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.
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Source: Beat The GMAT — Problem Solving |
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pradeepkaushal9518
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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
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 neoreavesneoreaves 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
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
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eaakbari wrote:Hey neoreavesneoreaves 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
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 ....
