I'm looking at and have a bit of a problem with data sufficiency question 94, of page 281 of the 12th edition of the official GMAT review where it says:
If line k in the xy-plane has equation y= mx + b, where m and b are constants, what is the slope of k?
(1) k is parallel to the line with equation y= (1-m)x + b + 1
Apparently the answer says that statement (1) alone is sufficient because the slope of line k and the other line are the same since the two lines are parallel, and thus m= 1 - m, and therefore m= 1/2.
I understand that the two lines will have the same slope since they're parralell, but does no one else see the impossibility of setting m = 1-m ??
If m is a constant or variable, it cannot possibly equal 1 minus itself, no?
That's like saying 5 = 1 - 5.
m = 1 -m
add m to both sides: 2m = 1
divide by 2 to both sides: m = 1/2
the equation holds only for 1/2, not any value. Plug in 1/2 into the equation and you see it holds true.
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