The value of X - Y such that the eight-digit number 7448X24Y is divisible by both 8 and 9 is 7
The eight-digit number is given as:
7448X24Y
Also, from the question
The number is divisible by 8 and 9
When a number is divisible by 8, then the last three digits of that number would be divisible by 8.
When a number is divisible by 9, the sum of the digits of the number would be divisible by 9.
So, we have:
24Y is divisible by 8
The possible value of Y from the above statement is 0
This is so because 240 is divisible by 8
The sum of the digits of the number would be divisible by 9.
This means that:
7 + 4 + 4 + 8 + X + 2 + 4 + Y = 29 + X + Y
Substitute 0 for Y
29 + X + Y = 29 + X + 0
Evaluate the sum
29 + X + Y = 29 + X
36 is divided by 9
So, we have
29 + X = 36
Subtract 29 from both sides of the equation
X = 7
So, we have
X = 7 and Y = 0
X - Y is calculated as:
X - Y = 7 - 0
Evaluate the difference in the above equation
X - Y = 7
Hence, the value of X - Y such that the eight-digit number 7448X24Y is divisible by both 8 and 9 is 7
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