If (243)x(463)y = n, where x and y are positive integers, what is the units digit of n?
Assumption: (243)x(463)y = 243*x*463*y, Unit's digit of n = Unit's digit of 9*x*y
So the question can be rephrased as; What is the Unit's digit of 9*x*y ?
(1) x + y = 7
(x,y) = (6,1) Unit's digit of 9*x*y = 9*6*1 = 4
(x,y) = (1,6) Unit's digit of 9*x*y = 9*6*1 = 4
(x,y) = (5,2) Unit's digit of 9*x*y = 9*5*2 = 0
(x,y) = (2,5) Unit's digit of 9*x*y = 9*2*5 = 0
(x,y) = (4,3) Unit's digit of 9*x*y = 9*4*3 = 8
(x,y) = (3,4) Unit's digit of 9*x*y = 9*3*4 = 8
Hence, Insufficient !
(2) x = 4
9*x*y = 9*4*y = 36*y
Unit's digit of 36*y = 6 if y = 1
Unit's digit of 36*y = 2 if y = 2
Unit's digit of 36*y = 8 if y = 3
Unit's digit of 36*y = 4 if y = 4
Unit's digit of 36*y = 0 if y = 5
Unit's digit of 36*y = 6 if y = 6
Unit's digit of 36*y = 2 if y = 7
Unit's digit of 36*y = 8 if y = 8
Unit's digit of 36*y = 4 if y = 9
Hence, Insufficient!
From 1 and 2, x = 4, y = 3 and Unit's digit of 9*x*y = 9*4*3 = 8
Answer C
