Question
Dear Mitch,
I'm taking the SAT on May 3rd, and although I already scored higher than most kids in my class (and it's a large class in a huge public school) I 'm studying and taking it one last time for a higher score. And so I'm going through 3 different SAT prep books and the thing I wanted to ask you was if you had any SPECIFIC tips on how kids should "plug in" numbers? Or does "plugging in" have so many rules to remember that if you don't know exactly what you're doing you could end up causing yourself more of a challenge than you'd have if you just did the problem using what you learned in school?
(I'm asking because the last time I took the test was before I read about the tricks they say you should do on the math questions, and I did pretty well using regular algebra and stuff like that so now that I'm trying to switch to the tricks recommended in the books by people who "decoded" the test, instead of the way I already know.)
Could I do worse?
Sincerely
Pierre, J. C.
Answer
Dear Pierre,
First, to be clear about the facts:
1. Yes, you can do worse on the SAT coming up than you did on your previous test(s). That is ALWAYS a possibility, and the likelihood of doing worse increases for students who have already received a high score on a previous test. You were wise to refrain from including your score in your note to me (This is not an appropriate forum for personal specifics or information that won't help others); but you did mention that you were already somewhat pleased with the already high score you achieved, and that puts you in the category of test-takers who do have something to lose; you could do worse. Even if you study more, know more, and are better at navigating your way through questions, you could -- like many students -- have guessed on a few questions in each section and your guessing might have been lucky. On another day, such as the day of May 3rd, which is coming quickly, your guessing may go the other way and with just a few unlucky ones here and there you could end up with a lower score.
Returning to your letter, I notice that you have 2 specific questions:
1, Can a score go down? Yes, though it is NOT quite as likely to go down as it is to go up; and
2, How does one apply the technique known as plugging in?
For this second point, the "plugging in", you need to know that there are 3 different types of questions for which the technique of "plugging in" becomes a powerful tool:
1) When a question uses fractions or percents but does not deal with specific numbers;
2) When a question asks about a rule for a whole class of numbers and you have to check to see if there are any exceptions; and
3) When a question tells a story, usually revealing the number of a certain item remaining at the end of the story, and asks how many of that something there were at the beginning. NOTE: There are other forms of this question type, and, though not appropriate to list all forms here, there is one type so common that I would be remiss to leave it out: These are the questions involving the ages of a person or people "then", "now", and in the "future". These are easily recognized and solved by trying the choices one at a time ('plugging them in') and drawing a 3-column chart with the words "past", "present", "future" at the top and filling it in as you read the story to see which choice works.
An example of the second type is this: John tells Mary that for all positive values, x,
x to the second power is always bigger than x. John is:
A) correct because the exponent is even
B) correct because the exponent is greater than one,
C) not correct because he forgot to exclude the case of x = 1,
D) not correct and would still not be correct if he had excluded the case of x = 1.
For this type, there are certain numbers that are very helpful to plug in because they tend to make the exceptions to a rule pop out (if there are exceptions).
For this situation I refer to these as the 'magic numbers'. Unless the particular problem excludes one or more of the following, the magic numbers are:
0,
1,
-1,
a fraction between 0 and 1 (such as 1/2),
and
a negative fraction between 0 and -1, (such as – 1/2).
Here it states that the value is a positive number, so you don't have to deal with 0 or negative integers or negative fractions. However, plug in a fraction between 0 and 1, such as 1/2, and you will discover that John is wrong for a whole class of positive values. CHOICE D.
The first type of question may show a figure, such as a square, and ask: If the sides of this square increase in size by 50%, what will happen to the area?
A) it will increase by 50%
B) it will increase by 100%
C) it will increase by 125%
D) it will increase by 135%
E) it will increase by 150%
For this type, plug in numbers that make the calculation simple. For example, if you make the square 2 x 2, an increase in fifty percent would make it 3 x 3. 2 x 2 has an area of 4 square units, and 3 x 3 has an area of 9 square units. The increase is from 4 to 9. To figure out a percent-change, you place the difference between the "before"-and-"after" over the original amount. Here, the difference between 4 and 9 is 5, and the original amount was 4. SO:
5/4 = 1.25, or 125%
(choice C).
Good luck on your test!
Hope that helps,
Mitch