If the 8- digit number 888x53y4 is divisible by 72, then what is the value of (7x + 2y), for the maximum value of y?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 23
Co -prime factors of 72 = 8 × 9.
If a number is divisible by 8 it means the last three digits of a number is divisible by 8.
So 3y4 must be divisible by 8.
It is only possible at y = 0, 4 and 8 (we need the maximum value of y so one can ignore 0 and 4 )
If a number is divisible by 9 it means the sum of the digits of the same number must be divisible by 9.
8 + 8 + 8 + x + 5 + 3 + y + 4 = 36 + x + y
36 is already a multiple of 9 so one can say that x + y must be divisible by 9.
y is 8 then the possible value of x will be 1.
Required value of 7x + 2y = 7 × 1 + 2 × 8 = 7 + 16 = 23.