If x and y are the number of possibilities that A can assume such that the unit digit of A and A3 are same and the unit digit of A2 and A3 are same respectively ,then the value of x−y is (where A is a single digit number)

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Here, according to the questionif A=1, then A3=1, We see that unit digit number of A and A3 are same.for, A=2⇒A3=8,, unit digits are not same      A=3⇒A3=27, unit digits are not same      A=4⇒A3=64, unit digits are same      A=5⇒A3=125, unit digits are same      A=6⇒A3=216, unit digits are not same      A=7⇒A3=343, unit digits are not same      A=8⇒A3=512, unit digits are not same      A=8⇒A3=512, unit digits are sameSo, there are five possible solutions where unit digits of A and A3 are same.      ∴x=5Again, if we take A=1,A2=1,A3=1, unit digits are same  A=2⇒A2=4,A3=8, unit digits are not same  A=3⇒A2=9,A3=27, unit digits are not same  A=4⇒A2=16,A3=64, unit digits are not same  A=5⇒A2=25,A3=125, unit digits are same  A=6⇒A2=36,A3=216, unit digits are same  A=7⇒A2=49,A3=343, unit digits are not same  A=8⇒A2=64,A3=512, unit digits are not same  A=9⇒A2=81,A3=729 unit digits are not sameHere, we can see that there are three possible solutions where unit digits of A2,A3 are same.So, y=3Hence, x−y=5−3=2.

Question Text	If $x$ and $y$ are the number of possibilities that $A$ can assume such that the unit digit of A and $A^{3}$ are same and the unit digit of $A^{2}$ and $A^{3}$ are same respectively ,then the value of $x - y$ is (where $A$ is a single digit number)
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If $x$ and $y$ are the number of possibilities that $A$ can assume such that the unit digit of A and $A^{3}$ are same and the unit digit of $A^{2}$ and $A^{3}$ are same respectively ,then the value of $x - y$ is (where $A$ is a single digit number)

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