If 243^x*463^y = n, where x and y are positive integers

Solution

Step 1: Analyse Question Stem

• \( 243^x*463^y = n\)

o Where x and y are positive integers.
• We need to find the unit digit of n.

o Now, the unit digit of both \(243^x\) and \(463^y\) will follow the cyclicity of 3.
o i.e. the unit digit of \(243^x\) = unit digit of \(3^x\)
o And, the unit digit of \(463^y\) = unit digit of \(3^y\)

 Therefore, the unit digit of \( 243^x*463^y\) = The unit digit of \( 3^x*3^y\) = The unit digit of \(3^{x+y}\)

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE

• The unit digit of \( 243^x*463^y = n\) = The unit digit of \(3^{7}\)
• We can easily find the unit digit of \(3^{7}\) and hence the unit digit of n from this statement.

• From this statement we know the value of x but we don’t know y.
• Therefore, we cannot find the unit digit of \(3^{x+y}\) and hence the unit digit of n from this statement.