If the 9-digit number 5x82y6588 is exactly by 99 (x + y < 10), then what is the value of y - x?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 1.
A number is divisible by 99 if it is divisible by both 9 and 11
Sum of digits = 5 + x + 8 + 2 + y + 6 + 5 + 8 + 8 = 42 + x + y
If x + y = 3 then 42 + x + y = 45 (divisible by 9)
Alternating sum = (5 + 8 + y + 5 + 8) - (x + 2 + 6 + 8) = (26 + y) - (16 + x) = 10 + y - x
If y - x = 1 then 10 + + y - x = 11 (divisible by 11)
From x + y = 3 and y - x = 1, we get x = 1 and y = 2
So, y - x = 2 - 1 = 1