# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-7/17

Exercises: Try Out - Set 7: Real exam simulation to sharpen your skills and build confidence. - Problem 17

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## Exercise 17

### Question

export const metadata = {
  title: "Problem 17",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

Given <InlineMath math="4" /> numbers as follows:
1. <InlineMath math="18" />
2. <InlineMath math="38" />
3. <InlineMath math="58" />
4. <InlineMath math="78" />

If these numbers are divided by <InlineMath math="5" />, the remainder is <InlineMath math="3" />, and if divided by <InlineMath math="4" />, the remainder is <InlineMath math="2" />. Among the four numbers, which one is correct?


### Choices

- [ ] $$1, 2, 3$$
- [ ] $$1, 3$$
- [ ] $$2, 4$$
- [ ] $$4$$ only
- [x] all

### Answer & Explanation

export const metadata = {
  title: "Explanation for Problem 17",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

We will check each number to see if it satisfies both conditions: divided by <InlineMath math="5" /> gives a remainder of <InlineMath math="3" /> AND divided by <InlineMath math="4" /> gives a remainder of <InlineMath math="2" />.

#### Analysis of Statement <InlineMath math="1" />

Number: <InlineMath math="18" />.

- Divided by <InlineMath math="5" />: <InlineMath math="18 = 3 \times 5 + 3" />. Remainder is <InlineMath math="3" />. (Satisfied)
- Divided by <InlineMath math="4" />: <InlineMath math="18 = 4 \times 4 + 2" />. Remainder is <InlineMath math="2" />. (Satisfied)

So, the number <InlineMath math="18" /> is correct.

#### Analysis of Statement <InlineMath math="2" />

Number: <InlineMath math="38" />.

- Divided by <InlineMath math="5" />: <InlineMath math="38 = 7 \times 5 + 3" />. Remainder is <InlineMath math="3" />. (Satisfied)
- Divided by <InlineMath math="4" />: <InlineMath math="38 = 9 \times 4 + 2" />. Remainder is <InlineMath math="2" />. (Satisfied)

So, the number <InlineMath math="38" /> is correct.

#### Analysis of Statement <InlineMath math="3" />

Number: <InlineMath math="58" />.

- Divided by <InlineMath math="5" />: <InlineMath math="58 = 11 \times 5 + 3" />. Remainder is <InlineMath math="3" />. (Satisfied)
- Divided by <InlineMath math="4" />: <InlineMath math="58 = 14 \times 4 + 2" />. Remainder is <InlineMath math="2" />. (Satisfied)

So, the number <InlineMath math="58" /> is correct.

#### Analysis of Statement <InlineMath math="4" />

Number: <InlineMath math="78" />.

- Divided by <InlineMath math="5" />: <InlineMath math="78 = 15 \times 5 + 3" />. Remainder is <InlineMath math="3" />. (Satisfied)
- Divided by <InlineMath math="4" />: <InlineMath math="78 = 19 \times 4 + 2" />. Remainder is <InlineMath math="2" />. (Satisfied)

So, the number <InlineMath math="78" /> is correct.

In conclusion, all four numbers are correct.


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