alleryIf the 7-digit number 5432y71 is divisible by 9, what is the single-digit value of y?
A5
B6
C7
D4
Answer & Solution
Correct answer: A. 5
A number is divisible by 9 if and only if the sum of its digits is divisible by 9.
Sum of digits = 5 + 4 + 3 + 2 + y + 7 + 1 = 22 + y.
For 22 + y to be divisible by 9, the nearest multiple of 9 greater than or equal to 22 is 27.
22 + y = 27 => y = 5.
Since y is a single digit (0 <= y <= 9), y = 5 is the unique valid value.
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