<p>Those of you who have read my posts will notice that I place a heavy emphasis on SAT specific math strategies. I have a standard list of strategies that I teach to my own SAT students - I go through these strategies slowly over a period of 3 to 4 months. Note that the strategies that I emphasize depend on the current SAT scores of the students I am teaching. When it comes to learning these strategies there is sometimes a misconception that every student should be learning every one of the strategies I teach. This isn't the case - each student needs to learn the strategies that will take them to the next score level. Also note that after learning each strategy it is important to practice each of them on SAT problems whenever possible. This is the only way that they will be internalized, and you will be able to use them effectively on test day.</p>
<p>In this thread I would like to teach you these strategies one at a time. I leave it up to you to find SAT problems where each one can be used and to practice implementing them. I will begin with the most basic strategies and slowly work up to more advanced techniques. </p>
<p>Please feel free to ask questions, discuss, agree, disagree, comment on, etc. with each strategy that I bring up. </p>
<p>I think it would be nice to discuss one strategy at a time, so I would prefer if you don't jump in with lists of your favorite strategies all at once. Instead try to add your input to any of the techniques that have already been mentioned.</p>
<p>Description: In many problems you can get the answer simply by trying each of the answer choices until you find the one that works. 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). The reason for this is simple. Answers are usually given in increasing or decreasing order. So very often if choice (C) fails you can eliminate two of the other choices as well. </p>
<p>Comments: I just love this strategy! It can be used on problems from all topics and all levels. Although it is not always the quickest method for solving an SAT problem, sometimes it is, and it often gives a very simple way to get an answer fairly quickly while avoiding messy algebra.</p>
<p>Dr. Steve, Thank you. I will be following–is there a way to know when you do new posts? Is this strategy only for when you are using plug in the answers?</p>
<p>I know that one thing you can do is to go to my profile, click on statistics, and then “Find all posts by DrSteve.” I’m not sure if there is an easy way to follow a particular thread. If anyone has a simple way to do this, please post the answer.</p>
<p>The short answer to your second question is yes - this is the most common method I teach for plugging in numbers. Stay tuned for one more.</p>
<p>Now, this particular strategy is clearly only useful for multiple choice questions. It usually works when the last part of the question says “What is_____” where the blank contains a single quantity.</p>
<p>Some examples:</p>
<p>(1) What is the value of x?
(2) What is the width of the original rectangle?
(3) What is the third number in the list?</p>
<p>This strategy will usually NOT work when you are asked to find a “compound expression.” For example, do not use this strategy if the question ends with “What is the value of x + y?” Don’t worry - we will see other strategies that can handle these types of problems.</p>
<p>Now, I gave you some of the obvious problems where this strategy will work. There are other problem types where this technique will still work. For example, a problem of the form “Which of the following is a ____?” where the blank could be anything. When practicing, you should think about using this strategy on any multiple choice question. The more experience you have attempting to use it, the easier it will be to detect when it can be applied.</p>
<p>And if you are unsure about a specific question, please post it in this thread, and I’ll let you know if this strategy works, and if it actually should be used for that particular problem.</p>
<p>Dr Steve, I am confused about “Basic Strategy: Start with choice (C)”
Could you please explain the reasoning behind this? I guess it has something to do with, “The reason for this is simple. Answers are usually given in increasing or decreasing order. So very often if choice (C) fails you can eliminate two of the other choices as well.” Please give an example or two showing how this might work.
Thanks</p>
<p>Here is a straightforward example of a Level 1 Number Theory problem where “starting with choice (C)” is a useful strategy.</p>
<p>Three consecutive integers are listed in increasing order. If their sum is 138, what is the second integer in the list?</p>
<p>(A) 45
(B) 46
(C) 47
(D) 48
(E) 49</p>
<p>I suggest you try to solve this problem in 3 ways:</p>
<p>(1) by starting with choice (C)
(2) algebraically
(3) using the fact that in a list of consecutive integers, the arithmetic mean is equal to the median.</p>
<p>I’ll give you one more example where this strategy is effective. This one is a Level 4 Geometry problem:</p>
<p>When each side of a given square is lengthened by 3 inches, the area is increased by 45 square inches. What is the length, in inches, of a side of the original square?</p>
<p>(A) 3
(B) 4
(C) 5
(D) 6
(E) 7</p>
<p>Try to solve this one in 2 ways:</p>
<p>(1) by starting with choice (C)
(2) algebraically</p>
<p>Feel free to post your solutions and I’ll tell you if you are using the strategy correctly.</p>
<p>Thanks, DrSteve. Those examples are helpful for seeing the virtues of the “start with c” strategy. They are examples of what you described, " Answers are usually given in increasing or decreasing order. So very often if choice (C) fails you can eliminate two of the other choices as well." Yes, I like it. Thanks again.</p>
<p>Basic Strategy: When NOT to start with choice (C)</p>
<p>Description: In the first strategy I explained that when plugging in answer choices you should usually start with choice (C). There is one big exception to this rule. The exception is when the word “least” or “greatest” (or words synonomous to these) is in the question. In this case you want to start with the least or greatest answer choice - generally choice (A) or (E).</p>
<p>Comments: The idea here is that even if choice (C) “works,” it still may not be the answer because it may not be the LEAST (or GREATEST) that works. So starting with choice (A) or (E) is more likely to save the most amount of time.</p>
<p>Here is a straightforward example of a Level 3 Number Theory problem where “NOT starting with choice (C)” is a useful strategy.</p>
<p>What is the largest positive integer value of k for which 3^k divides 18^4?</p>
<p>(A) 2
(B) 4
(C) 6
(D) 7
(E) 8</p>
<p>I suggest you try to solve this problem in 2 ways:</p>
<p>(1) by starting with choice (E)
(2) by using prime factorizations and laws of exponents</p>
<p>And here’s a Level 4 Geometry problem where this strategy is effective:</p>
<p>The sum of the areas of two squares is 85. If the sides of both squares have integer lengths, what is the least possible value for the length of a side of the smaller square?</p>
<p>(A) 1
(B) 2
(C) 6
(D) 7
(E) 9</p>
<p>You should solve this problem by starting with choice (A).</p>
<p>Thanks for the tips Steve!
