Thanks Danaj,DanaJ wrote:Actually, you should consider that there are some situations where number picking is the only way. This is one situation. There are countless others where you can solve algebraically, but just breaking it down into cases according to x and y is waaay too tedious and not worth it (at least in my head).
Normally, for this type of exercise, you'd use one of the classical rules of units digit:
A number with units digit 1, 5 or 6 will keep its units digit throughout all its >=1 powers.
It's important to remember that rule, so you'll have to check for some <1 powers (as you did with 0.5).
Extra: @wccotton: don't use negative powers when establishing the units digit (unless specifically asked). Most of the time, when we talk about units digits, we only use positive powers. Units digits for non-integers (i.e. 0.5) are usually not discussed.
Can you please tell....how to quickly find out which approach we should take...number substitution or algebraic....as in Test time most likely we will not have that much liberty to try first method...if that does not work then try second....IMO it will be better if we somehow have fair bit of idea of how to attack a question before hand.....
