Question

if x and y are the number of possibilities that I can assume such that the unit digit of a and a cube are same and the unit digit of Y is square and a cube are same respectively then the value of x minus y is where a is a single digit number

Answer 1

Thank you for asking this question. Here is your answer:

These are the possibilities  

For a single digit number A  

it's cube  is equal to it's number itself  

if A ={1,-1,0}

it's square is equal to it's number itself

if A={1,0}

x-y=3-2=1

If there is any confusion please leave a comment below.

Answer 2

Total number of digits={0,1,2,3,4,5,6,7,8,9}=10

→0²=0,1²=1,2²=4,3²=9,4²=16,5²=25,6²=36,7²=49,8²=64,9²=81

→0³=0,1³=1,2³=8,3³=27,4³=64,5³=125,6³=216,7³=343,8³=512,9³=729

⇒ As given unit digit of a and a³ are same.

X=Total number of ordered pairs=(0,0³),(1,1³),(4,4³),(5,5³),(6,6³),(9,9³)=6 in number

⇒ It is also given that unit digit of a² and  a³ are same.

Y=Total number of ordered pairs=(0²,0³)(1²,1³),(5²,5³),(6²,6³),=4, in number

As,X=6,Y=4, So, X -Y=6-4=2