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
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
