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Question

Pick a two digit number with distinct digits. Now, reverse the digits. Subtract the smaller number from the larger number. The result will always be the multiple of ____ .


A
11
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B
12
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C
18
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D
9
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Solution

The correct option is D 9
Let the two digit number be ab = 10a + b and its reverse will be ba = 10b + a.

If a > b, ab - ba
= 10a + b - (10b + a)
= 10a + b - 10b - a
= 9a - 9b
= 9(a - b)

If b > a, ba - ab
= 10b + a - (10a + b)
= 10b + a - 10a - b
= 9b - 9a 
= 9 (b - a)

Therefore, the difference between 10a + b and 10b + a will be 9(a - b) if a > b and 9(b - a) if b > a.

Either way, the number obtained will be a multiple of 9.

Mathematics

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