Q. Let X be a two-digit number and Y be another two-digit number formed by interchanging the digits of X. If (X+Y) is the greatest two-digit number, then what is the number of possible values of X?

Explanation:

X+Y is the greatest two-digit number

Let’s approach this step-by-step:

1) First, we need to understand what the question is asking:
– X is a two-digit number
– Y is formed by interchanging the digits of X
– The sum of X and Y is the greatest two-digit number

2) The greatest two-digit number is 99.

3) So, we’re looking for pairs of numbers X and Y that add up to 99.

4) Let’s represent X as ‘ab’ where ‘a’ is the tens digit and ‘b’ is the ones digit.
Then Y would be represented as ‘ba’.

5) We can write an equation:
ab + ba = 99

6) This can be rewritten as:
(10a + b) + (10b + a) = 99
11a + 11b = 99
a + b = 9

7) Now, we need to find all possible integer combinations of a and b where:
– a and b are single digits (0-9)
– a + b = 9

8) The possible combinations are:
0 and 9
1 and 8
2 and 7
3 and 6
4 and 5
5 and 4
6 and 3
7 and 2
8 and 1
9 and 0

9) However, we can’t use 0 as the first digit of a two-digit number, so we eliminate the first and last combinations.

10) This leaves us with 8 possible combinations.

Therefore, the correct answer is d) 8. There are 8 possible values for X.