ETS Quantitative reasoning mixed practice set question

[fallen_ranger]

The question is from ETS official quant reasoning book vol 1 edition 3

Question 1: (Set 3, Pg. 184)

For this question I used the choosing number approach but couldn’t do it because when I made the Venn diagram the numbers didn’t add up to 100 (assumed total # of students as 100). When I looked at the solution I could understand until the Venn diagram part but couldn’t understand why they are dividing 15%/20%. So could someone explain that?

Solution:

[cylverixxx]

@fallen_ranger

For this question I used the choosing number approach but couldn’t do it because when I made the Venn diagram the numbers didn’t add up to 100 (assumed total # of students as 100).

The union of the science and band clubs is not the universal set. In other words, you could have students in the population who belong to neither club. If you account for this group of people as well, then you can make the “numbers add up to 100.”

Here are the numbers you should have:

• |\mathcal{U}| = 100

• |S| = 20

• |B| = 30

• |S \cap B| = 30 - 25 = 5

• |S \cup B|^c = 100 - (20 + 30 - 5) = 55