<p>So the question is: </p>
<p>If d + e = 27, f= 13-e, and f= 20-d, what is d+e+f? (Grid-in Question btw) </p>
<p>I know theres an easy way to solve this but I can't seem to get it :/</p>
<p>Rearrange the equations to put all the variables on one side:</p>
<p>d + e = 27
e + f = 13
d + f = 20</p>
<p>Now add all three equations:</p>
<p>2d + 2e + 2f = 60</p>
<p>Divide both sides by 2:</p>
<p>d + e + f = 30.</p>
<p>The most brute-forcey way would be to plug it in your ti84 or 89 as a augmented matrix and use the rref function. But I think solving it the way above would actually save you a few seconds.</p>
<p>Oh I see! haha I really suck at basic algebra problems. Thank You both! :D</p>
<p>6th, this one is tricky because it really relies not only on learned math skills, but also on some mathematical intuition–of which I usually have very little. The thing that prompted me to do it this way was noticing that a different variable was missing from each equation, which would leave me with 2 d’s, 2 e’s and 2 f’s. Another clue is that they asked only for (d + e +f) rather than d or e or f.</p>
<p>Where did you find this problem, anyway?</p>
<p>hm I thought it looked easy because of they’ve already given you half the answer 
But I really liked your method! I guess you can apply the same “mathematical intuition” for similar algebraic manipulation problems too right? </p>
<p>And this problem was in my 3rd SAT diagnostic test (Princeton Review), Section 3, question #14.</p>
<p>That kind of figures, because the most efficient way to do this problem is not to do what we taught you in algebra class (i.e., find d, e and f), but rather to solve for (*d *+ *e *+ f). Princeton Review is all about finding a way to take the test that’s smarter than what your teachers taught you in school.</p>
<p>This is a standard SAT math strategy. In my book I call it “trying a simple operation.” In this particular problem the simple operation is addition. A hint that addition will work is given by the form of what they’re asking for…in this case it’s d + e + f. If addition didn’t work, then subtraction would almost certainly work.</p>
<p>For what it’s worth, you could also do this like an Algebra I problem. You really don’t need anything more.</p>
<p>If f = 13 - e, and f = 20 - d, then 13 - e = 20 - d.</p>
<p>Rearrange: 13 + d = 20 + e.
So, d = 7 + e.</p>
<p>If d + e = 27,
then (7 + e) + e = 27.
2e + 7 = 27
e = 10</p>
<p>f = 13 - e = 13 - (10) = 3.</p>
<p>If d + e = 27, then
d + (10) = 27, so
d = 17.</p>
<p>d + e + f = 17 + 10 + 3 = 30.</p>
<p>^That’s how I did it. It really doesn’t take that much longer.</p>
<p>Using the strategy is MUCH quicker if you’re doing it right. Once you get good at it you can get the answer just by adding 27, 13 and 20, and then dividing by 2. This can be done in 5 to 10 seconds. </p>
<p>Doing the problem Sikorsky’s way will take most students at least 1 minute, and leaves more opportunities for computational errors.</p>
<p>Time is precious on the SAT! If you want to get a perfect or near perfect score, learn and practice the correct strategies.</p>
<p>Sikorsky’s way is not a bad way to do the problem. It’s just not the ideal way to do it to maximize your SAT score.</p>
<p>Oh I see. I’m still new at this so I guess learning a couple different strategies would be beneficial. ^^"</p>
<p>And I have another math question: </p>
<p>If the function f is defined by f(x) = 4x -1, then what is the value of 3f(x) + 2 ? </p>
<p>(A) 7x-4
(B) 7x-1
(C) 12x-4
(D) 12x-1
(E) 12x+2</p>
<p>^ 3(f(x))= 12x-3, add 2, and you get 12x-1. Answer choice D</p>
<p>@DrSteve: Are you criticizing Sikorsky’s original method, or his second method? His original method is very quick and leaves almost no room for error. Also, the second method could still be employed in <30 seconds by a skilled student–easily quick enough to finish the section early. (18 questions at 30 seconds = 9 minutes, leaving 16 minutes to spare for longer problems and reviewing answers). When a time difference between problem solving methods is so small, the effect really is negligible. I could understand changing a method that’s 3 minutes too slow, but 20 seconds? At that point, it really doesn’t matter. Both methods work.</p>
<p>Studious,</p>
<p>First let me be clear that I’m not criticizing either method. They are both good. I didn’t realize that Sikorsky gave both methods, so props for that. I am saying that the second method is quite inferior to the first. Here is a list of reasons why:</p>
<p>(1) I disagree with you that saving 20 seconds is negligible. 20 seconds for one problem is quite significant on the SAT. Imagine if you saved 20 seconds on each of 3 problems. That’s a whole minute! That’s enough time to do a whole other SAT problem. And if you’re applying SAT strategies throughout the whole test, you might save 20 seconds on 7 or 8 problems. That’s huge! Note that there are 2 ways to save time - one good and one bad. The good way to save time is by applying SAT strategies. The bad way to save time is by speeding up and not checking over answers.
(2) A really strong student can solve this particular problem both ways. But the same strong student might not be able to solve a seemingly different problem (but same strategy) the second way - especially if the problem involves multiplication or division. When solving a problem it is more important to learn the strategy that will work on many other problems. After all, this particular problem will most likely NEVER appear on an SAT again.
(3) The weak to average student will have A LOT of trouble with the second method. The first method however is quite straightforward after practicing it just a few times. And it comes up on the SAT ALL THE TIME in different forms.
(4) Most students are not very good in algebra and will take a very long time using the second method if they can even solve it that way at all.</p>
<p>By the way, for those of you going for a very high score (like 750 to 800), I recommend that you practice solving problems in multiple ways - using SAT specific strategies, and also using regular mathematics (as was done here), but on the SAT you should be using the second method here.</p>
<p>The one weakness that the strongest students have is that they tend to refuse to use strategies because they think they can do it just as easily the long way. It is almost impossible to get an 800 with this attitude. There are always 1 or 2 questions that will trick even the best students if they refuse to do this. These same students will always rationalize these mistakes as careless errors that they won’t make the next time. Well they wouldn’t if that same problem appeared on the test. But of course that never happens. So if you want an 800, try to have an open mind.</p>
<p>I’ll definitely keep an open mind. I just figured my time was better spent studying more of the test material than figuring out how to finish the test as quickly as possible. Remember, it’s okay to finish a section with just one minute remaining, as long as you are confident in your answers. It’s not a race, and I figured that even with the ‘inferior’ method, I’d have enough time to go back and check my answers. I find that I have more trouble with accuracy than with speed (it’s not very hard for me to finish a section quickly). I do see your point, though, and I appreciate your response.</p>
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<p>No props necessary. Sikorsky is an algebra teacher.</p>
<p>^^ Cool. Is he or she also an helicopter parent? :)</p>
<p>Xiggi, exactly!</p>