# GMAT Math : Stress testing

Many times the most efficient way to solve GMAT quant questions is just by taking numeric examples and counterexamples. However, instead of boiling the ocean by testing with numbers randomly, there is a efficient way of choosing which numbers to test with – this method is what we call stress testing.

Let’s illustrate with an example :

The flow rate of water in Dam sigma is x liters/second during the monsoons. The flow rate of water in Dam alpha is z liters/second during the monsoons. Is the ratio of the flow rate in Dam sigma to the flow rate in Dam alpha at least 4?

1. x is between 10,000 and 80,000
2. z is between 10,000 and 50,000

We essentially have to determine if (x/z) > 4 always or if (x/z) < 4 always. Instead of randomly choosing the values of x and z from the ranges given, we will ‘stress test’ with ‘boundary values’.

So we are testing for x = 10,000 and 80,000 and y = 10,000 and 50,000

x = 10,000 and y = 10,000

x/y = 1

x = 10,000 and y = 50,000

x/y = 0.2

x = 80,000 and y = 10,000

x/y = 8

We can stop here as we have found x/y can be > 4 and < 4 with the information given. Hence we go with Option (E). This is relatively simple example to illustrate testing with boundary values. We look at other question types which can be solved through stress testing efficiently in our Hackbook