A two digit number and its inverse

Algebra Level 2

Supposing I have a two digit number XY , I subtract the inverse YX from it, the resultant number will always be divisible by ------?

X Y 9 11

Srinivasa Gopal by Srinivasa Gopal , 53, India

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2 solutions

Saksham Jain
Oct 18, 2017

1 no. Is 10x+y 2 no. Is 10y-x Clearly the difference is divisible by 9

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Srinivasa Gopal
Oct 17, 2017

Let the two digit number be XY. XY can be written as 10X + Y. The inverse of XY is YX which is nothing but 10Y + X. The difference between XY and YX is 9X - 9Y which is nothing but 9 (X-Y). It can be easily seen that this is divisible by 9.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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