Written by John B., Super Tutor for Enhanced Prep
The above problem appeared on the April 2019 SAT Math – No-Calculator section. In the high school math classes I have taught, I would hope to see the following solution:
Why? The student shows their work: how they ‘move’ the 4 and how they cancel out the radical with a squared. I can also determine from the work the student understands the procedures involved. That’s why I call this type of solution good math student work when I’m working with students on the SAT Math. But, this procedure isn’t necessarily the most efficient for solving the SAT math problem above.
Why? We already know the answer! It’s right there! One of them… So now what? We become a good SAT Math student. A good SAT Math student finds the solution to the problem as efficient as possible. Use other methods:
Process 1: Eliminate! We can eliminate several solutions’ choices immediately because 12 is a nice whole number, which means x must simplify to a similarly nice, whole number. That means any solution that is not a perfect square cannot be the answer. That removes 2 options, A and D.
Process 2: Use the possible answers! Unlike most traditional math tests, the answers for most SAT Math problems are given to you. Use them to your advantage. For the problem above, there’s no need to do any algebraic manipulation – just plug in answers and solve! Let’s try B:
B cannot be the solution. That leaves only C! If we have time left on the test, we can come back and double-check C as well. To summarize, being a good SAT Math student can sometimes mean doing ZERO math to find the answer. Sometimes it means using the provided solutions to work backwards. In both cases, it means not jumping straight into the traditional problem-solving process math teachers emphasize.