SAT Geometry Strategy: Plugging in Numbers

A great strategy on the SAT is plugging  in our own numbers. Many students forget this and instead try to set up ugly algebraic equations (while some have a knack for this, for the rest of us it is easier to think in 1, 2, 3, then in x, y, z).

Other times students think plugging in only refers to problems in which their variables in either the question or in the answer choices. As you will see in the question below, plugging in can help in a question free of any variables.

The length of Rectangle WXYZ is increased 20% and the width is decreased 20%. The area of the resulting figure is what percent that of Rectangle WXYZ?

(A)  4%

(B)  96%

(C)  100%

(D) 120%

(E)  Cannot be determined from the information given.

 

Explanation:

Notice we are dealing with percent signs, so a nice easy number is to work with 10. Let’s assume both sides are 10 – after all a square is a quadrilateral. The length becomes 12 and the width becomes 8. 12 x 8 = 96. WXYZ had an area of 10 x 10 = 100. Therefore the resulting figure is 96/100 or 96% the area of WXYZ.

Now you are maybe thinking, “Oh, yeah, well what if we are dealing with a really skinny rectangle and the length is 10 and the width is 1?”

Well, if you have a theory, test it out. Increasing 10 by 20% gives us 12. Decreasing 1 by 20% gives us .8. 10 x 1 = 10, and .8 x 12 = 9.6. Hmm…these numbers look really familiar, right?

So now matter what length and width we plug-in, we will always get the same answer. (B).

This is an important observation, for if we didn’t always get 96%, then the answer would be (E) Cannot be determined….

A good rule of thumb: “(E) Cannot be determined…” is usually a trap answer.

 

Takeaway

Plugging-in is a very versatile technique that can be applied to a multitude of math problems. So don’t ever feel that you are stuck using algebra. Indeed, questions do not even need to be full of variables for you to plug in.

 

Author

  • Chris Lele

    Chris Lele is the Principal Curriculum Manager (and vocabulary wizard) at Magoosh. Chris graduated from UCLA with a BA in Psychology and has 20 years of experience in the test prep industry. He's been quoted as a subject expert in many publications, including US News, GMAC, and Business Because. In his time at Magoosh, Chris has taught countless students how to tackle the GRE, GMAT, SAT, ACT, MCAT (CARS), and LSAT exams with confidence. Some of his students have even gone on to get near-perfect scores. You can find Chris on YouTube, LinkedIn, Twitter and Facebook!

By the way, Magoosh can help you study for both the SAT and ACT exams. Click here to learn more!

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