Question
When you reverse the digits of the number 13, the number increases by 18. How many other two digit numbers increase by 18 when their digits are reversed?
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Answer:
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Let 10x + y be a two digit number, where x and y are positive single digit integers and x>0.
Its reverse = 10y + x
Now, 10y + x - 10x - y = 18
∴ 9(y - x) = 18 ∴ y - x = 2
Thus y and x can be (1, 3), (2, 4), (3, 5), (4, 6), (5, 7), (6, 8) and (7, 9)
∴ Other than 13, there are 6 such numbers.
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:
Let 10x + y be a two digit number, where x and y are positive single digit integers and x>0.
Its reverse = 10y + x
Now, 10y + x - 10x - y = 18
∴ 9(y - x) = 18 ∴ y - x = 2
Thus y and x can be (1, 3), (2, 4), (3, 5), (4, 6), (5, 7), (6, 8) and (7, 9)
∴ Other than 13, there are 6 such numbers.
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