It’s easier than you think!

SAT Math: It’s easier than you think!

In this blog post, we are going to discuss a deceptively simple technique called plugging-in that will boost your scores on the SAT.  By mastering this solo technique, you will find yourself suddenly ready to ace a good number of SAT Math questions.

The SAT Game changer Math Technique – Plugging-in

Before we begin, let me ask you a question: Do you like chocolates? Probably yes….

Suppose you have visited a chocolate store and you have $10 in total and you want to buy 3 chocolates that cost 50 cents each, then how much change in dollars have you received from the shopkeeper? $8.50 right?

Now let’s frame the same problem in a context in terms of variables. Let us assume, you have x dollars in total, you want to buy y chocolates at z cents each, how much change in dollars will you receive from the shopkeeper? Is it x-yz? It is, isn't it? In my experience, most of the students will generally answer x-yz.

Now let’s check whether that is correct or not.  

Let’s plug-in the corresponding values i.e. x=10, y= 3 & z=50 

After putting these values in x-yz we get:

10 – 3*50 = - 140,

See what happened here? The answer should be $8.5 but it comes out to be -140, which is not possible at all.

So definitely we did something wrong! But what?

Actually most of the SAT aspirants missed the word “change in dollars”. In the above problem ‘z’ is in cents so we have to convert ‘z’ into dollars first i.e. z/100. Now the required change would be x- (y*z/100).

The conclusion of this whole story is that when a problem is framed in terms of numbers, most test-takers solve it correctly. When algebra is involved, things get more challenging. So what’s the way out? Put the brakes on arithmetic and work on algebra?  Not at all! Arithmetic will always be more natural for us than will algebra. We will now learn about a technique called “Plugging-in” that works on this very powerful insight.

Let's solve a simple question to see how plugging-in works.

Robert is d years old and he is 5 years younger than Maria, in terms of d, how many years old will Maria be in 4 years? 

1. d-5
2. d-4 
3. d+4 
4. d+9 

So this question seems very easy but here we are only focusing on the technique, not the difficulty level.

The plugging-in approach:  

Step 1: Give a practical value/plugging-in to the variable/s 

First, you have to figure out the variable component and assign a practical value to it. Here, you can see, Robert’s age is d years, so let’s give a real age to Robert- assume he is 10 years old; d=10.

Now according to the situation,

Maria’s age = 10+5

= 15 years  

Step 2: Solve the question 

Now, the question is asking us to calculate Maria's age in 4 years 

Therefore, Maria's age in 4 years = 15+4

= 19 years.

Let's circle this 19 as our target value.

Step 3: Plug-in the value of an assumed variable(d) into the options

Now we plug-in the value of 'd=10' into the options and will check which option becomes equal to our target value. 

1. d-5
2. 10 – 5 = 5 (not equal to the target value) 
3. d-4
4. 10 – 4 = 6 (not equal to the target value) 
5. d+4
6. 10 + 4 = 14 (not equal to the target value) 
7. d+9
8. 10 + 9 = 19 (equal to the target value) 

Therefore, option D is the correct answer choice. 

Important points to take care of:

1. You can use this technique in all the questions which have variables in their answer choices.
2. Make sure you have checked all the answer choices. There may be a possibility that more than one answer choice will be equal to your target value. If that happens, plug-in a different value and try again.
3. Avoid taking values like 0 & 1.

Now it’s time to practice and see how you fare.