Multiple choice

In a series of positive integers each term is divisible by the sum of its digits. The 10th number of the series of such integers (with 12 being the first term) is

  1. 48

  2. 42

  3. 45

  4. 36

  5. 40
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B Correct answer
Explanation

The series consists of Harshad numbers (numbers divisible by the sum of their digits). The sequence is 12, 18, 20, 21, 24, 27, 30, 36, 40, 42. The 10th number is 42.

AI explanation

Starting with 12, the sequence of integers divisible by their digit sum continues as 18, 20, 21, 24, 27, 30, 36, 40, and 42. We check 42 because 4 plus 2 equals 6, and 42 is divisible by 6. Counting 12 as the first term, 42 is the tenth term in this exact sequence. Thus, the required tenth number is 42.

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