Final answer:
The student will correctly answer 42 out of the 100 items by marking every multiple of 4 as true and every multiple of 3 as false when considering the overlap of multiples of 12, which must be subtracted from both counts.
Step-by-step explanation:
To find out how many of the 100 items are correctly answered, recognize that a question is correctly answered only if the rules defined by the test maker and the rule used by the student match. Since every question that is a multiple of 4 is true, and the student marks every item that is a multiple of 3 as false, there will be questions marked correctly only when they are not multiples of 3 but are multiples of 4 or when they are not multiples of 4 and are not multiples of 3.
Let's calculate the number of multiples of 4 up to 100: there are 100 / 4 = 25 of them. Now, let's calculate the number of multiples of 3 up to 100: there are 100 / 3 = 33, with the understanding that we round down to the nearest whole number since we cannot have a fraction of a question. However, since some numbers are multiples of both 3 and 4 (multiples of 12), we must subtract these from both counts to avoid double-counting. There are 100 / 12 = 8 multiples of 12. So, the questions correctly marked true are multiples of 4, but not 12, giving us 25 - 8 = 17.
The questions correctly marked false are not multiples of 4 and are multiples of 3, so we subtract the multiples of 12 from the multiples of 3: 33 - 8 = 25. Therefore, in total, the student will correctly answer 17 (true) + 25 (false) = 42 questions.