I came across this problem (attached) on one of GMAT Club's quant tests (Math # 8, question # 7). I find the solution flawed because:
1. The question asked is: "what is the largest number of people who like Raspberry Jam, but do not like either Strawberry or Apple Jam.
2. However, in the solution, the equation for the answer contains a term which = people who like strawberry, raspberry and apple jam. This clearly contradicts the question. Please clarify.
The question asks "What is the largest POSSIBLE number of people.......
In such questions, you do need to take into consideration the number of people who do not like any of the jam ("N").
Had the question asked "What is the number of people who liked Raspberry ONLY ?", question would have either specifically mentioned the value of N or ruled out the possibility of N.
Hope it helps.