Question : A 9-digit number $846523X7Y$ is divisible by 9 and $Y - X = 6$. Find the value of $\sqrt{2X+4Y}$.
Option 1: 4
Option 2: 2
Option 3: 6
Option 4: 8
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Correct Answer: 6
Solution :
Given number = $846523X7Y$
Sum of digits = $35+X+Y$
Maximum value of $35+ X+Y = 35+18=53$
Minimum value of $35+X+Y = 35$
For a number to be divisible by 9, the sum of digits of the number should be divisible by 9.
So, the sum can be 36 or 45.
Case 1: $X + Y = 1$ and $Y - X = 6$
$Y=\frac{7}{2}$, which is not possible.
Case 2: $X + Y = 10$ and $Y - X = 6$
$Y=8$ and $X=2$.
So, $\sqrt{2 X+4 Y}=\sqrt{36}=6$
Hence, the correct answer is 6.
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