# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-10/4

Exercises: Try Out - Set 10: Real exam simulation to sharpen your skills and build confidence. - Set Operations on Numbers

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## Exercise 4

### Question

export const metadata = {
  title: "Set Operations on Numbers",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/27/2025",
};

Set <InlineMath math="A" /> contains all negative integers, set <InlineMath math="B" /> contains all positive even integers, and set <InlineMath math="C" /> contains all positive integers divisible by <InlineMath math="3" />.

Which of the following numbers is NOT included in the product of two members of sets <InlineMath math="A" />, <InlineMath math="B" />, or <InlineMath math="C" />?


### Choices

- [ ] $$-14$$
- [ ] $$-15$$
- [ ] $$-18$$
- [x] $$14$$
- [ ] $$18$$

### Answer & Explanation

export const metadata = {
    title: "Set Operations Explanation",
    authors: [{ name: "Nabil Akbarazzima Fatih" }],
    date: "12/27/2025",
};

Let's define the members of each set:

<MathContainer>
  <BlockMath math="A = \{-1, -2, -3, \dots\}" />
  <BlockMath math="B = \{2, 4, 6, \dots\}" />
  <BlockMath math="C = \{3, 6, 9, \dots\}" />
</MathContainer>

We will check each option to see if the number can be formed by multiplying two members of these sets.

#### Analysis of Options

1.  **Option A**: <InlineMath math="-14" />

    <MathContainer>
       <BlockMath math="-14 = (-7) \times 2" />
    </MathContainer>

    Here, <InlineMath math="-7 \in A" /> and <InlineMath math="2 \in B" />. So, <InlineMath math="-14" /> is possible.

2.  **Option B**: <InlineMath math="-15" />

    <MathContainer>
       <BlockMath math="-15 = (-5) \times 3" />
    </MathContainer>

    Here, <InlineMath math="-5 \in A" /> and <InlineMath math="3 \in C" />. So, <InlineMath math="-15" /> is possible.

3.  **Option C**: <InlineMath math="-18" />

    <MathContainer>
       <BlockMath math="-18 = (-3) \times 6" />
    </MathContainer>

    Here, <InlineMath math="-3 \in A" /> and <InlineMath math="6 \in B" /> (also <InlineMath math="6 \in C" />). So, <InlineMath math="-18" /> is possible.

4.  **Option D**: <InlineMath math="14" />

    <MathContainer>
       <BlockMath math="14 = 2 \times 7" />
    </MathContainer>

    Here, <InlineMath math="2 \in B" />. However, <InlineMath math="7" /> is a positive odd integer that is not divisible by <InlineMath math="3" />. This means:
    -   <InlineMath math="7 \notin A" /> (since <InlineMath math="A" /> contains negative integers).
    -   <InlineMath math="7 \notin B" /> (since <InlineMath math="7" /> is odd).
    -   <InlineMath math="7 \notin C" /> (since <InlineMath math="7" /> is not divisible by <InlineMath math="3" />).

    Since one of the factors (<InlineMath math="7" />) is not present in sets <InlineMath math="A" />, <InlineMath math="B" />, or <InlineMath math="C" />, <InlineMath math="14" /> cannot be formed (assuming the pattern involves factors from different sets or positive factors).

5.  **Option E**: <InlineMath math="18" />

    <MathContainer>
       <BlockMath math="18 = 2 \times 9" />
    </MathContainer>

    Here, <InlineMath math="2 \in B" /> and <InlineMath math="9 \in C" />. So, <InlineMath math="18" /> is possible.

Therefore, the number that is NOT included in the product is <InlineMath math="14" />.


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