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Math Help - Another SAT Question

  1. #1
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    Another SAT Question

    for all numbers x and y, let the operation # be defined as x#y=x-xy. If a and b are positive integers, whuich can be equal to zero?

    1) a#b
    2) (a+b)#b
    3) A # (a+b)


    1 only
    2 only
    3 only
    1 and 3
    1 and 2
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  2. #2
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    Re: SAT question

    Quote Originally Posted by RK29 View Post
    for all numbers x and y, let the operation # be defined as x#y=x-xy. If a and b are positive integers, which can be equal to zero?

    1) a#b
    2) (a+b)#b
    3) A # (a+b)


    1 only
    2 only
    3 only
    1 and 3
    1 and 2
    What have you tried?

    Where are you stuck?
    Last edited by SammyS; August 13th 2011 at 07:33 PM.
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  3. #3
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    Re: SAT question

    well, i tried each option but non of them give me zero. I used number 4 for a and 2 for b
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  4. #4
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    Re: SAT question

    Just picking any two numbers to plug in, virtually never gets the job done --- especially for this problem.

    For a#b:
    Use the definition of a#b, set it to zero & solve for a and/or b.

    a-ab = 0

    a(1-b) = 0

    What are the solutions?
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  5. #5
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    Re: SAT question

    Quote Originally Posted by SammyS View Post
    Just picking any two numbers to plug in, virtually never gets the job done --- especially for this problem.

    For a#b:
    Use the definition of a#b, set it to zero & solve for a and/or b.

    a-ab = 0

    a(1-b) = 0

    What are the solutions?
    i have a=0
    and b=1

    how does that help me to get my solution. I am not getting a clear picture
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  6. #6
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    Re: Another SAT Question

    Quote Originally Posted by RK29 View Post
    for all numbers x and y, let the operation # be defined as x#y=x-xy. If a and b are positive integers, whuich can be equal to zero?
    1) a#b
    2) (a+b)#b
    3) A # (a+b)
    Here is a huge hint: \left( {\forall x} \right)\left[ {x\text{*} 1 = 0} \right]. (*=#)

    BTW: 0 is not a positive integer.
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  7. #7
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    Re: SAT question

    Quote Originally Posted by RK29 View Post
    i have a=0
    and b=1

    how does that help me to get my solution. I am not getting a clear picture
    Those are two independent solutions. In other words: Either a=0, OR b = 1, will ensure that a#b = 0. As Plato points out, 0 is not positive, so that leaves you with b=1. Of course (check for yourself) if b = 1, then a can be any (positive for this problem) number.

    So you know that 1) can be equal to zero.

    Now try 2) and 3) .
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  8. #8
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    Re: SAT question

    x#y= x- xy= x(1- y). In order to be 0, either x= 0 or y= 1.

    1) a#b. x= a, b= y. a cannot be 0 but b can be 1.

    2)(a+ b)#b. x= a+ b, y= b.

    3)a#(a+ b). x= a, y= a+ b. Remember that a and b must be positive integers.

    This looks to me exactly like your previous "SAT question".
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