SAT Math Test-Taking Logic on the No Calculator Section
In my most recent post, Multiple Choice Strategies for SAT Math: Interpreting Information and Understanding Vocabulary, we looked at two of the three key strategies for SAT answer selection: understanding vocabulary and interpreting information. In this post, we’ll look at the third important SAT multiple choice strategy: understanding processes and logic.
Processes and logic are the cornerstone to selecting the right answers in SAT Math. Most SAT Math questions require you to either go through problem-solving steps or understand the logical of a mathematical pattern. Frequently, both skills are used in the same question.
Correctly following processes and logical patterns is especially important in section three of the New SAT, the section entitled “Math Test—No Calculator.” The calculator-free questions are designed to test your ability to think through operations, completing specific steps. Very often the wrong answer choices are the result of skipping a step, applying the wrong operation, or failing to recognize a numerical pattern. Let’s look at an example Math Test—No Calculator multiple choice question, selecting the right answer with strategic use of processes and logic.
If c/d=2, then what is the value of 10d/c?
This is a great question, because if you know both the way numbers function in fractions (mathematical patterns) and know how to plug the numbers in to the equations (mathematical processes), you can quickly weed out the wrong answers and detect the right ones.
Let’s first apply mathematical logic to this problem. Immediately, you can rule out answer (C). The only way the third answer choice could be correct would be if d equaled zero and if d=0, then c/d can’t equal 6. It can’t equal anything, because you can’t divide by 0. C over zero, or any number over zero, would be undefined.
So answer (C) can be eliminated purely through logic. You can check the rest of the answers through a combination of mathematical logic and the application of problem-solving steps. The first thing you’ll want to do as you scrutinize the other answers is to solve for d. This is easy, if you understand the relationship, the logical pattern that connects whole numbers to fractions. Remember, any whole number can be expressed as a fraction, by making the original whole number into the numerator (the top number in the fraction) and putting in a denominator (the bottom part of the fraction) of 1. So 3=3/1, 200=200/1 and so on.
Logically then, if c/d=2, then c/d also equals 2/1, the fraction expression of the whole number 2. So d on its own must logically equal 1 and c must equal 2. From there, you plug in the values of c and d to solve for 10d over c.
So with this simple 3 step process (which you should be able to do in your head), you can tell that the correct answer is (D) 5. To get answers of 10 or 1 from 10d/c, you’d need different values than (2,1) for (d,c).
Now this problem is relatively simple, as SAT Math problems go. You could probably find the right answer just by using logic to solve for d and c, and then plugging the numbers in; eliminating the answer of 0 by using broader math logic is not an essential step in this case.
Eliminating mathematically illogical answer choices like (A) above is a much more crucial step in complex story problems though. If you haven’t already been given an equation and you need to derive the right equation from the data before solving the problem, always check for mathematically impossible answers first. Sometimes, this can eliminate all but two answers or even bring you down to just one answer, saving you lots of time and hassle.
SAT Math Test Taking Logic on the Calculator Section
Now we’ll take a look at how processes and logic can help you select right answers in the second Math section in the New SAT, where a calculator is allowed.
In the Section 4 of the New SAT, the section headed “Math Test—Calculator,” process and logic take on special importance. Although the SAT allows you to use a calculator in this final section, calculator use is often a trap. The SAT loves to trick you into assuming a problem is more complex than it is, because unnecessary calculator use can cause you take overthink, waste precious test time, and make mistakes in your steps and operations.
So it’s very important to really think about the logic and steps required to get the right answer. Do NOT let the test lure you into having the calculator do the thinking for you, because calculators can’t think. They can only do the operations you key in and you don’t want to unthinkingly key in an incorrect math sign or unnecessary step.
Take this example SAT Math calculator-free question:
1 decameter = 10 meters
1,000 centimeters= 1 meter
A group of interior designers has been asked to line the edges of a large rectangular room with marble tile trim. The tiles must all touch each other, and each tile is 1 centimeter wide. If one side of the room is 3.5 decameters long, how many 1-centimeter tiles must be used for the trim on that side of the room?
To get the correct answer, you need to first figure out how many centimeters there are in a decameter, and then multiply that figure by 3.5, the number of decameters given in the problem. The basic operation goes as follows: 1,000*10*3.5. This can easily be simplified to 10,000*3.5, or 35,000. So the correct answer is (D).
Note that all of the incorrect answers are potential results of calculator misuse. (A) is what you get if you accidentally divide 3.5 by 10,000 instead of multiplying. (B) is the result of multiplying by one thousand instead of ten thousand, something that can easily happen if you accidentally don’t key in enough zeroes on the calculator. (C) is what you get if you accidentally add 3.5 to 10,000 instead of multiplying it by 10,000.
It’s easy to hit the wrong key if you use your calculator, and also easy to hastily enter the wrong result before rushing on to the next question in this timed exam. To select the right multiple choice answer, you need to really think about the process of solving the problem, and the logic of the answers. Answer (A) above is an especially illogical mistake. Accidentally hitting the division key when you meant to hit “multiply” is easy enough. It’s just as easy to realize there’s no way a tiny fraction of a tile would cover an entire side of a room!
So don’t use your calculator blindly, and strange as this sounds, don’t use your calculator at all if you don’t have to. Calculator use will trip you up and waste precious time on many of the multiple choice questions in this section. Rely on a calculator only for truly hard problems and for double checking mentally calculated answers, if you have time to do so.