X and Y Too Confused me ?

To be divisible by 5, the last digit must be 5 or 0. if y = 0, then it will become a three digit number. So it must be y = 5 and the digits are now 57X5.

For X, let's focus on the number's divisibility on 3. X must not be negative because there's no such number that has negative tens digit. X also must be below 10.

The sum of digits is X + 17. If we will think of the values of X, then those are 1, 4 and 7 and the ordered pairs are (1, 5), (4, 5) and (7, 5). So there are 3 ordered pairs....

Y has to be 5 or 0 to be divisible by 5 and can only be 5 for Y7XY to be a four didget number. (57X5) since 5700 is divisible by 5 and 3 we can concentrate on 100 where multiples of 3 only create a units didget of 5 at 15, 45 and 75. Therefore (X,Y) can only be (1,5) (4,5) and (7,5)

Given

Y7XY is divisible by 3 & 5

$\Rightarrow$ The given number is divisible by 15

The value of Y must be 5.If it is 0 then the given number is not a four digit number

$\Rightarrow$ The given number is 57X5

The only thing is the given number must be divisible by 3

By applying the divisibility rule for 3, we get

5+7+X+5=17+X

The given number should be divisible by 3, then the value of X are

1,4,7

Therefore the ordered pairs of (X,Y) are

(1,5);(4,5);(7,5)

Therefore there are 3 ordered pairs

only one value for Y, i.e. 5, since Y7XY is divisible by 5, and three values for X:1,4,7 for divisibility of Y7XY by 3... thus 4 values

The values of Y = 5, 4 The values of X = 1, 7

So, there are total of 4 values.