Bunuel wrote:
If x and y are positive integers and n = 5^x + 7^(y + 3), what is the units digit of n?
(1) y = 2x – 16
(2) y is divisible by 4.
Kudos for a correct solution.
Analysis :
X > 0 , Y > 0
5 raise to anything (greater than zero) will have 5 in unit digit. 7 has power cycle of 4 - 7,9,3,1
So unit digit will depend on unit digit of n will depend on 7^(y + 3), that means Unit digit of n will depend on Y.
statement 1 :
y = 2x – 16, y can be anything hence statement 1 is not sufficient.
Statement 2 :
y is divisible by 4,
Y = 4K, and Y + 3 = 4K +3
so 7 ^(Y + 3) will have unit digit of 3.
Statement 2 is sufficient.
Hence Option B is correct.