If a 10-digit number 5432Y1749X is divisible by 72, then what is the value of (5X - 4Y)?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 14
When a number is divisible by 72 it means it will be also divisible by 8 × 9
When last 3 digit of any number is divisible by 8 then the number is also divisible by 8
When the sum of all digit of any number is divisible by 9 then the number is also divisible by 9
Given number = 5432Y1749X
The given number will be divisible by 8 when 49X is divisible by 8
If we put X = 6 then 496 will be divisible by 8
Now
The number = 5432Y17496
Sum of its digit = 5 + 4 + 3 + 2 + Y + 1 + 7 + 4 + 9 + 6 = 41 + Y
Minimum possible value of Y = 4
Because 41 + 4 = 45 will be divisible by 9
∴ X = 6 and Y = 4
∴ 5X - 4Y = 5 × 6 - 4 × 4 = 30 - 16 = 14