Dan's Test Prep Digest (1/28/24)

Week #20 - Solve in Seconds

Welcome, SAT/ACT preppers!

Today we'll be covering a tip that will help you solve a system of equations question in seconds, with hardly any actual work needed. By the way -- this tip comes straight out of the Digital SAT bootcamp that I just released, complete with an SAT course, live group tutoring sessions, and an adaptive learning question platform (discount code at the end of this email for anyone interested).

Now, let's get into this week's SAT tip.

From the given question, you can see a wide collection of information. We know that (1) a company is taking groups of people, (2) the people can be split into adults or children, and (3) the revenue per adult/child is given along with the total revenue.

All this information serves as a perfect candidate for forming a system of equations. By setting two variables -- A for the number of adults and C for the number of children -- we can form two linear equations:

A + C = 21

80A + 60C = 1440

Given that we're taking the Digital SAT, we no longer need to solve it out by hand. In fact, once you've reached this point, all it takes is a few seconds in Desmos to obtain your solution for the number of children!

If you plot both equations in Desmos as-is, you'll need to do one more step: set A equal to x and C equal to y (Desmos only supports implicit equations of x and y). But once you've done that, you can see that the (x, y) pair corresponding to our solution is (9, 12).

Given that y is equivalent to C in this case (the number of children), our solution is also going to be answer choice C (12).

Even for harder questions, Desmos can still be useful. Take a look at this one, for example:

In this question, you're asked to solve for the value of p given that the system has no solution. Of course, we can solve it out by hand, but some test takers find it easier to visualize the solution.

If you plug these equations into Desmos, you'll notice an option to add a slider for p - go ahead and do that.

If you add that slider, you'll notice that you still have a solution for the system of equations. We want there to be no solution, meaning the lines are parallel.

Play around with the value of the slider until you make the lines completely parallel, meaning they don't ever intersect. You may want to zoom out a little bit just to make sure they don't intersect further outside of your screen.

In this case, the answer we needed was p = 6. And again, no solving needed!

I have more questions like this (in fact, 85 more questions across all 29 topics of the SAT) in the SAT bootcamp I mentioned. If you're interested in getting an SAT course, live tutoring, and practice questions all in one, you can use code "DAN20" for 20% off your first month!

Hope you learned something new. Stay prepping!