<p>1) <a href="http://i.imgur.com/fykNin3.png%5B/url%5D">http://i.imgur.com/fykNin3.png</a>
2) <a href="http://i.imgur.com/RR6G7K7.png%5B/url%5D">http://i.imgur.com/RR6G7K7.png</a></p>
<p>Can someone explain how to do them?
Thanks in advance</p>
<p>1) Since the triangle is equilateral NP = 4. Now just look at the formula for a 30, 60, 90 triangle to see that the measure of angle NOP is 30 degrees, choice (B).</p>
<p>For the first one:
Triangle NOP is a 30-60-90 triangle, with the answer (the angle NOP) being (B) 30 degrees. To recognize a lot of SAT math questions related to triangles, you should familiarize yourself with the Pythagorean triples in addition to the length-angle ratios of the two classic right triangles (i.e. 1-1-sqrt(2) 45-45-90 and 1-2-sqrt(3) 30-60-90).</p>
<p>For the second one:
Multiply 25 by 40. This will give you the sum of the ages of the 25 managers. Multiply 30 by 43. This will give you the sum of the ages of the 30 managers. Subtract the first product from the second. This provides the sum of the years of the 5 managers that were added onto the original 25. Divide the difference by 5 to get the average age of the 5 additional managers.</p>
<p>2) Use the strategy of changing averages to sums: </p>
<p>The answer is then (30<em>43 - 25</em>40)/5 = 58, choice (D).</p>
<p>I will be talking about this strategy in more detail soon in my thread “SAT Math Strategies.”</p>
<p>For the 2nd question incase you don’t see the formula you can plug in the answers (start with choice C, like Steve’s tip says) and do 25X40 + 5X(plugged in answer) and divide all that by 30 to see if you get 43.
When plugging in C you’ll get 42.5, then its pretty obvious it will be D, but plug it in just in case and it works :)</p>
<p>Very nicely explained Tomer. In fact, in most multiple choice questions involving averages you can use either of these two strategies. “Changing averages to sums” is generaly the best choice in these situations, but “Starting with choice (C)” is effective as well. Even if you do the first strategy, then plugging the answer you got back in is a nice way to “check” your answer to ensure that you didn’t make a careless error.</p>
<p>I will again offer a slightly different opinion about the plugging in. This is NOT a good case for plugging in, and in fact, there are very few questions that are better solved by using this method. I cling to the notion that the plug-in is far from being an optimal method. And why I’d use it very sparingly. </p>
<p>A. In this case, this is how I solve it, but that is by using a technique that is very simple to apply but a tad difficult to explain. </p>
<p>Here is what MY paper looks like:
+? 3 (that comes from 43-40)</p>
<h1>Diff? 1/6 (that comes from 5/30)</h1>
<p>A = 40 + 18 = 58</p>
<p>What that means is that an increase of 3 in average was contributed by 1/6 of the group. This also means that the average age of that new group is 3 x 6 higher, or 18. Answer is 40 + 18 or 58.</p>
<p>B. This is how I would make a beginner SATer solve it, by following the narrative and avoiding equations. This works because the SAT gives such EASY numbers that this can be done in your head and by writing down the essential numbers. There is no need for a calculator here.</p>
<p>Current Total = 40 x 25 = 1000
New Total = 43 x 30 = 1290
Average New = 290/5 = 58.</p>
<p>Fwiw, this is not very different from DrS’ equation, just a bit more idiot-proof! And is also what ChewyDog did. </p>
<p>C. In both cases, anyone should be DONE with the problem by the time the plugger decides on which one to pick since the two methods above take about 10 to 20 seconds.</p>
<p>I would like to defend the strategy of plugging in, while attempting to remain objective at the same time. </p>
<p>First let me say that I agree with Xiggi that plugging in is generally not the best strategy for statistics problems involving averages. “Changing averages to sums” is a much better strategy in this case - it’s quicker and can be internalized pretty quickly with just a little practices. I always start out by teaching students Xiggi’s method B. I would only have very advanced students do it in a single computation, and even then only after I’m certain they are comfortable with the method.</p>
<p>Now back to my defense of plugging in. I think it is an important startegy to learn for the following reason:</p>
<p>(1) There are a few SAT problems that come up where it actually is the most efficient method - see my “SAT math strategies” thread for a few examples.</p>
<p>(2) It’s a fantastic “fallback” method. You can often use this method when you aren’t comfortable with a quicker method.</p>
<p>(3) It’s a fantastic way to “check” your answer. When “checking” over your answers you should always re-solve the problem from the beginning wthout looking at your previous solution. Ideally you want to use a different method from the first time. If you can plug in, then use this method the second time around.</p>
<p>(4) It’s the preferred method for lower scoring students - I tend to really emphasize techniques like this for students currently scoring below a 500. These students can often answer a lot more questions when they have basic techniques like this at their disposal. Yes, it sometimes takes longer, but who cares? These students do not have to get to the end of each section (in fact getting there will probably hurt their score), so they have lots of time to plug in.</p>
<p>For the record, I plug in quite often, its pretty fool proof and saves me the time to re-check (cuts out with the extra time i’m wasting plugging in). I usually get 0-2 mistakes per test (and usually dumb ones). Then when i’m done with it I just re-do every question that took me some extra time/ I plugged in and check to see how i’d solve it quicker or with an equation or something.</p>
<p>^^</p>
<p>Well, let me also answer, and try to remain objective. First of all, there is not a single better method to solve a problem. Different people use different strategies, and that is based on different aptitudes. That is the beauty of the SAT in that it does NOT follow a dogmatic method a la HS Math. Some problems can be solved by mere logic or by merely “seeing” the problem. </p>
<p>There is, however, one persistent issue and that it is to benefit for a student to solve the problems fast and accurately. In this sense, relying on circular methods (which plugging is) comes at an expense in the form of time. </p>
<p>And, fwiw, Tomer, if you routinely only make 1-2 mistakes, you should be able to SOLVE the problem without having to use a PR routine that was developed for the average scorer. </p>
<p>All in all, I am NOT discrediting the plug method to the extent of never using it. I know there are times I use the method or better stated a variance of the method because my plug choice will not be based on a strict “start with C” but with an educated guess. Without going into details, my choice is rarely the C, but it highly depends on my reading of the problem.</p>
<p>I actually agree with everything in Xiggi’s last post. I want to just emphasize something in the “start with choice (C)” strategy as stated by me. Let me just quote part of text from the strategy:</p>
<p>“Unless you have some intuition as to what the correct answer might be, then you should always start with choice (C) as your first guess (exceptions will be the topic of the next strategy).”</p>
<p>The thing is that Xiggi uses an educated guess as opposed to starting with choice (C) most of the time he plugs in numbers (as do I) because he has a strong number sense and excellent mathematical intuition. The beginning of the first sentence above in the strategy itself suggests that you follow Xiggi’s lead on this approach. But there is a reason I emphasize starting with (C). And that is because the average math student’s mathematical intuition is much lower and can’t always be counted on, especially in a high stress testing environment. </p>
<p>Also Tomer, let me take Xiggi’s advice one step further. During your SAT math practice whenever you solve a problem by starting with choice (C) (or one of the other very basic strategies), start trying to solve the same problem at least one more way. Then decide for yourself which method is the best. As you do this with more and more problems you may start to become more comfortable with more advanced techniques.</p>
