another one whose solution eludes me if (3^4n)+1 is divided

Question

another one whose solution eludes me

if (3^4n)+1 is divided by 10, can hte remainder be 0?
1. n=2m+1
2. n>4 

pls explain your answer

boksana · Answer

something wrong with the question formulation :roll:

If it's divided by 10, it already means rem. =0

lastochka · Answer

let me clarify the question stem. If you take the following product (3^4n)+1 and devide it by 10, is it possible to have zero for remainder?

1. n=2m+1 
2. n>4

Paul · Answer

weird question. E it is
1) 3^4n + 1 = 81^n + 1 --> introduction of "m" is intriguing. "m" could be any number which makes it that 81^n + 1 equals something with 0 as remainder
2) there could be some fraction "n" which makes it that when 81^n + 1 is divided by 10, the remainder could be 0. Haven't work it out yet.

I suspect the quality of this question though

ashkg · Answer

I go for D

1. let E= 3^4n + 1 = 81^(2m+1) + 1

 81 to the power of anything will end in 1

 so E will always end in 2. Not divisible by 10 . Remainder can't be 0. Therefore , Sufficient

2. let E= 3^4n+1 . Here n>4

 E = 81^n + 1

 81 to the power of anything will end in 1

 so E will always end in 2. Not divisible by 10 . Remainder can't be 0. Therefore , Sufficient

Answer should be D.

- ash

carsen · Answer

Hi 3^6 will give 9 as the last number...then 9+1=10, which is divisible by 10. (Note, it is not given that n is an integer- tricky one :-D

). The same explaination goes for statement A and B. Hence the answer should be E.

ashkg · Answer

I can't understand how you came up with 3^6 ?

B says n>4

and we want to find out what 3^4n ends in......which should be 1 as n>4.

I still feel B is sufficient.

For A, it depend on the value of m.

If m is +ve integer or 0, exp is definitely not div by 10.
If 2m+1 = 1/2, exp is div by 10.
For all other values of m, exp would not be div by 10.

Therefor A is insufficient. ( assuming we dont have any more info on m)

- ash.

OA and more info on n and m would clear things

carsen · Answer

Hi

Let us consider statment by statement.

The stem says... if  (3^4n)+1 is divided by 10, can the remainder be 0? 

Statement 1. n=2m+1 (If n=30) then the equation will result in divisble by 10. Fro N to be 30, m=14.5. (It has not been mentioned that either N or M is a integer. Hence M can take any value. FOr other values, the result may be not divisible by 10. Hence NOT SUFFICIENT.

2. n>4 - The same case as above. It is not been mentioned that N is an integer, hence n can take a value 30 for the equation to be divisible by 10. Or any other value that wud result in as not divisible by 10. Hence NOT SUFFICIENT.

Combining both the cases. - We do not know the value of M. Hence it is not possible to get one value of N to say that the equation is divisible by 10. NOT SUFFICIENT.

Hence the answer is E.

Correct me if I am wrong. Am i missing something here.

Regards

carsen · Answer

Hi

I missed giving another value of N where the equation wud result in as a divisible of 10.

When N=14, then the result wud come to remainder 0, when divided by 10.

Regards

ashkg · Answer

true......my assumption of n ( and earlier m ) being an Integer is wrong

therefore B and A are both insufficient...... - ash

Emmanuel · Answer

3^4n + 1 : n = 0 => remainder = 2,
n = 1 => remainder = 2,
n = 2 => remainder = 2,
n = 3 => remainder = 2,
n = 4 => remainder = 2,

3^4n = 81^n = (8*10+1)^n = 10*m + 1.

=> 3^4n + 1 is NEVER divided by 10, therefore, we can't answer this question.

lastochka · Answer

I fell in the same trap as you when I originally looked at this question, and I couldn't believe that the answer provided, D, was correct.
If n=1.5, then (3^4n)+1 gets us 730, which is fully divisible by 10. 
just read ashkg's post above for further clarification.

Ashkg, great job solving this one!

another one whose solution eludes me if (3^4n)+1 is divided

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