Num Properties - GMAT Prep

ReenaMo wrote:Hi, I searched this question through the Beat the GMAT archives and found 2 posts on it. However (before anyone deletes this), I want to note that each of the posts gave a different response/explanation for the right answer (one arrived at A, while the other arrived at B). Can someone take a look at this and explain it again? By the way, OA is B. Thanks so much!

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

3^(4n+2) = 3^2(2n+1)= 9^(2n+1)

2n+1 is an ODD number

and 9^(2n+1) will always have 9 at its unit digit

Remember that N is Positive and an integer!

9^3 = XX9
9^5 = xxxx9
......

So we really don't need to know what N is to tell what the unit digit is, but we have to know what "m" is so we can find out the unit digit of :

3^(4n+2) + m

You also need to remember that when you divide any number by 10, the remainder is the unit number!

So,

1) Insuf
2) Suf

Hence, B

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[/b][/quote]

3/10...remainder = 3

3^2/10..........9

3^3/10 .........7

3^4/10...............1

3^5/10...........3

3^6/10...........9

so we have a sequence repeating every 4 exp multiple of 3, now lets look at the question

from one if n = 1

thus 3^(6)+m if m = 1 , then 3^7.remainder is 7, if m=2 remainder is 1


insuff

from 2

3^(4n+2)+1..........if n = 1 thus 3^7 has emainder of 7

if n = 2 then 3^(11) has remainder of 7

if n = 3 then 3^15 has remainder of 7...........suff

B

Awesome - thanks!