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Thread: New and clever SAT problem

20180415, 23:14 #1
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New and clever SAT problem
For your solving minds...

20180417, 12:19 #2
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Nobody seems to have bitten yet, so I say
BATcher
Existence is useful.

20180417, 12:24 #3
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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.

20180424, 06:46 #4
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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 rearranges to:
x^2(4a  1) + x(4a4b) = 0
and the solution for x is that it equals 0 or (4a4b)/(4a1). 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(4a1) + x(4a4) == 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; 20180424 at 06:48.

20180424, 11:01 #5we know a must be 1/4
I used to be good at this sort of thing
The stein is BACK
(4x+4)(ax1)x^2+4=bxLast edited by wavy; 20180424 at 11:12.
David
Just because you don't know where you are going doesn't mean any road will get you there.

20180424, 11:17 #6
http://www.wolframalpha.com/input/?i...t+does+b+equal
wolframalpha could not get it eitherDavid
Just because you don't know where you are going doesn't mean any road will get you there.

20180424, 13:05 #7
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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:

20180424, 13:17 #8
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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
Existence is useful.

20180424, 13:35 #9
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Last edited by kweaver; 20180424 at 13:38.

20180531, 13:16 #10
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.

20180531, 17:08 #11
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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.

20180601, 09:09 #12

20180603, 16:47 #13
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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.

20180604, 09:21 #14
Of course, you can't just eliminate the constants and the x^2 terms; you have to eliminate them in a mathematicallyvalid way. I'm sure you know that; I just thought I would point it out.