Adia writes a list in increasing order of the integers between 1 and 100, inclusive, that cannot be written as the product of two consecutive positive integers. What is the 40th integer in her list?
The integers less than 50 that can be written as a product of two consecutive positive integers are $1 \cdot 2=2,2 \cdot 3=6,3 \cdot 4=12,4 \cdot 5=20,5 \cdot 6=30$, and $6 \cdot 7=42$.

Therefore, there are $50-6=44$ positive integers less than or equal to 50 that cannot be written as the product of two consecutive positive integers.

This means that 50 would be the 44th integer in Adia's list.

Counting backwards from 50, this means that the 40th integer in Adia's list is $50-4=46$. (None of the numbers eliminated are between 46 and 50.)

ANSWER: 46