Problem Solving

I can see 2 overlapping sets questions that are solved in 2 different types with different formulas.
Could someone please help me understand these ?

Question from MGMAT word translation:
Q1: Workers are grouped by their areas of expertise, and are placed on at least one team. 20 are on the marketing team, 30 are on the Sales team, and 40 are on the Vision team. 5 workers are on both the Marketing and Sales teams, 6 workers are on both the sales and Vision teams, 9 workers are on both the Marketing and Vision teams, and 4 workers are on all three teams. How many workers are there in total?

Solution: Marketing + sales + vision - (marketing and sales +marketing and vision + vision and sales) + (in all three)
= 20+30+40 - (5+6+9) + 4 = 74 (answer)

Question from MGMAT CAT test:
Q2: Each of the 59 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 22 students sign up for the poetry club, 27 students for the history club, and 28 students for the writing club. If 6 students sign up for exactly two clubs, how many students sign up for all three clubs?
Solution:
Total = Poetry + History + writing - (poetry and history + poetry and writing + writing and history) - 2 (in all three)
59 = 22+27+28 - (6) - 2x
so, x = 6

Can you try to reverse engineer question 2?

That is assume that you are given the value x = 6. And you have to find out how many students are there in the class in total. Just try this and let me know what method you employed. You will know exactly why that is done.

I am preparing a detailed explanation if you need.

Q1: Workers are grouped by their areas of expertise, and are placed on at least one team. 20 are on the marketing team, 30 are on the Sales team, and 40 are on the Vision team. 5 workers are on both the Marketing and Sales teams, 6 workers are on both the sales and Vision teams, 9 workers are on both the Marketing and Vision teams, and 4 workers are on all three teams. How many workers are there in total?

yes making Venn diagram makes it look easy. i have broken the values to make it clearer. the only catch is that the question doesnt use the word only... I always prefer the Venn diagram instead of formulas.



All the best...