For the last 2 questions, the 2nd was pretty straightforward, however, I didn’t really get what the 2nd question is asking? (when can 18^4 be divided by 3^k and get an integer as an answer?)</p>
<p>I think you understand Tomer. We say that an integer n divides an integer m if there is another integer k such that m = nk. So for example, 3 divides 15 because 15 = (3)(5).</p>
<p>An easy way to check if n divides m is to type m/n in your calculator. If the answer is an integer (no decimal), then n divides m. If there are digits after the decimal point, then n does NOT divide m. </p>
<p>So, for example in your calculator 18^4/3^8 = 16, an integer. So 3^8 divides 18^4.</p>
<p>My dilemma with SAT math is silly mistakes.</p>
<p>Recently, I’ve understood every problem I’ve come across, save for maybe one problem every few tests. I come away confidently after every test, having checked the difficult problems.</p>
<p>However, I usually miss ~1 question per section from the dumbest mistakes. For instance, I apparently manage to forget what direction clockwise is, or what 9x7 equals. How do you recommend practicing combating these silly errors?</p>
<p>I recommend you start by reading my article “Stop Making Careless Errors in SAT Math.” It’s posted on this forum - just do a search. If you follow the advice I give there carefully, I’ll bet that your careless mistakes will go away.</p>
<p>Note that this thread is directly applicable to point (3) in that article.</p>
<p>What you are describing leads me to believe that your mistakes are genuinely careless, and not due to you being tricked. I recommend paying extra attention to points (1), (2), (9) and (10) in the article. But listen to the other points as well.</p>
<p>Intermediate Strategy: Change averages to sums</p>
<p>Description: Most SAT problems involving averages become much easier when we first convert the averages to sums. To make the conversion just use the following simple formula:</p>
<p>Sum = Average * Number</p>
<p>where Number = the number of things we are averaging</p>
<p>Comments: (1) I consider this an Intermediate strategy because it requires just a little bit of practice to internalize. But once you get it, it’s a foolproof strategy that will have you answering questions involving averages in 5 to 10 seconds.</p>
<p>(2) Many problems involving averages require 1 or 2 conversions to sums, followed by a subtraction. Sometimes a simple division will need to be performed at the end if the final answer is itself supposed to be an average.</p>
<p>(3) The defintion of average is Average =Sum/Number. We get the formula above by eliminating the denominator in this definition.</p>
<p>Description: This is another example of a “plugging in” strategy, except this time you’re not using the answer choices. Try to make as reasonable a guess as possible, but don’t over think it. Keep trying until you zero in on the correct value.</p>
<p>Comments: This strategy can be used in multiple choice questions that ask for a more complicated expression than a single variable. For example, if the end of the question says “What is the value of x + y?” maybe you want to take a guess for x in this case (or possibly y). Or maybe the question is asking for the area of a geometric figure. In this case you may want to take a guess for the length of a side of the figure. This strategy also works well on certain grid-in questions. In particular, if “Start with choice (C)” is a good strategy for a certain multiple choice question, then “Take a guess” is a good strategy for the same question without choices (as a grid-in).</p>
<p>Here is an example where “Taking a Guess” is the quickest and easiest way to solve the problem.</p>
<p>Tom has dogs, cats and birds for pets. The number of birds he has is three times the number of cats, and the number of cats he has is 2 more than the number of dogs. Which of the following could be the total number of these pets?</p>
<p>(A) 14
(B) 15
(C) 16
(D) 17
(E) 18</p>
<p>Try to solve the above problem both by “Taking a Guess,” and algebraically.</p>
<p>When taking a guess, what quantity are you guessing? </p>
<p>When attempting this algebraically what are the common traps you need to avoid?</p>
<p>The thread itself has a nice debate about which of 3 methods for solving the given problem is best. There is an algebraic solution, a solution by guessing, and a nice clever logical solution given by Xiggi.</p>
<p>Hi,
I am currently doing SAT practice. The problem I have is:
For the math section, I tend to rush the questions and end up making unnecessary mistakes. I was wondering if there were any suggestions on how much time I should spend on each question(I know there are different sections: Easy, Medium, Hard: But how much time should I spend on each of these different sections?)?</p>
<p>I do have fairly specific instructions for this, but to answer I need to know what you are currently scoring in SAT math on college board practice tests.</p>