In the set of consecutive integers from 12 to 30, inclusive, there are four integers that are multiples of both 2 and 3. How many integers in this set are multiples of neither 2 nor 3?
- A5
- B6
- C13
- D15
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Correct answer: B
The question asks for integers from 12 to 30 that are not divisible by 2 or 3. The set of consecutive integers is
{12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30}
Since all even numbers are divisible by 2, eliminate all even numbers, leaving the odd numbers in the set:
{13, 15, 17, 19, 21, 23, 25, 27, 29}
Eliminate those integers that are multiples of 3 (15, 21, and 27). The remaining integers are:
{13, 17, 19, 23, 25, 29}
Therefore, there are 6 numbers in the set that are multiples of neither 2 nor 3.