<p>From the Barron’s book:</p>
<p>Given the statement “All girls play tennis,” which of the following negates this statement?</p>
<p>(A) All boys play tennis.
(B) Some girls play tennis.
(C) All boys do not play tennis.
(D) At least one girl doesn’t play tennis.
(E) All girls do not play tennis.</p>
<p>The correct answer is D, which makes sense, but why couldn’t it be E?</p>
<p>Maybe it’s because D is the choice that would directly negate the statement “All girls play tennis”. If one girl does not play tennis, then the statement is untrue at once. Choice E is also very absolute. I’m not sure if that made any sense, but it’s the way I see it. Then again, I do agree with you that E does work, but the SAT always wants you to pick the better answer.</p>
<p>Choice E describes only a single circumstance in which the original statement is not satisfied. It’s possible for the original statement and choice E to be false simultaneously (for example, if half the girls play tennis).</p>
<p>Only choice D captures all possible circumstances under which the original statement is false.</p>
<p>Thanks nilkn. That makes sense.</p>
<p>I have another question (from the Kaplan book).</p>
<p>If 3^n = n^6, n^18 =</p>
<p>(A) 3^n * n^3
(B) 3^n * n^12
(C) 9^n
(D) 3^3n
(E) 3^(n+12)</p>
<p>The correct answer is B. But suppose I cubed n^6, which = (n^6)^3 = n^18, and I did the same to 3^n, which = (3^n)^3 = 3^3n, then wouldn’t D be correct as well?</p>
<p>D would not be correct because you would have to cube 3 as well.
Simply put they just multipied each side by N^12 and therefore B is correct.</p>
<p>I thought (x^a)^b = x^ab? Am I missing something?</p>
<p>(X^a)^b=(X^b)^ab</p>
<p>So if x, a, and b = 2, (2^2)^2 = (2^2)^4?</p>
<p>Foil, I think your rule looks right to me - (x^a)^b = x^ab. Thats how I learned it.</p>
<p>But when i take (3^n)^3 i get 27^n on my TI-89
it basically takes 3^3 and the n remains</p>
<p>that helped me too… thanks for the question</p>
<p>I’m fairly sure that question is flawed. Foil’s rule is correct. I solved the equation numerically, calculated n^18, and compared it to the values of 3^n * n^12 and 3^3n (answer choices B and D respectively)–both were equal to the value of n^18. If you want to try it yourself, n = -0.855075082.</p>