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  1. #1
    Silver Lounger kweaver's Avatar
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    New and clever SAT problem

    For your solving minds...
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  2. #2
    Super Moderator BATcher's Avatar
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    Nobody seems to have bitten yet, so I say
    BATcher

    If you mention Botox nowadays nobody raises an eyebrow...

  3. #3
    Silver Lounger kweaver's Avatar
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    Well, (a) that's not an answer option and (b) it's not the case. There is a specific value for b.

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    I am puzzled: I can work out that setting b to one of those values makes the expression simple (and I know which one), but cannot see why it has to be so. It all boils down to the exact meaning of the phrase "is equivalent to bx". If that means simply numerically equivalent, then (surely?) the equation re-arranges to:

    x^2(4a - 1) + x(4a-4-b) = 0

    and the solution for x is that it equals 0 or -(4a-4-b)/(4a-1). So 'b' can have any value we like. But that is clearly not what the puzzler intends. If 'equivalent' means 'algebraically equivalent' (if that is a valid term), then
    x^2(4a-1) + x(4a-4) == bx
    and then


    Maybe I need to go and read some SAT test rules, but I don't like this! I may have to accept I am just not clever enough. I am certainly not clever (or informed) enough to create a spoiler box as BATcher did - oh, I just found out something - who knew that option was there? (I did a reply with quote to see what Batcher had used).

    Martin

    PS Glad to see a puzzle here after so long. I do have one of my own I rather like...
    Last edited by mngerhold; 2018-04-24 at 06:48.

  5. #5
    Gold Lounger wavy's Avatar
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    we know a must be 1/4
    I am missing this
    I used to be good at this sort of thing
    The stein is BACK

    (4x+4)(ax-1)-x^2+4=bx
    Last edited by wavy; 2018-04-24 at 11:12.
    David

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    Gold Lounger wavy's Avatar
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    http://www.wolframalpha.com/input/?i...t+does+b+equal

    wolframalpha could not get it either
    David

    Just because you don't know where you are going doesn't mean any road will get you there.

  7. #7
    Silver Lounger kweaver's Avatar
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    This is, what I consider, an awful problem from the College Board. However, the "key" to solving this is realizing that "b" is a constant (one of the values in the answer choices) and is the coefficient of "x". Therefore, you have to clear everything on the left side of the equation EXCEPT for some number of "x" values.

    That means:

  8. #8
    Super Moderator BATcher's Avatar
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    I'm not sure that you have told us what is the value of b, which is the original question!
    BATcher

    If you mention Botox nowadays nobody raises an eyebrow...

  9. #9
    Silver Lounger kweaver's Avatar
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    Last edited by kweaver; 2018-04-24 at 13:38.

  10. #10
    WS Lounge VIP mrjimphelps's Avatar
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    x has to be -1, in order for b to be -3. If these are true, then you end up with -4a + 1 = 1 - 4a.

  11. #11
    Silver Lounger kweaver's Avatar
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    Since the problem stated that the expression equals "bx" you're then looking for the coefficient of the "x" term. When you expand the problem, the -4 and +4 cancel. That, I suspect, was the College Board's attempt at a clue. The x^2 terms must also be eliminated because the expression = "bx" and there are no x^2 terms.
    So, if 4ax^2 - x^2 must = 0 then, 4ax^2 = x^2 and 4a = 1, so a = 1/4. Consequently, 4ax - 4x becomes 4(1/4)x - 4x = x - 4x = -3x; therefore, b = -3.

  12. #12
    WS Lounge VIP mrjimphelps's Avatar
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    Quote Originally Posted by kweaver View Post
    Since the problem stated that the expression equals "bx" you're then looking for the coefficient of the "x" term. When you expand the problem, the -4 and +4 cancel. That, I suspect, was the College Board's attempt at a clue. The x^2 terms must also be eliminated because the expression = "bx" and there are no x^2 terms.
    So, if 4ax^2 - x^2 must = 0 then, 4ax^2 = x^2 and 4a = 1, so a = 1/4. Consequently, 4ax - 4x becomes 4(1/4)x - 4x = x - 4x = -3x; therefore, b = -3.
    Are you sure you aren't making an unjustified assumption here about simply eliminating the x^2 terms?

  13. #13
    Silver Lounger kweaver's Avatar
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    Don't think so. Since the expression was equal to "bx", you need to convert the expression to have only an "x" variable. That means eliminating the constants and the x^2 terms.

  14. #14
    WS Lounge VIP mrjimphelps's Avatar
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    Of course, you can't just eliminate the constants and the x^2 terms; you have to eliminate them in a mathematically-valid way. I'm sure you know that; I just thought I would point it out.

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