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If (243)^x(463)^y = n, where x and y are positive integers, what is the units digit of n?

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If (243)x(463)y = n, where x and y are positive integers, what is the units digit of n

(1) x + y = 7

(2) x = 4

Official Answer

1 Best Answer

Best answer
Both the numbers have their last digit 3^x and 3^y so the units digit will be decided by the power of x+y i.e. 3^(x+y)
3^0 = 1
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
here we can see,  a pattern with a cycle of 4
Statement 1)  x+y = 7, as per the above discussion we can see this is SUFFICIENT
Statement 2)  x = 4, we dont know the value of y, hence this is INSUFFICIENT.
answered Jun 18, 2014 by Senior Associate (475 points)
selected Jun 18, 2014 by
perfect answer :)
commented Jun 18, 2014 by Guru (5,808 points)
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