# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-5/16

Exercises: Try Out - Set 5: Real exam simulation to sharpen your skills and build confidence. - Problem 16

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## Exercise 16

### Question

export const metadata = {
  title: "Problem 16",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

The following numbers form a series <InlineMath math="72, x, 65, 60, 30, 27, y, 8" />. The values of <InlineMath math="x" /> and <InlineMath math="y" /> respectively are...


### Choices

- [ ] $$81 \text{ and } 10$$
- [x] $$65 \text{ and } 9$$
- [ ] $$66 \text{ and } 11$$
- [ ] $$68 \text{ and } 12$$
- [ ] $$68 \text{ and } 8$$

### Answer & Explanation

export const metadata = {
  title: "Solution to Problem 16",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

The given number series is <InlineMath math="72, x, 65, 60, 30, 27, y, 8" />. Let's analyze the pattern:

<MathContainer>
  <BlockMath math="72 \xrightarrow{-7} 65" />
  <BlockMath math="65 \xrightarrow{\div 1} 65" />
  <BlockMath math="65 \xrightarrow{-5} 60" />
  <BlockMath math="60 \xrightarrow{\div 2} 30" />
  <BlockMath math="30 \xrightarrow{-3} 27" />
  <BlockMath math="27 \xrightarrow{\div 3} 9" />
  <BlockMath math="9 \xrightarrow{-1} 8" />
</MathContainer>

The pattern involves alternating operations of subtraction and division.
1. Subtraction by decreasing odd numbers: <InlineMath math="-7, -5, -3, -1" />.
2. Division by increasing integers: <InlineMath math="\div 1, \div 2, \div 3" />.

Based on this pattern:
- The value of <InlineMath math="x" /> is obtained from <InlineMath math="72 - 7 = 65" />.
- The value of <InlineMath math="y" /> is obtained from <InlineMath math="27 \div 3 = 9" />.

So, the values of <InlineMath math="x" /> and <InlineMath math="y" /> respectively are <InlineMath math="65" /> and <InlineMath math="9" />.


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