<p>Page 182 of Princeton Review's 2012 Cracking the SAT. Their page long example to illustrate factoring quadratics is this:</p>
<ol>
<li>In the expression x^2 + kx + 12, k is an integer and k <0. Which of the following is a possible value of k?
A) -13<br>
B) -12<br>
C) -6<br>
D) 7<br>
E) It cannot be determined from the information given</li>
</ol>
<p>They then go into a long winded explanation of why the answer is A.</p>
<p>Uh, excuse me??? Why can't k be any negative integer? The answer is E.</p>
<p>I think they meant to say "In the equation x^2 + kx + 12 = 0, k and x are integers...". </p>
<p>Am I missing something obvious here? Did the PR ask ANYBODY mathematically inclined to review for errors???</p>
<p>k can’t be a negative integer because that was a condition given in the question.</p>
<p>No. The question reads “k is an integer and k < 0”. k IS a negative integer! That’s all we know the way the question reads! Therefore, it could be ANY negative integer, unless more conditions are laid out for us. Merely writing out a quadratic expression is not a condition. An equation is needed. In this case, an equation is needed AND an additional restriction that x is an integer is needed. If we don’t say x has to be an integer, then you could just use any negative integer value for k along with the quadratic formula (assuming b^2 - 4ac > 0).</p>
<p>One thing that I’ve noticed is that SAT prep books (with the exception of the blue book) are not infallible. The Kaplan PSAT also has a very blatant math error, which didn’t help when I was taking the pre-test. The Barron’s math workbook is so terribly unedited that there was probably at least one error for every one or two sets of practice problems. Another thing about Kaplan, their big book of 12 practice tests actually has a lot of questions copied directly from the BB, maybe with a few words changed. The lesson here is that a lot of the prep books out there aren’t as well edited as they should be, and some are just downright awful.</p>
<p>Does it say root or something like that in the question?</p>
<p>Oh i meant so say “can” lol</p>
<p>I realize that many of the prep books have errors of various kinds. This one struck me as just inexcusably bad because they went on for a full page in the book discussing it and using it as an example of how to tackle a quadratic problem. And it wasn’t just a minor typo. They omitted 2 important conditions necessary to answer the problem. PR is making $millions off this book selling it all over the world! I grabbed my copy off a high stack in a Bangkok bookstore. It just boggles the mind that either: (1) they didn’t even bother to ask a few people to read over everything looking for mistakes, or (2) they were too cheap to hire the types of people (teachers, professors) who should have checked it instead of those who they did hire (interns?).</p>