there are certain two digits numbers. the difference between the number and the one obtained on reversing it is always 27. How many such maximum 2 digit numbers are there?
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The answer has to be a factor of 27, the only option that's a factor of 27 is 3.
Sice (10x+y)−(10y+x)=27(10x+y)−(10y+x)=27, you can simplify this relationship by subtracting with a common factor --> 9x - 9y = 27 ---> 9(x - y) = 27 ---> here, you already notice that the difference has to be a factor of both 9 and 27, but you can simplify further ---> x - y = 3, and thus we have the answer.
But these last steps are superfluous if you already notice that the answer has to be a factor of 27, this way you save time without having to calculate.
Hope This Helps :)
Sice (10x+y)−(10y+x)=27(10x+y)−(10y+x)=27, you can simplify this relationship by subtracting with a common factor --> 9x - 9y = 27 ---> 9(x - y) = 27 ---> here, you already notice that the difference has to be a factor of both 9 and 27, but you can simplify further ---> x - y = 3, and thus we have the answer.
But these last steps are superfluous if you already notice that the answer has to be a factor of 27, this way you save time without having to calculate.
Hope This Helps :)
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