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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

### 1 Best Answer

1
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
commented Jun 18, 2014 by Guru (5,808 points)
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