How many 2-digit-numbers are multiples of neither 5 or 7

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2-digit numbers range from 10 to 99 (90 numbers). The multiples of 5 range from 10 to 95, that is, 2×5 to 19×5 (18 multiples); and the multiples of 7 range from 14 to 98, that is, 2×7 to 14×7 (13 multiples). The multiples of 35 (=5×7) are 35 and 70 (2 multiples). So the number of numbers not divisible be 5 or 7=90-(18+13-2)=90-29=61.

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