skalevar wrote:If n and m are positive integers what is the remainder when 3^(4n +2) + m is divided by 10?

1) n = 2
2) m =1

Patrick_GMATFix wrote:

skalevar wrote:If n and m are positive integers what is the remainder when 3^(4n +2) + m is divided by 10?

1) n = 2
2) m =1

Hi Skalevar,

The key is to solving this Q quickly is to come up with a strong rephrase. Recognize 2 general rules:

1) remainder when an integer is divided by 10 is the units digit of that integer. So the question can be rephrased as: What is the units digit of 3^(4n+2) + m?

2) units digit of an exponential expression follows a cyclical pattern as the exponent is incremented

In this case rephrasing is key. Since 3^(4n+2) is 9^(2n+1). In other words, it is 9 raised to an odd exponent. Regardless of the exponent, the units digit of 9^(odd) is 1. So to determine the units digit of 3^(4n+2) + m, we only need the units digit of m.

Rephrase: What is the units digit of m?

Statement 2 gives us this info so it's sufficient. The answer is B.

A more detailed explanation and a step-by-step video solution is available at GMATPrep Question 1395. If you struggle with advanced remainder problems, set topic='Number Properties' and difficulty='700+' in the Drill Engine.

Good luck,
Patrick

PLease explain. Regardless of the exponent, the units digit of 9^(odd) is 1. So to determine the units digit of 3^(4n+2) + m, we only need the units digit of m..
Regards
Deeyah