<p>Freaking triangles man. Thanks Silver! :)</p>
<p>Hey guys! Back at it again. And yes, it’s another triangle question. :(</p>
<h1>7, pg. 415</h1>
<ol>
<li>Two sides of a triangle each have length 5. All of the following could be the length of the third side EXCEPT…</li>
</ol>
<p>A. 1</p>
<p>B. 3</p>
<p>B. 4</p>
<p>D. sqrt50</p>
<p>E. 10</p>
<hr>
<p>Answer: E. </p>
<p>Now, I’m almost sure there’s some sort of rule where x side cannot be larger than y+z sides or something, but I honestly cannot think straight right now due to extreme dizziness, and so it’d be awesome if you guys could help me out.</p>
<p>The rule is:</p>
<p>The value of any one side of a triangle cannot 1) exceed the sum of the two other sides or 2) be less than the difference of the other two sides.</p>
<p>In this case, the sum of the other two sides is 10. The difference of the two other sides is 0. The length of the 3rd side falls between 0 and 10, non-inclusive. </p>
<p>A - C all check out.
D checks out - think about it. sqrt49 = 7. sq50 ≈ 7.
E is the right answer.</p>
<p>
</p>
<p>your number of posts on CC. :)</p>
<p>Or stated differently … For any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.</p>
<p>Thank you so much!
Two more:
</p>
<p>The answer is 90, but I got 60.
I know this problem is a bit difficult to figure since I didn’t offer a drawing, but it wasn’t drawn to scale anyway. :p</p>
<p>
[quote]
16. A four-digit integer, WXYZ, in which W, X, Y, and Z each represent a different digit, is formed according to the following rules.</p>
<ol>
<li>X = W + Y + Z</li>
<li>W = Y +1</li>
<li>Z = W - 5</li>
</ol>
<p>What is the four-digit integer?
[quote]
</p>
<p>I honestly don’t know how to do this at all. At first I tried to set everything in terms of Y for rule 1, but each time I get stuck with two letter variables. Then I tried to use elimination, but that didn’t work out too well as I was still stuck with two letter variables.</p>
<p>16 is a system of equations. A really hard one at that.</p>
<p><a href=“http://talk.collegeconfidential.com/sat-preparation/774569-some-bb2-questions.html[/url]”>http://talk.collegeconfidential.com/sat-preparation/774569-some-bb2-questions.html</a></p>
<p>See post 3 and the last ones.</p>
<p>If there is one thing I’ve learned from #16, it is to step back and look at the grand scheme of things rather than just diving straight into the problem.</p>
<h1>16 is as much of a logic game as it is an addition/subtraction game.</h1>
<p>Silverturtle presented a truly elegant solution to #16. But here are my own pointers for solving #16 and all related problems. </p>
<p>Logic: Don’t dive into the problem - analyze the problem. Read in between the lines!</p>
<p>1) Z = W - 5 -----> W is equal to or greater than 5. Remember, Z CANNOT be negative (that would make no sense).</p>
<p>2) W = Y + 1 -----> Y is equal to or greater than 4. Look at the above equation again. W is at least 5. For that to happen, Y must be at least 4. </p>
<p>3) Given the above pieces of information, it’s time to plug-and-chug. Or, one could do what silverturtle did and derive the equation 3y - 3 = X. </p>
<p>I don’t know if it is coincidence or not, but the answers are:</p>
<p>W = 5 - note how the answer exactly equals 5!
X = 9
Y = 4 - note how the answer exactly equals 4!
Z = 0</p>
<p>As xiggi said, the SAT writers reward ingenuity. Perhaps the writer of this question was trying to reward those people who didn’t start attacking the problem mathematically, </p>
<p>
</p>
<p>I offered a solution that was previously posted on CC. I would solve this problem a bit differently and “look” at the equations (but not mess with them)</p>
<p>Starting with X = W + Y + Z, I would use the smallest digit for Z, namely zero. This gives me two numbers and … 5XY0. Since Y is W-1, it becomes 5X40. Since X is total of WYZ, it is 9. Answer is 5940.</p>
<p>Fwiw, you could also have started with the fact that W has to be AT LEAST 5 and Y at least 4. However, W cannot be 6 because Y would be 5 and X = W + Y + Z would be impossible. This means that W has to be 5!</p>
<p>Wow, thanks guys so much!</p>
<p>I still do not understand number 17 though, even after reading the solutions.</p>
<p>Edit: Actually, never mind. Man, this Benadryl is really making me more stupid than usual. :p</p>
<p>17) The length of the bottom is 30. </p>
<p>The length of each side of the equilateral triangles is 20. </p>
<p>The perimeter of the depression on the left is 20. </p>
<p>30 + 20 + 20 + 20.</p>
<p>Yeah, I understand it now. The reason I was making a mistake was because I kept thinking each side was 10. 
</p>
<p>Thanks again!</p>
<p>^No problem :).</p>