Question : If the number 476xy0 is divisible by both 3 and 11, then in the hundredth and tenth places, the non-zero digits are, respectively:
Option 1: 2 and 3
Option 2: 3 and 2
Option 3: 5 and 8
Option 4: 8 and 5
Correct Answer: 8 and 5
Solution :
Let the given number be 476xy0.
Then (4 + 7 + 6 + x + y + 0) = (17 + x + y) must be divisible by 3.
And, (0 + x + 7) − (y + 6 + 4) = (x − y − 3) must be either 0 or 11.
From these conditions, we get x = 8 and y = 5.
Hence, the correct answer is 8 and 5.
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