# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-6/17

Exercises: Try Out - Set 6: 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: "12/23/2025",
};

Given an integer <InlineMath math="m" />, if <InlineMath math="m" /> is divided by <InlineMath math="7" /> the remainder is <InlineMath math="3" />, and if <InlineMath math="m" /> is divided by <InlineMath math="3" /> the remainder is <InlineMath math="2" />. Possible values for <InlineMath math="m" /> are
1. <InlineMath math="52" />
2. <InlineMath math="59" />
3. <InlineMath math="42" />
4. <InlineMath math="38" />


### Choices

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

### Answer & Explanation

export const metadata = {
  title: "Solution to Problem 17",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

Given the conditions for integer <InlineMath math="m" />:
*   <InlineMath math="m \equiv 3 \pmod{7}" /> (If divided by <InlineMath math="7" />, remainder is <InlineMath math="3" />)
*   <InlineMath math="m \equiv 2 \pmod{3}" /> (If divided by <InlineMath math="3" />, remainder is <InlineMath math="2" />)

Let's check each statement:

#### Analysis of Statement 1
Value <InlineMath math="m = 52" />. Divided by <InlineMath math="7" />: <InlineMath math="52 = 7 \times 7 + 3" />. Remainder <InlineMath math="3" /> (Satisfied). Divided by <InlineMath math="3" />: <InlineMath math="52 = 17 \times 3 + 1" />. Remainder <InlineMath math="1" /> (**Not satisfied**, should be <InlineMath math="2" />). Thus, statement <InlineMath math="1" /> is **incorrect**.

#### Analysis of Statement 2
Value <InlineMath math="m = 59" />. Divided by <InlineMath math="7" />: <InlineMath math="59 = 8 \times 7 + 3" />. Remainder <InlineMath math="3" /> (Satisfied). Divided by <InlineMath math="3" />: <InlineMath math="59 = 19 \times 3 + 2" />. Remainder <InlineMath math="2" /> (Satisfied). Thus, statement <InlineMath math="2" /> is **correct**.

#### Analysis of Statement 3
Value <InlineMath math="m = 42" />. Divided by <InlineMath math="7" />: <InlineMath math="42 = 6 \times 7 + 0" />. Remainder <InlineMath math="0" /> (**Not satisfied**, should be <InlineMath math="3" />). Divided by <InlineMath math="3" />: <InlineMath math="42 = 14 \times 3 + 0" />. Remainder <InlineMath math="0" /> (**Not satisfied**, should be <InlineMath math="2" />). Thus, statement <InlineMath math="3" /> is **incorrect**.

#### Analysis of Statement 4
Value <InlineMath math="m = 38" />. Divided by <InlineMath math="7" />: <InlineMath math="38 = 5 \times 7 + 3" />. Remainder <InlineMath math="3" /> (Satisfied). Divided by <InlineMath math="3" />: <InlineMath math="38 = 12 \times 3 + 2" />. Remainder <InlineMath math="2" /> (Satisfied). Thus, statement <InlineMath math="4" /> is **correct**.

Since statements <InlineMath math="2" /> and <InlineMath math="4" /> are correct, the correct answer is **If <InlineMath math="(2)" /> and <InlineMath math="(4)" /> are correct**.


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