Re: M25-31
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07 Nov 2015, 12:44
My 2 cents: It doesn't matter whether you start your powers at 0 or at 1; all that matters is recognizing the pattern.
let mn = 0,1,2,3,...; then let last digit = x = 1,3,9,7,....; Because x repeats in these 4 numbers; we can tell that x = 1 implies mn = 0,4,8,12....; x=3 implies mn = 1,5,9...; x=9 implies mn = 2,6,10,...; x=7, implies mn = 3,7,11,.... The question that becomes, which series gets you to 27? x=1 and x =3 gives evens, so rule out, leaving x=3 and x=7. From here you can manually add 4 to each series and see which one gets to 27. The answer is x=7. Or if you like algebra, find the series formula for each. For x=3; we have mn = 1,5,9...= 4a -3. There is no integer a such that 4a-3 = 27. On the other hand, for x=7, we have mn = 3,7,11,... or 4a-1. And 4a-1=27 yields an integer value of a, meaning that this series will reach 27