number properties

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by mj78ind » Fri Jan 27, 2012 10:37 am
sud21 wrote:What is the remainder when K^4 is divided by 10?
1). K is not divisible by 5.
2). K is even.
Stmt 1 - k can end in all digits 0 to 9 except, 0 and 5. If we look at the last digit of the k^4, when k does not end in 0 or 5, we find that it either ends in 1 or 6, depending if k is odd or even. Thus INSUFFICIENT.

Stmt 2 - if k is even, it can end in 0 or (2,4,6 or8) the remainders in such as case are 0 or 6, as discussed above. INSUFFICIENT.

Stmt 1 and 2 - Leaves k with an ending digit of 2,4,6 or8 and for any of these cases, k^4 ends in 6 and thus the remainder has to be 6. SUFFICIENT.

Hence C
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