# Thread: New and clever SAT problem

1. ## New and clever SAT problem

For your solving minds...  Reply With Quote

2. Nobody seems to have bitten yet, so I say  Reply With Quote

3. Well, (a) that's not an answer option and (b) it's not the case. There is a specific value for b.  Reply With Quote

4. 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...  Reply With Quote

5. 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  Reply With Quote

6. http://www.wolframalpha.com/input/?i...t+does+b+equal

wolframalpha could not get it either   Reply With Quote

7. 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:  Reply With Quote

8. I'm not sure that you have told us what is the value of b, which is the original question!  Reply With Quote

9.  Reply With Quote

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.  Reply With Quote

11. 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.  Reply With Quote

12. Originally Posted by kweaver 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?  Reply With Quote

13. 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.  Reply With Quote

14. 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.  Reply With Quote

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