<p>Okay, I'm stuck on 3 problems in the Blue Book - page 721 #'s 15,17,18...if anyone can be kind enough to explain to me how to solve them I'd greatly appreciate it. Thanks again</p>
<p>Can you post the problems?</p>
<ol>
<li><p>If x² - y² = 10 and x + y = 5, what is the value of x - y?</p></li>
<li><p>For all positive interegers j and k, let j [R] k be defined as the whole number remainder when j is divided by k. If 13 [R] k = 2, what is the value of k?</p></li>
<li><p>The average (arithmetic mean) of the test scores of a class of p students is 70, and the average of the test scores of a class of n students is 92. When the scores of both classes are combined, the average score is 86. What is the value of p/n?</p></li>
</ol>
<h1>15 tests your knowledge of the common binomial product (x+y)(x-y)=x^2 - y^2 (read: x squared minus y squared). This is called the ** difference of squares**.</h1>
<p>So if x+y = 5 and x^2 - y^2 = 10 then x-y = 2.</p>
<p>If the first 2 sentences I wrote sounds completely strange to you, get a book or take a class on Algebra and it will make sense. For the SAT, you will benefit TREMENDOUSLY from knowing basic Algebra things like the difference of squares, factoring, quadratics, etc. I myself didn't know these basic ideas up until last year... I actually learned the common binomial products from Barron's How to Prepare for the SAT. I would recommend that book for basic SAT knowledge. It was very helpful and easy to understand. </p>
<h1>17. This one really explains itself. The SAT usually has 1 or 2 problems that involve some made-up notation/symbol that they define for you. You won't know the symbols before the test, because the SAT made it up. You have to read and decipher the meaning of the symbol. In this case, they tell you the</h1>
<p>j [R] k = the remainder when j is divided by k. E.g, 5[R]2 = 1</p>
<p>You know 13[R]k = 2, so k must be a number that will divide 13 with two left over. That number is 11. </p>
<h1>18. This is the hardest one you mentioned. It requires you understand the concept of average (sum of things)/(over number of things). If you understand that and how to solve an equation, and don't get confused, it will be easy:</h1>
<p>The sum of the scores of p students = 70p </p>
<p>The sum of the scores of n students = 92n </p>
<p>Now when you combine those sums, and divide them by the total number of students (p+n), you will get 86... translating into algebra:</p>
<p>70p + 92n/p+n = 86
multiply both sides by p+n, use distributive property:
70p + 92n = 86(p + n)
70p + 92n = 86p + 86n
subtract 70p, 86n</p>
<p>6n = 16p
therefore, p/n = 6/16 which reduces to 3/8. It is NOT 8/3 (n is more than p...)</p>
<p>Hope this helped!</p>
<p>Thanks a lot for the quick response! It helped a lot. Just wondering...is there a trick to doing the last problem or is that the only way?</p>
<p>That's the way I would do it, too.</p>
<p>Alternate ways:</p>
<p><a href="http://talk.collegeconfidential.com/showthread.php?t=85528%5B/url%5D">http://talk.collegeconfidential.com/showthread.php?t=85528</a>
(start at post #8)</p>
<p>the "other ways" are actually the same as this one, just explained differently...and more confusingly ;-)</p>
<p>heh heh ya the last one's tricky.</p>
<p>I need help answering this sat question. If 10#H is 98 What is H?</p>