# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-5/3

Exercises: Try Out - Set 5: Real exam simulation to sharpen your skills and build confidence. - Problem 3

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## Exercise 3

### Question

export const metadata = {
  title: "Problem 3",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

Given an integer <InlineMath math="n" />. If <InlineMath math="n" /> is divided by <InlineMath math="4" />, the remainder is <InlineMath math="2" />, and if the number is divided by <InlineMath math="6" />, the remainder is <InlineMath math="2" />. The possible value(s) of <InlineMath math="n" /> is/are ...

1. <InlineMath math="18" />
2. <InlineMath math="24" />
3. <InlineMath math="36" />
4. <InlineMath math="38" />


### Choices

- [ ] If $$(1)$$, $$(2)$$, and $$(3)$$ are correct.
- [ ] If $$(1)$$ and $$(3)$$ are correct.
- [ ] If $$(2)$$ and $$(4)$$ are correct.
- [x] If only $$(4)$$ is correct.
- [ ] If all are correct.

### Answer & Explanation

export const metadata = {
  title: "Solution to Problem 3",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

We are given two conditions for the integer <InlineMath math="n" />:
1. <InlineMath math="n \equiv 2 \pmod{4}" /> (remainder is <InlineMath math="2" /> when divided by <InlineMath math="4" />)
2. <InlineMath math="n \equiv 2 \pmod{6}" /> (remainder is <InlineMath math="2" /> when divided by <InlineMath math="6" />)

We will check each statement to see if the value of <InlineMath math="n" /> satisfies both conditions.

#### Checking Statement 1

Value <InlineMath math="n = 18" />.
- Divided by <InlineMath math="4" />: <InlineMath math="18 \div 4 = 4" /> remainder <InlineMath math="2" />. (Satisfied)
- Divided by <InlineMath math="6" />: <InlineMath math="18 \div 6 = 3" /> remainder <InlineMath math="0" />. (Not Satisfied)

Thus, statement <InlineMath math="(1)" /> is **incorrect**.

#### Checking Statement 2

Value <InlineMath math="n = 24" />.
- Divided by <InlineMath math="4" />: <InlineMath math="24 \div 4 = 6" /> remainder <InlineMath math="0" />. (Not Satisfied)

Thus, statement <InlineMath math="(2)" /> is **incorrect**.

#### Checking Statement 3

Value <InlineMath math="n = 36" />.
- Divided by <InlineMath math="4" />: <InlineMath math="36 \div 4 = 9" /> remainder <InlineMath math="0" />. (Not Satisfied)

Thus, statement <InlineMath math="(3)" /> is **incorrect**.

#### Checking Statement 4

Value <InlineMath math="n = 38" />.
- Divided by <InlineMath math="4" />: <InlineMath math="38 \div 4 = 9" /> remainder <InlineMath math="2" />. (Satisfied)
- Divided by <InlineMath math="6" />: <InlineMath math="38 \div 6 = 6" /> remainder <InlineMath math="2" />. (Satisfied)

Thus, statement <InlineMath math="(4)" /> is **correct**.

#### Conclusion

Of the four options, only statement <InlineMath math="(4)" /> satisfies both conditions.


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