What’s the Triangle Inequality Theorem?

Triangle Inequality Theorem is fair game on the SAT, ACT, GRE, or GMAT. It’s often forgotten by test-takers, but when it pops up, you’ll be glad you know it! The theorem essentially states that the third side of a triangle must be between the difference and sum of the other two sides.

For example, if we had a triangle in which two sides were 6 and 9, then the third side must be between 3 (9-6) and 15 (9+6). The third side cannot actually equal 3 or 15, it’s important to remember.

Let’s try a practice question utilizing this math rule!

If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?

I. 9
II. 15
III. 19

A) None
B) I only
C) II only
D) II and III only
E) I,II and III

If two of the sides are 2 and 5. Then the range of possible values for the third side can be expressed as:

3 < x < 7

Perimeter is the sum of the sides. Let’s choose 3 and 7 as values for the 3rd side (even though we know they are the end-limits only) to create a range for the perimeter.

On the low end:

2 + 5 + 3 = 10

On the upper end:

2 + 5 + 7 = 14

So the perimeter range can be expressed as:

10 < x < 14

The perimeter must be BETWEEN 10 and 14. The answer is (A).

Here’s a link to a lot of great Triangle review topics if you want more Geometry practice: http://www.beatthegmat.com/mba/category/tags/gmat-math/geometry/triangles.

Learnist: 10 Tips to Rock the ACT Test this December 14th!

December 14th is the final ACT Test date of 2013. Planning to take the exam? Here’s how to focus your studies and rock the test!

Step 1 – Commit to a Study Schedule! To make sure you get the ACT test date and testing center you want, register early, at least 2-3 months before the exam. That way you can create a study schedule, working backwards from the test date. Be realistic with yourself? How much time can you commit each week to ACT practice questions? Work in 2-3 hour blocks maximum. It’s better to study 20-30 minutes a day than 4 hours once a week.

This site offers free 1, 2, or 3 month schedules! While the 3-month one is ideal, if you’re planning to take the December exam, you’ll want to modify the 1-2 month plans to fit your needs.

Step 2 – Focus on your weaknesses ASAP! Are you a slow reader? Is your ACT Math knowledge so-so? Grammar got you down? Know going in to your ACT test prep what areas need more work and plan to address them first. You’ll need more time for the weaknesses. Don’t put off studying for a section just because you dread it!

Luckily, the ACT SparkNotes website gives a great breakdown of what you’ll see on Test Day, so you can start to get a sense of what will need the most work.

Check out steps 3-10 on this Learnist board: 10 Tips to Rock the ACT Test!