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There are 19 two-digit positive integers greater than 60.

62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98

Edit: Since you didn't specify greater than 60 up to 100, the answer to your question as written is infinite.

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