The SAT Math Section Explained: Part I
So first thing: The SAT math is not at all like your typical math class. Show your work, step by careful step? Hah! Those steps count for nothing on the SAT—unless you get the correct answer. Setting up equations? It doesn’t really matter how you get the answer—as long as you get the answer. In fact, the SAT math section is more of a test of the following things:
#1 – Can you avoid carefully placed traps
#2 – Can you analyze the answer choices to eliminate a few of the answer choices
#3 – Can you find a quick solution
To apply these three points, let’s take a look at a tricky word problem (something the SAT is fond of putting on the test).
Myra has a drawer filled with 3 pairs of socks, 5 blouses, and 3 jeans. She can wear a combination of any of the socks, blouses, and jeans, except for her one pair of charcoal jeans, which do not go with her silver blouse. How many possible outfits can Myra don?
One option is to write out all the possible outfits (Socks 1, Blouse 1, Jeans 1; Socks 1, Blouse 1, Jeans 2; etc.). Doing so would totally go against point 3—and you’d probably end up getting the problem wrong, as running out of time for the other questions.
Another approach is to reason that you are combining outfits—therefore just add (3+5+3 = 11). And, lo and behold, there is the answer (B). But, oops, you just forgot to take into account the bit in the problem about her charcoal jeans and silver pants fashion faux pas. So the answer must be 11 – 1= 10, answer (A).
The reality: both are wrong.
So #1 is very important. Avoid traps.
Of course it helps to know what is called the fundamental counting formula. Basically, when you are looking for the different number of ways to combine things you multiply, not add. Imagine, you were just focusing on the 3 pairs of socks and 5 blouses. Each pair of socks can match with 5 different blouses. There are 3 pairs of socks: 3 x 5 = 15. Throw in the jeans and you get a total of 3 x 5 x 3 = 45 outfits.
Look back at #2. Which answer choice can we eliminate? (E). It’s way too high. In fact, we could also eliminate (D), because we know we have to subtract some number of outfits from the total of 45. Which answer is slightly lower? (C) is the only one even close to 45. So that’s our answer.
The math/logic version: we have to subtract the total number of outfits that includes charcoal jeans and silver blouses. You may be tempted to think the answer is 1. But remember, there are three pairs of socks for the charcoal jean and silver blouse get ups. So we get 45 – 3 = 42 (C).
What’s the takeaway from all this? You have to change your thinking and not be hung up creating an equation or recalling some handy formula. You also have to be able to think on the spot. You didn’t really need the Fundamental Counting Formula to get the answer. Remember how I reasoned out the logic behind this concept just by imagining the number of outfits we get from combining socks and blouses?
Anyhow, that question was tough (I like to keep students on their toes!) So let’s try an easier one. But remember, the logic of the three steps still apply.
A sweater goes on sale for 10% off. After a few days, it goes on sale for an additional 10% off and is sold. If the original price of the sweater was $100, what is the selling price of the sweater?
Your first instinct is to just add up the percents and think that the sweater is 20%. Therefore, (B). But the SAT is never that easy. The trap is you first have to take 10% off $100, which is $90. Then 10% off 90, which is a $9 discount, giving us 90 – 9 = 81 (C).
Not all problems are going to be word problems, of course. But you can bet that each problem are going to have answer choices waiting to trap you. And you can also bet that you can be on guard against these traps by using the answer choices to your advantage. Look at which ones are too big, too small, or, as we saw in the sweater problem, too easy.
Stay tuned for the sequel to this post, The SAT Math Section Explained: Part II!