We can approach this problem by running a scenario and looking for a pattern.
What is the remainder when 3^1 is divided by 7? 3
What is the remainder when 3^2 is divided by 7? 2
What is the remainder when 3^3 is divided by 7? 6
What is the remainder when 3^4 is divided by 7? 4
What is the remainder when 3^5 is divided by 7? 5
What is the remainder when 3^6 is divided by 7? 1
What is the remainder when 3^7 is divided by 7? 3
and then the sequence repeats.
But how can we know that 3^7 / 7 has a remainder of 3? Doesn't that involve a lot of math?
Not really. It only involves figuring out the unit digit in base-7 math.
At first we have a 3. When we multiply by 3, that gives us a 9, but in base-7 math, that is a 12. The first digit represents the 7s place, and the second digit is the unit digit, which is all we care about.
We can construct our chart easily and quickly by focusing only on the units digit.
Once we know the pattern, what is 1989/6? Well, since we're only concerned with the remainder, we don't need to worry about the number of times it divides. We can easily take away 1800 to make the number more manageable. That leaves us with 189/6, and again we can take away 186 to yield a remainder of 3. Thus, it will have the same units digit as 3^3 has. If we consult our chart, we can see that this units digit will be 6.
Thus, (C) must be the best answer.
Elias Latour
Verbal Specialist @ ApexGMAT
blog.apexgmat.com
+1 (646) 736-7622
