Question : If a nine-digit number 789x6378y is divisible by 72, then the value of xy is:
Option 1: 10
Option 2: 12
Option 3: 8
Option 4: 15
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Correct Answer: 8
Solution :
Given number = 789x6378y
Since the number is divisible by 72
It means it is divisible by 8 and 9 both.
For divisible by 8 ⇒ last 3 digits 78y is divisible by 8 when y = 4
Now, the number becomes 789x63784
For divisible by 9 ⇒ 7 + 8 + 9 + x + 6 + 3 + 7 + 8 + 4 = (52 + x)
This is divisible by 9 only when x = 2
Now, The value of xy = 2 × 4 = 8
Hence, the correct answer is 8.
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