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Thread: Rose, Sam and Tina

  1. #1
    Super Member harpazo's Avatar
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    Rose, Sam and Tina

    Today Rose is twice as old as Sam and Sam is 3 years younger than Tina. If all three individuals are alive 4 years from today, which of the following must be true on that day?

    1. Rose is twice as old as Sam.
    2. Sam is 3 years younger than Tina.
    3. Rose is older than Tina.

    A. 1 only
    B. 2 only
    C. 3 only
    D. 1 and 2
    E 2 and 3

    My Work:

    Rose: 2(x - 3) + 4
    Sam: (x - 3) + 4
    Tina: x + 4

    Reducing Rose, I get 2x - 2.
    Reducing Sam, I get x + 1.
    Tina remains x + 4.

    If I factor Rose, I get 2(x - 1).

    Is Rose twice as old as Sam based on my work? No.
    Is Rose older than Tina? No.
    Reducing Sam, I get x + 1.
    Tina is x + 4.

    Is (x + 4) three years older than (x + 1)?

    I say yes. Answer is B. Correct? If correct, is my reasoning correct and sensible?
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  2. #2
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    Re: Rose, Sam and Tina

    No. Look at it this way:

    T = Tina, S = Sam, R = Rose

    Now:
    Tina = T
    Sam = T - 3 (Sam is 3 years younger than Tina)
    Rose = 2(T - 3) = 2T - 6 (Rose is twice as old as Sam)

    4 years later:
    Tina = T + 4
    Sam = T - 3 + 4 = T + 1
    Rose = 2T - 6 + 4 = 2T - 2

    Try again!
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  3. #3
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    Re: Rose, Sam and Tina

    Quote Originally Posted by DenisB View Post
    No. Look at it this way:

    T = Tina, S = Sam, R = Rose

    Now:
    Tina = T
    Sam = T - 3 (Sam is 3 years younger than Tina)
    Rose = 2(T - 3) = 2T - 6 (Rose is twice as old as Sam)

    4 years later:
    Tina = T + 4
    Sam = T - 3 + 4 = T + 1
    Rose = 2T - 6 + 4 = 2T - 2

    Try again!
    This is pretty much the same as what harpazo has done. All you forgot to do harpazo, is to define what x is. In your case, x = Tina's age now.


    Harpazo, I agree with your conclusion.


    (Note that Rose is older than Tina means 2x-2>x+4, ie x>6, so "Rose is older than Tina" is only true if Tina is currently older than 6. So the statement COULD be true, but not "MUST" be true as in the question.)
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  4. #4
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    Re: Rose, Sam and Tina

    Quote Originally Posted by harpazo View Post
    Today Rose is twice as old as Sam and Sam is 3 years younger than Tina. If all three individuals are alive 4 years from today, which of the following must be true on that day?
    1. Rose is twice as old as Sam.
    2. Sam is 3 years younger than Tina.
    3. Rose is older than Tina.

    A. 1 only, B. 2 only, C. 3 only, D. 1 and 2, E 2 and 3

    Answer is B. Correct? If correct, is my reasoning correct and sensible?
    Whereas one example does prove any of those statements, one example can disprove some of the statements.
    Consider: Rose is six. Sam is three, and Tina is six. That set satisfies all the given conditions.
    Now four years from today: Rose will be ten. Sam will be seven, and Tina will be ten.
    In this example Rose is not older than Tina four years from today. Therefore, #3 is false. Moreover, it shows #1 is false.

    You, harpazo, have proven #2 must be true in all cases.
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  5. #5
    Super Member harpazo's Avatar
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    Re: Rose, Sam and Tina

    Quote Originally Posted by DenisB View Post
    No. Look at it this way:

    T = Tina, S = Sam, R = Rose

    Now:
    Tina = T
    Sam = T - 3 (Sam is 3 years younger than Tina)
    Rose = 2(T - 3) = 2T - 6 (Rose is twice as old as Sam)

    4 years later:
    Tina = T + 4
    Sam = T - 3 + 4 = T + 1
    Rose = 2T - 6 + 4 = 2T - 2

    Try again!
    Is this not what I said?
    Last edited by harpazo; Feb 3rd 2019 at 07:15 AM.
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  6. #6
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    Re: Rose, Sam and Tina

    Quote Originally Posted by harpazo View Post
    Is this not what I said?
    YES...I should have read your post in full...
    A thousand apologies of which you may have one.
    Plus I will go stand in the corner for T+4 minutes.
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  7. #7
    Super Member harpazo's Avatar
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    Re: Rose, Sam and Tina

    Thank you everyone.
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