SAT Substitution Questions
SAT Substitution Questions
In this blog, we’ll discuss a common type of question that’s encountered on the SAT – the Substitution Questions. These questions usually seem tricky because of how they are worded but are actually quite easy. The process usually involves picking any value based on the restrictions they give you in the question, substituting that value in each of the answer choices and seeing which one gives you the desired result. It’s that easy! Let’s take a look with some examples:
So, first, let’s ask ourselves: What restrictions did they give me for choosing a random value to substitute? In this case, they told us that n must be an even integer and that’s all. So, let’s choose an even integer to work with – how about 2? Make sure to choose a value that will make your calculations much easier (you shouldn’t have to use a calculator usually).
Now we ask: What is the desired result? They told us that the answer must give us an odd integer.
So let’s start substituting values into each answer choice: Choice A gives us 4 (which isn’t odd); Choice B gives us 5 (which IS odd); Choice C gives us 10 (which isn’t odd); Choice D gives us a fraction (which isn’t even an integer!); Choice E gives us 8 (which isn’t odd).
Therefore, we see that by substituting the value 2 into each answer choice, we get our desired result (an odd integer) only from Choice B – which is our answer.
Why didn’t we stop substituting once we had already found that Choice B gave us what we were looking for? Well, because on the SAT you will get questions were two of the answer choices may give you the correct answer based on the random value that you chose to substitute with. Then you have to choose another value to substitute with to see which answer choice is actually the correct one. The next example will demonstrate this:
What are our restrictions: n is a positive integer (any whole number greater than or equal to 1)
What is our desired result: the equations/inequalities given in the answer choice must be true.
So, let’s choose a positive integer to substitute with – how about 1? (remember to make your life easier by choosing easy values to work with!)
Choice A is (1 < 2) True; Choice B is (6 >= 6) True; Choice C is (0 < 1 < 20) True; Choice D (1 = 1) True; Choice E is (1 > 1 ) False.
So, using the value of 1 for substitution we see that we eliminated Choice E, but we still have 4 answers that work! Now we are forced to choose another value to substitute in the Choices A to D to find the right answer. Let’s go with the number 2.
Choice A is (2 < 2) False; Choice B is (10 >= 8) True; Choice C is (0 < 2 < 20) True; Choice D is (2 = 1) False.
So, using the value of 2 for substitution we see that Choice B and Choice C are True. We must choose another value now to see which choice is true. We notice that Choice C will hold true for any value between 0 and 20. So, clearly the number 21 will make Choice C False. So, the answer must be Choice B!
This may seem like a long and tedious way to do a problem. But we can make things faster by taking a look at all the answer choices and noticing which values will eliminate some of the choices right away. For example, we could have notice a value greater than 20 would have eliminated Choices A, C, and D right away!
Again, let’s ask ourselves “What is the restriction?” – X and Y must be perfect squares.
What is our desired result: The answer must not be a perfect square.
So, let’s choose the easiest perfect square to work with: 4 –> we’ll use this value for both x and y, since they didn’t tell us that both numbers had to be different!
Choice A gives 16 (which is a perfect square); Choice B gives 16 (which is a perfect square); Choice C gives 16 (which is a perfect square); Choice D gives 8 (which is NOT a perfect square); Choice E gives 1024 (which is a perfect square – of 32!).
So, clearly the answer is Choice D!
As you can see, these SAT substitution questions are always worded tricky but once you break them down and figure out what your restrictions and desired results are they become quite easy. Practice picking the most efficient substitution values for these types of questions and you will find that these questions are easy points.
If you find that you are having a great deal of trouble with these questions, I highly recommend you get The New Math SAT Game Plan: The Strategic Way to Score Higher by Philip Keller. Philip Keller is an award winning teacher and his book is just awesome! It can really help you if you’re in the 500 – 600 range.
If you’re in the 600 – 700 range and want a significant improvement, then I highly recommend you get PWN the SAT: Math Guide by Mike McClenathan. This guy scored a perfect 2400 on the SAT. The book is hilarious and the methods are genius. Get this book if you dare to attempt for a perfect 800.
And be sure to keep following our blog – next time we’ll cover functions!