yvonne12 wrote:if n is not equal to m are positive integers, what is the remainder, when 3^4n+2 + m is divided by 10?
1. n=2
2. m=1
.. when u divide a number by 10 the remainder is the last digit ( the unit digit ) ... so for finding the reminder of 3^4n u need to know thelast digit of 3^4n ...
... now look at successive powers of 3 ... 3^1=3, 3^2=9, 3^3=27, 3^4=81, 3^5 = 243 .... so if u see the last digit keeps repeating itself at intervals of 4 so if 3^2 has a last digit of 9... then the last digit of 3^6 = is also 9 ..(3^6=729) ... similarly if 3^4 = 81 has a last digit of 1 then 3^8 has a last digit of 1 also 3^12 has a last digit of 1 ... hope u get the point ...
now look at the statements ... the first one says n=2 .. so u get 3^8+ 2 + m /10 has a remainder ... of 1 (bcoz the last digit of 3^8 is 1) +2 + m... that is 3 + m .. but since we dont know the value of m .. the statemnet is insufficient ..
the second statement says that m = 1 .. so we have (3^4n+2+1)/10 .. now comes the intereting part ... look at 3^4n ... 4n means that the power raised to 3 will always be a multiple of 4 .. so the last digit of 3^4n will always be 1 (bcoz it is given that n is a positive integer) ... it doesnt matter what is the value of n.. 3^4 , 3^(4*2), 3^(4*3) .. when n=1,2,3... these numbers will always have the last digit of 1 .. so for (3^4n+2+1 )/10 will have a remainder of 1+2+1 = 4 .. so B is sufficient .. ans is B ... hope this helps ..
