<p>This question was taken from a Blue Book test. I gave the answer E, but the correct choice was C.</p>
<p>My question is, how can we assume that the linear function doesn't have a constant, if f(x) is never expressed? How can the question simply assume f(x) = 0 when x = 0? A quick google search defines a linear function as simply being a straight line; nothing to do with the y-intercept or x-intercept.</p>
<p>In terms of test-taking, you could assume f(0) = 0 since the answer should be the same no matter what a and b are (provided f is linear). But 1 is halfway between 0 and 2, so 24 should be halfway between a and b, so a+b = 48.</p>
<p>In general on the SAT, if you can make up an example that fits the given parameters of the problem, go ahead and do it. My laziest students make the function a horizontal line! So they are using the points (0,24) (1,24) and (2,24). You can’t say that their example isn’t linear! And 24 + 24 = 48.</p>
<p>That’s true. It just feels so sneaky and unfair, though, for the test to include an option for “Not enough info to determine answer.”. It seems deliberately misleading to the test-taker; not only do they have to determine the answer, if they are unable to derive one, then they have to determine whether an answer exists or not. I’m certain that if that option was not there, I would have had no choice but to try harder to obtain/justify an answer, or at worst, skip the question.</p>
<p>I don’t think choice E is sneaky/misleading. However it does make it more difficult to justify randomly plug in numbers, since 48 is a correct answer, but you’d have to determine whether another correct answer exists. However in this case you can provably show that 48 is the only correct answer, hence C.</p>
<p>Very rarely is “it cannot be determined” the correct answer (from my POV) but I remember on my last SAT that “it cannot be determined” was one of the correct answers, and that problem almost tripped me up.</p>