# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-8/19

Exercises: Try Out - Set 8: Real exam simulation to sharpen your skills and build confidence. - Question 19

---

## Exercise 19

### Question

export const metadata = {
  title: "Question 19",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

In a class, there are <InlineMath math="30" /> students participating in extracurricular activities. There are <InlineMath math="12" /> students who join the scouts extracurricular and <InlineMath math="15" /> students who join the futsal extracurricular, and <InlineMath math="7" /> students who join both. The number of students who do not join either is...


### Choices

- [ ] $$3$$
- [x] $$10$$
- [ ] $$13$$
- [ ] $$19$$
- [ ] $$22$$

### Answer & Explanation

export const metadata = {
  title: "Solution to Question 19",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

Let:
- <InlineMath math="n(S)" /> = Total number of students in the class
- <InlineMath math="n(P)" /> = Number of students in scouts
- <InlineMath math="n(F)" /> = Number of students in futsal

Given:

<MathContainer>
  <BlockMath math="n(S) = 30" />
  <BlockMath math="n(P) = 12" />
  <BlockMath math="n(F) = 15" />
  <BlockMath math="n(P \cap F) = 7" />
</MathContainer>

The number of students who do not participate in either (<InlineMath math="n(P \cup F)^c" />) can be found using the universal set formula:

<MathContainer>
  <BlockMath math="n(S) = n(P) + n(F) - n(P \cap F) + n(P \cup F)^c" />
</MathContainer>

Substitute the known values:

<MathContainer>
  <BlockMath math="30 = 12 + 15 - 7 + n(P \cup F)^c" />
  <BlockMath math="30 = 20 + n(P \cup F)^c" />
  <BlockMath math="n(P \cup F)^c = 30 - 20" />
  <BlockMath math="n(P \cup F)^c = 10" />
</MathContainer>

Thus, the number of students who do not join scouts and futsal extracurriculars is <InlineMath math="10" />.


---
