Here is the answer to yesterday's GMAT challenge (courtesy of Integrated Learning)

Answer: C

Explanation:
When numbers increase exponentially, the units digit of each successive increase follows a pattern. For example, think of 2:



Notice that after 24 the units digit starts to repeat. In fact, the units digit for any number ending in 2 when increasing exponentially will always follow this pattern: 2, 4, 8, 6, 2, 4, 8, 6,…

If you follow that logic, you can figure out the pattern for every units digit:



In this diagram, we highlight the 5th power. Numbers certainly can be interesting, huh? At the 5th power, every number has returned to its original. That’s good stuff to know going into the GMAT.

How does that apply to this problem? The question asks for the units digit of q4.

The first statement says that q is even. Looking at the chart above, if q is even, the units digit of the 4th power is almost always 6. In fact, only zero results in a units digit that’s not 6. So this isn’t enough information (it could be 0 or 6) but it’s close.

The second statement tells us that q is not a multiple of five. From the chart, we can see that that’s not immediately helpful. It excludes numbers with a units digit of 0 or 5, but that’s not enough for a definitive answer.

Together, though, we know that q is even, but not a multiple of 5. That means it’s even but doesn’t end in 0. With that information, we know the units digit of the 4th power must be 6. So together there is enough information.

A quick note: this seems like a lot to know for the GMAT. It is. But it’s a very possible question. The more you know about these random question types ahead of taking the test, the better off you will be.

To see more GMAT challenges, visit Integrated Learning.