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

Official answer is B, 2) along is sufficient but I don't understand why. Any takers?

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- sk818020
- Master | Next Rank: 500 Posts
**Posts:**214**Joined:**29 Mar 2010**Location:**Houston, TX**Thanked**: 37 times**GMAT Score:**700

3^1=3

3^2=9

3^3=27

3^4=81

3^5=243

3^6=729

3^7=2187

3^8=6561

3^10=59049

Some other thing to note;

3^(4n+2)

- 3 will always in this example be raised to a positive power. So you should tell yourself to look for patterns in the even powers.

- The power that 3 will be raised to will always be 2 or a multiple of 4, plus two. So, 2, 6=[4(1)+2], 10=[4(2)+2] and so forth. Note this and then look at the numbers above. 2, 6, and 10 all end in 9. When you notice a pattern like this you need to take advantage of it.

Going off the notion that 3^(4n+2) will have a nine in it's digits place we only need to know what the value of m is to solve the question.

(2) tells us what m is so we can solve the problem. Thus, 2 is sufficient.

- Patrick_GMATFix
- GMAT Instructor
**Posts:**1053**Joined:**21 May 2010**Thanked**: 335 times**Followed by:**98 members

Hi Skalevar,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

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

- Check out my site: GMATFix.com

- To prep my students I use this tool >> (screenshots, video)

- Ask me about tutoring.

Hi Skalevar,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

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 atGMATPrep 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