I guess the answer is 4.

Since the question imposes that remainder will be same for all values of n. I took n as 1

that gives us 3 ^11

To find out the units place, we know

3^2 = 9
3^3 = 27
3 ^4 = 81
3 ^ 5 = _9

So we can say the units digit is a repeating pattern of 9,7,8.

Hence 11 will be 7

Now ____7 + 2 = _____9

If we divide this by 5 , by looking solely at the units digit we can say remainder is 4, as needs units digit as either 0 or 5.

imO answer is 4 what is the OA

IMO 1


3^8n --> lets figure this out

Lets take a look at the unit digits for 3^n
3^1 = 3
3^2 =9
3^3 = 7
3^4 = 1
3^5 = 3

thus we have iterations of 3971 and we can safely say that 8n is a multiple of 4 so no matter what 3^8n has unit digit of 1


Now lets add the unit digit with the rest of the expression

1+ 3 + 2 = 6

6 /5 = 1

Thus answer should be 1

neoreaves wrote:IMO 1


3^8n --> lets figure this out

Lets take a look at the unit digits for 3^n
3^1 = 3
3^2 =9
3^3 = 7
3^4 = 1
3^5 = 3

thus we have iterations of 3971 and we can safely say that 8n is a multiple of 4 so no matter what 3^8n has unit digit of 1


Now lets add the unit digit with the rest of the expression

1+ 3 + 2 = 6

6 /5 = 1

Thus answer should be 1

Hey neoreaves
I agree your solution is correct but I think the question is 3^(8n+3) + 2 not 3^8n+3 + 2. Then again I may be wrong and you right

eaakbari wrote:

neoreaves wrote:IMO 1


3^8n --> lets figure this out

Lets take a look at the unit digits for 3^n
3^1 = 3
3^2 =9
3^3 = 7
3^4 = 1
3^5 = 3

thus we have iterations of 3971 and we can safely say that 8n is a multiple of 4 so no matter what 3^8n has unit digit of 1


Now lets add the unit digit with the rest of the expression

1+ 3 + 2 = 6

6 /5 = 1

Thus answer should be 1

Hey neoreaves
I agree your solution is correct but I think the question is 3^(8n+3) + 2 not 3^8n+3 + 2. Then again I may be wrong and you right

I think on actual gmat there wont be any ambiguity about that but for now I think we have to go by what is presented to us ....in this case--> without the parenthesis ....so thats why i solved like that ....

thanks so much... the answer is 4