Plugging in Numbers

If you took math tests in school, chances are that you had to write down a bunch of math to get the problem right. And that's a good thing. You are doing what your teachers want you to, thus earning you a good grade. 

Now I am telling you to kick that old school technique to the backseat. 

You know what's crazy? The SAT is notorious for beating students at their own game. Meaning that if you try to solve SAT Math problems by doing math like on school tests, you are likely to get the problem wrong, or run out of time. 

Here's an example:

Source: http://www.sat-tutors-blog.com/2009/02/11/sat-math-when-to-plug-in-numbers-ii-w-examples/

You can solve this question without plugging in numbers, but if you do, chances are that you will make a mistake or just plain confuse yourself during the process (I tested it out myself). 

Let's pick a number for "x". 

I feel like using the number "2" today.

Step 1

Before: "An integer x is multiplied by 3"

After: "An integer 2 is multiplied by 3"

What I did was replace the "x" with "2", just in case you didn't get what I just did.

So 2 times 3 equals 6. 

Step 2

Before: "and the result is decreased by 3"

After: "and 6 is subtracted by 3"

Here, the "result" means the "6" we just solved for. 

6 minus 3 equals 3.

Step 3

Before: "This result is divided by 3"

After: "3 is divided by 3"

"This result" is talking about the "3" we just solved in Step 2.

3 divided by 3 is 1.

Step 4

Before: "Finally, that result is increased by 3"

After: "1 + 3 = ?"

"That result" is referring to the "1" we got back in Step 3. 

Finally, 1 + 3 = 4. (What a coincidence.)

Step 5

Now plug in our x value, "2" into the multiple choice answers. 

The answer that equals the number we found in Step 4, "4", is the correct one.

(A) x+3 

2 + 3 = 5 (Rejected!)

(B) x-3

2 - 3 = -1 (Nope!)

(C) x+2

2 + 2 = 4 (Correct)

(D) 3x-3

3(2) - 3 = 6 - 3 = 3 (Wrong)

(E) x

(2) = 2 (Incorrect)

Congrats! The answer is (C)! 

Let's do one more question.

Source: http://magoosh.com/sat/2012/sat-geometry-strategy-plugging-in-numbers/

Step 1

Remember your Geometry. A square is a rectangle, therefore we can make the length and width of Rectangle WXYZ the same. 

You may not want to plug in a small number like "2" for this question, because we will end up with decimals, and that can potentially confuse us while solving.

When you're dealing with problems that involve percentages, it's a good idea to plug in numbers like 10 or 100.

And because this question deals with percentages, let's plug in "10" for our length and width. We can use 100, but in this case, a 10 is much more simpler to calculate.

Step 2

Before: "The length of Rectangle WXYZ is increased 20%"

After: "10 x 1.20 equals?"

Remember that percents can be expressed into decimals? 20% = .20

So you might be wondering why I multiplied 10 by 1.20.

Here's why: 

20% of 10 is 2, because 10 x .2 = 2. The length increased by 20%, so 10 + 2 = 12.

If we multiply 10 by 1.20, we will still get 12. 

Thus the length of Rectangle WXYZ is 12.

Step 3

Before: "The width is decreased 20%"

After: "10 x .8 equals?"

Again, we do the same thing in Step 2, but in reverse.

20% of 10 is 2, and because 10 is decreased by 20%, we subtract 2 from 10.

10 - 2 = 8

If we multiply 10 by .8, we still get 8. 

Step 4

Before: "The area of the resulting figure"

After: "12 times 8 equals?"

The area of a rectangle (in this case, square) is length x width.

So 12 x 8 = 96.



Step 5

Before: "What percent that of Rectangle WXYZ?"
After: "What is the percent change?"

Remember this formula:

Source: http://www.satprepget800.com/wp-content/uploads/2013/11/Percent_Change.png



The area of our original rectangle/square is 100 (10x10=100).

The area of our new rectangle/square is 96.

Plug in our numbers:

(96/100) x 100 = 96%.

Therefore our answer is (C) 96%. (Again)




If you think that making the rectangle into a square isn't correct, then plug in some numbers yourself, you will still end up with the same answer.

Hey, I'll do one right now (but much more briefly).

Width = 1
Length = 10

Width x .8 = 1 x .8 = .8
Length x 1.2 = 10 x 1.2 = 12

Width of rectangle = .8 x 12 = 9.6

Percent Change = (9.6/10) x 100 = 96%

As you can see, the answer is the same.







When do I use this stuff?

- When you see variables in the question and answers, plugging in might be the best choice
- On percent questions (10 or 100 is a good choice"
- Triangle questions with no given angles (make sure angles add up to 180 degrees)
- Some Geometry questions
- If you are having trouble, plugging in might be the key


Anything else...?

- Rule of thumb: do NOT plug in 0 or 1.
- Another rule of thumb: try to use small numbers when possible
- Check out EVERY answer choice when plugging in. If two or more choices work, then you are doing something wrong. If all choices don't work, then you are doing something wrong, UNLESS, there is a choice "Cannot be determined from the information given".