Question

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)

Answer 1

Hi there!
Here's the answer:

•°•°•°•°•°•<><><<><>><><>°•°•°•°•°•

¶¶¶ Step-1: Find Values of x and Y

There exists 10 possible cases for Unit digit of 'A':

Unit digit of : 
A ______ A² ______ A³
0 ______ 0 _______ 0
1 _______ 1 _______ 1
2 ______ 4 _______ 8
3 ______ 9 _______ 7
4 ______ 6 _______ 4
5 ______ 5 _______ 5
6 ______ 6 _______ 6
7 ______ 9 _______ 3
8 ______ 4 _______ 2
9 ______ 1 _______ 9

Now, 

x = No. of possible cases in which unit digit of A and A³ are the same

When Unit digit of A ={0, 1, 4, 5, 6}, Unit digit of A³ remains unchanged.

•°• x = 6

y= No. of possible cases in which unit digit of A² and A³ are the same

This is possible are when Unit digit of A = {0, 1, 5, 6}

•°• y = 4

¶¶¶ Step- 2: Find x-y

x - y = 6 -4 = 2

•°• Required value = 2

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Hope it helps