# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-8/7

Exercises: Try Out - Set 8: Real exam simulation to sharpen your skills and build confidence. - Problem 7

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## Exercise 7

### Question

export const metadata = {
    title: "Problem 7",
    authors: [{ name: "Nabil Akbarazzima Fatih" }],
    date: "12/25/2025",
};

The operation <InlineMath math="\odot" /> on the set of integers is defined by <InlineMath math="a \odot b = 3ab - 2(1 + b)" />. The value of <InlineMath math="(5 \odot 2) \odot 3 = \dots" />


### Choices

- [ ] $$96$$
- [ ] $$110$$
- [ ] $$128$$
- [ ] $$156$$
- [x] $$208$$

### Answer & Explanation

export const metadata = {
  title: "Solution for Problem 7",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

Based on the definition of the operation <InlineMath math="\odot" />, we will calculate the value of <InlineMath math="(5 \odot 2) \odot 3" /> step by step. First, we calculate the part inside the parentheses, which is <InlineMath math="5 \odot 2" /> with <InlineMath math="a = 5" /> and <InlineMath math="b = 2" />.

<BlockMath math="\begin{aligned} 5 \odot 2 &= 3(5)(2) - 2(1 + 2) \\ &= 30 - 2(3) \\ &= 30 - 6 \\ &= 24 \end{aligned}" />

Next, we operate the result with <InlineMath math="3" />. Now we calculate <InlineMath math="24 \odot 3" /> with <InlineMath math="a = 24" /> and <InlineMath math="b = 3" />.

<BlockMath math="\begin{aligned} 24 \odot 3 &= 3(24)(3) - 2(1 + 3) \\ &= 216 - 2(4) \\ &= 216 - 8 \\ &= 208 \end{aligned}" />

Thus, the value of <InlineMath math="(5 \odot 2) \odot 3" /> is <InlineMath math="208" />.


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