last edited by CaptainBlack; July 21st 2006 at 11:30 PM.
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  7. #7
    Grand Panjandrum
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    Quote Originally Posted by Quick
    I got that too, but than I realized that the smaller rectangle is equal to b/(2a) and therefore you have to do this:
    \sqrt2a=b\longrightarrow\sqrt2=\frac{b}{a}<br />
\longrightarrow<br />
\frac{\sqrt2}{2}=\frac{b}{2a}
    and I couldn't figure out how to simplify from there...
    I have revised my earlier post, and it is now correct.

    RonL
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