# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-7/3

Exercises: Try Out - Set 7: Real exam simulation to sharpen your skills and build confidence. - Question 3

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## Exercise 3

### Question

export const metadata = {
  title: "Question 3",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/24/2025",
};

Given the following <InlineMath math="4" /> numbers:

1. <InlineMath math="19" />
2. <InlineMath math="29" />
3. <InlineMath math="39" />
4. <InlineMath math="49" />

When these numbers are divided by <InlineMath math="5" />, the remainder is <InlineMath math="4" />, and when divided by <InlineMath math="4" />, the remainder is <InlineMath math="3" />. Which of the following is correct...


### Choices

- [ ] $$1, 2, \text{ and } 3$$
- [x] $$1 \text{ and } 3$$
- [ ] $$2 \text{ and } 4$$
- [ ] $$4 \text{ only}$$
- [ ] All correct

### Answer & Explanation

export const metadata = {
  title: "Question 3 Explanation",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/24/2025",
};

We will check each number to see if it satisfies the following two conditions:
1. When divided by <InlineMath math="5" />, the remainder is <InlineMath math="4" /> (<InlineMath math="n \equiv 4 \pmod 5" />).
2. When divided by <InlineMath math="4" />, the remainder is <InlineMath math="3" /> (<InlineMath math="n \equiv 3 \pmod 4" />).

#### Checking Number 19

<MathContainer>
  <BlockMath math="19 = 3 \times 5 + 4 \quad (\text{remainder } 4)" />
  <BlockMath math="19 = 4 \times 4 + 3 \quad (\text{remainder } 3)" />
</MathContainer>

The number <InlineMath math="19" /> satisfies both conditions. (Correct)

#### Checking Number 29

<MathContainer>
  <BlockMath math="29 = 5 \times 5 + 4 \quad (\text{remainder } 4)" />
  <BlockMath math="29 = 7 \times 4 + 1 \quad (\text{remainder } 1)" />
</MathContainer>

The number <InlineMath math="29" /> does not satisfy the second condition because the remainder is <InlineMath math="1" /> when divided by <InlineMath math="4" />. (Incorrect)

#### Checking Number 39

<MathContainer>
  <BlockMath math="39 = 7 \times 5 + 4 \quad (\text{remainder } 4)" />
  <BlockMath math="39 = 9 \times 4 + 3 \quad (\text{remainder } 3)" />
</MathContainer>

The number <InlineMath math="39" /> satisfies both conditions. (Correct)

#### Checking Number 49

<MathContainer>
  <BlockMath math="49 = 9 \times 5 + 4 \quad (\text{remainder } 4)" />
  <BlockMath math="49 = 12 \times 4 + 1 \quad (\text{remainder } 1)" />
</MathContainer>

The number <InlineMath math="49" /> does not satisfy the second condition because the remainder is <InlineMath math="1" /> when divided by <InlineMath math="4" />. (Incorrect)

#### Conclusion

The numbers that satisfy the conditions are <InlineMath math="19" /> and <InlineMath math="39" /> (Statements <InlineMath math="1" /> and <InlineMath math="3" />).


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