SAT Tip of the Week: Math Traps

GMAT TrapsYou’re near the end of the last math section on the SAT. You’re feeling confident; you’ve answered every question so far, and you only have a couple of questions left to answer. You know that you’re so close to that dream score you’ve been pushing for. You glance at the clock: four minutes remaining. You take a quick look at the third to last question:

 

 

RP - math problem 2

 

 

 

 

 

 

 

 

 

 

 

The question seems simple enough. If the can is eight inches tall, then four of the pencils cannot fit entirely inside the can. You circle D and move on, since you only have a few minutes left to answer the last two questions.

Unfortunately, if you choose D as the answer, you’d have missed one and a quarter points, which is enough to knock you out of the percentile you may have been aiming for. Newsflash: this seemingly simple math problem is a trick question! But before you groan and say to yourself, “How am I supposed to know when an SAT math question is just plain easy and when it’s a trap?”, heed this simple rule of thumb: on the SAT, trick questions tend to appear near the end of the section, say about the last 5-6 problems.

So, although you may be able to do math questions at the beginning of the section in less than thirty seconds, if you do a problem at the end of the section easily and in little time, chances are you fell for a trap! In fact, if a problem at the end of the section seems strangely easy, an alarm bell should go off in your head.

Be sure to always pause and consider the question carefully, instead of circling the first plausible answer. Also, be sure to always give yourself extra time for the end of the section, since you’ll need to spend a couple of minutes on the tricky problems to avoid traps. Let’s take another look at that problem.

One great way to deal with geometry-based questions at the end of the math section is to draw on the provided diagrams as you think your way through the problem. In other words, thinking visually. Doing will help you consider possible solutions you may otherwise overlook, such as in our tricky problem. So, let’s start by “drawing” the nine inch pencil in the tin can:
RP - math problem 2

 

 

 

 

 

 

 

Clearly, the pencil sticks out of the can. But, seeing the pencil sticking nearly straight up from inside the can gives me a new idea: What if the pencil were tilted? Couldn’t a pencil longer than eight inches fit inside the can? And if so, what would be the longest possible length of a titled pencil that could fit entirely inside the can?

To get a better grasp of this idea, I would draw the longest possible tilted line that fit inside the can, meaning a line starting in a bottom corner of the can, and stretching to the top corner, like so:

RP - math problem 4

 

 

 

 

 

 

As you can see, the line that represents the longest possible length of a pencil that fits entirely inside the can is also the hypotenuse of a right triangle with side lengths of 6 inches and 8 inches. Because I can identify the side lengths of this triangle as multiples of the lengths of a 3-4-5 triangle, I know the hypotenuse is 10 inches, meaning that any pencils less than or equal to 10 inches long can fit inside the can. Therefore, my answer is B, only two of the pencils cannot fit entirely inside of the can.

The more tricky math questions you practice working through, the better you will become at spotting traps and using strategies like drawing on the figures. Consider signing up for the SAT question of the day to keep sharpening your skills!

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By Rita Pearson, an 99th percentile SAT instructor for Veritas Prep.