GMAT Math : Triangle formation

The GMAT Math section often tests a few timeless classics on triangle formation rules

Let’s start with a GMAT Data sufficiency example:

Do points A, B and C constitute a triangle?

  1. The positive difference between any two lengths is less than the length of the third side
  2. Two of the points lie on the line y = mx + b and one of the points lies on y = nx + d

Readers are encouraged to take some time to tackle the question 🙂

How do we tell if three points constitute a triangle? There are two classic tests (each one independently sufficient)

  1. The three points are not col-linear (i.e., not all the points fall on the same line)
  2. The sum of the lengths of any two sides (by joining the points) is greater than the length of the third side

The question has cleverly masked the above two principles.

Statement (1) tells us:

Side 1 – Side 2 < Side 3

If we reorder this, we get:

Side 1 < Side 2 + Side 3

Hence, statement (1) is essentially a different ‘form’ of test (2) and is independently sufficient

Statement (2) seems to be sufficient as well. mx + b and nx + d are different lines. No? 🙂

If m = n and b = d the two lines become ‘overlapping’ and consequently the three points also become col-linear.

Hence statement (2) is also not sufficient by itself.

We go with option (A)

Remember these two classic tests and their different forms as you tackle tricky GMAT triangle questions. For more next level GMAT Math Data sufficiency practice, do check out our guide here