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z = (54 * 89 ) ^ n
The unit digit of this product is 6 and any number which has unit digit of 6 raised to any integer number will always be 6
However if N is not integer then the story is different.

z = (54 * 89 ) ^ n The unit digit of this product is 6 and any number which has unit digit of 6 raised to any integer number will always be 6 However if N is not integer then the story is different.

Looking at the equations X=54^n ---- in this for every odd value of "n" the unit number will be 4 and for every even value of "n" the unit number will be 6. This pattern 4,6,4,6 wil follow ---

As for the second one y=89^n, a similar one, for all odd value of n the unit number will be 9 and for even it is 1, hence following the pattern 9,1,9,1,...

Important - The above statements hold good only when n is a positive integer and not negetaive

Now, let us look at the statements

Statement A - N is a positive integer ... emm not good enough to kow the unit of z as n can be odd or even.

Statement B - N is a even integer .. emmm not good enough to know the unit as n can be a negetive even interger or positive even integer.

Let us combine them and see A and B, if it is +ve and even then we will get the unit digit as 6 (6x1=6). There is no other possibilty. Hence the answer is C. I hope this is right.

good try, but you all missed on trying out 0 (is even) in statement 2.

Ans is A.
1. is sufficient . if n=1, x=54^n =54, y=89^n =89, and x*y will have a units digit of (4*9=36) 6.
If n = 2 , x= 54^2 = ...6, y= 89^2 = ...1, and x*y will have a unit's digit of (4*9=36) 6.

2. is insufficient . if n=2, x=54^2 = ...6, y =89^2 =.. and x*y will have a units digit of (9*4=36) 6.
However, if n= 0, x = 54 ^0 = 1, y =89^0 =1, and thus x*y will have a units digit of 1.