(a) How many two-digit positive integers are multiples of 3?
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All multiples of 3 can be expressed as , where n is a positive integer. A two digit number is at least 10 (greater than 9), and no more than 99 (lesser than or equal to99).
2 digit numbers which are multiples of 3: 12, 15, 18, 21, …, 90, 93, 96, 99. Consider this A.P. : a = 12, d = 3, 99 = 12 + (n- 1) (3) => n - 1 = 87/3 = 29 => n = 30. There are 30 multiples of 3 in all 2 digit numbers.
2 digit numbers which are multiples of 3: 12, 15, 18, 21, …, 90, 93, 96, 99. Consider this A.P. : a = 12, d = 3, 99 = 12 + (n- 1) (3) => n - 1 = 87/3 = 29 => n = 30. There are 30 multiples of 3 in all 2 digit numbers.
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Answer:
30 multiples lie on two digit number on multiplying of 3
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