How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the number formed by interchanging the positions of its digits?
Explanation:
Let the original number be 'xy' = 10x + y and the number formed by reversing the digits = 'yx' = 10y + x.
We have the following:
10x + y > 3(10y + x)
∴ x > 297y
When y = 1, x = 5, 6, 7, 8 or 9 (Total 5 values)
When y = 2, x = 9 (Total 1 value)
If y > 3, x has to be a 2 digit number which is not possible.
∴ The required answer is 5 + 1 = 6.
Hence, option (a).
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