Seven times a two-digit positive number is equal to four times the number obtained by reversing the order of the digits. How many such two-digit numbers are there ?

Explanation

Let the number be 10x + y. Given 7(10x + y) = 4(10y + x), which simplifies to 66x = 33y, or y = 2x. Possible digits (x, y) are (1, 2), (2, 4), (3, 6), and (4, 8). Thus, there are 4 such numbers.

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