<p>ohhkay is it me or are there 2 answers for this question??</p>
<p>An integer is subtracted from its square. The result could
be which of the following?
(A) A negative integer.
(B) An odd integer.
(C) The product of two even integers.
(D) The product of two odd integers.
(E) The product of two consecutive integers.</p>
<p>I guess that either the question shud say "must" instead of "could" or both c and e are correct..</p>
<p>Am I right?!</p>
<p>Correct, if “could” is in the question, C and E are both correct. If it’s “must,” then only E is correct. What test preparation source is this from?</p>
<p>Wait a second…</p>
<p>“An integer is subtracted from its square.” That’s x^2 - x, or x(x -1).</p>
<p>Now, if the integer, x, is odd, then (x-1) will be even. And if the integer, x, is even, then (x-1) will be odd.</p>
<p>So B is out. x(x-1) is the product of an odd integer and an even integer, so x(x-1) is even.</p>
<p>Similarly, C and D, “the product of 2 even integers” and “the product of two odd integers,” are out.</p>
<p>And A is out. If the integer, x, is negative, then x^2 is positive, and x^2 - x is something positive minus something negative, which must be positive. If the integer, x, is 0 or 1, then x^2 - x = 0. And if the integer, x, is greater than 1, then x^2 > x, so x^2 - x > 0.</p>
<p>The answer is E.</p>
<p>Yes… But 9^2-9, for example, is 72 which is also the product o 36*2 (2 even nbs)
Sooo… ? </p>
<p>@rspence, this is from
<a href=“http://www.erikthered.com/tutor/sat-math-hard-practice-quiz.pdf[/url]”>http://www.erikthered.com/tutor/sat-math-hard-practice-quiz.pdf</a></p>
<p>It looks pretty tustworthy though… What do u think</p>
<p>Btw they solved it in a way similar to urs, @sikorsky.</p>
<p>It said:
Suppose that the integer is n. The result of subtract-
ing n from its square is n2 − n = n(n − 1), which is
the product of two consecutive integers, so answer E is
correct.
Notice that if you multiply any two consecutive integers,
the result is always even, since it is the product of an
even integer and an odd integer. To win an Erik The
Red Viking Hat, see if you can determine why the result
is never a negative integer.</p>
<p>Which I think wud be true if the question said “must”…</p>
<p>Oh, of course. I see your point.</p>
<p>The question ought to say must instead of could.</p>
<p>But since I did explain why the result can never be a negative integer, does somebody owe me a Viking hat?</p>
<p>Yes, but for example, if x = 8, 8^2 - 8 = 56. 56 can be written as the product of two even integers (e.g. 2 and 28). It doesn’t matter if the test-makers were expecting you to obtain x(x-1) which isn’t explicitly written as a product of two even integers…the bottom line is that 56 can be written as the product of two even integers.</p>
<p>Edit: Sorry I posted this at the same time as the previous two posts, didn’t get to read them first</p>
<p>And yes it says “could.” Shame shame shame.</p>
<p>@2200andbeyond, even though it “looks” trustworthy with its fancy LaTeX font, looks and title names can be deceiving. lots of people (including myself) have caught mistakes in Kaplan and Princeton Review books.</p>
<p>ok ok… ppl make mistakes… It’s ok… :)</p>
<p>I owe u a Viking hat @sikorsky… :D… mm… why the hell wud u want that for?! :P</p>
<p>btw, can u guys help with Nov 2012’s math? does anyone know where i can get that?
I found it especially hard! Although i was usually doing well on math secs! </p>
<p>and thanks! :D</p>
<p>Well, just by graphing, x^2 - x is negative only when -1 < x < 0, so therefore non-negative on all integers. +1 Viking Hat</p>
<p>About mistakes, yes people do make them, but no one’s going to buy a test preparation book with lots of mistakes…</p>
<p>I can help you with Nov 2012 math problems, but I also don’t know where to find them. Don’t know if I can obtain them either.</p>
<p>do u know someone who can?</p>