Meenakshi picks a 3-digit number and subtracts it from the same number after reversingorder of its digits. This difference will always be fully divisible by which number?
Question
Meenakshi picks a 3-digit number and subtracts it from the same number after reversingorder of its digits. This difference will always be fully divisible by which number?
Solution
The difference will always be fully divisible by 9. Here's why:
Step 1: Let's assume the 3-digit number Meenakshi picks is XYZ (where X, Y, and Z are its digits).
Step 2: The number after reversing its digits will be ZYX.
Step 3: The difference between XYZ and ZYX can be written as (100X + 10Y + Z) - (100Z + 10Y + X).
Step 4: Simplifying this, we get 99X - 99Z, which can be factored to 99(X - Z).
Step 5: Since 99 is divisible by 9, the difference (X - Z) will also be divisible by 9, regardless of the values of X and Z. Therefore, the difference between the original number and its reverse will always be divisible by 9.
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