the five-digit number 24X8Y is divisible by 4, 5, 9. calculate the sums of X and y

Question

the five-digit number 24X8Y is divisible by 4, 5, 9. calculate the sums of X and y.

i need to now explenation step by step ty

Answer 1

The previous tutor is correct that it has to be an even number for it to be divisible by 4 and Y has to be 0 for it to be divisible by 5. So we know that Y is 0. For the number to be divisible by 9 the sum of all the digits must add up to a number that is also divisible by 9. So far we have 24X80 which adds up to 2+4+X+8+0=14+X. Seeing as X can only be a single number from 0 to 9 the only number that can be added to 14 that the total sum will equal to a number that can be divisible by 9 is 4: 2+4+4+8+0=18 which is divisible by 9. Therefore, X=4 and Y=0. You can check this by dividing the number, 24480, by 4, 5 and 9 and you will see that this is correct.

Answer 2

I can't give you an answer, but I can give you some things to think about.

The number is divisible by 4; therefore, it must be even.

It is also divisible by 5. The only even numbers divisible by 5 end in 0; i.e. Y must be 0.

Since the number is divisible by 9, it is also divisible by 3; therefore, the sum of the digits must be divisible by 3, i.e. 14+x must be divisible by 3. The only digits which will satisfy this requirement are 1 and 7.

Neither 24780 nor 24180 are divisible by 9.

You need to take it from here!