# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-9/13

Exercises: Try Out - Set 9: Real exam simulation to sharpen your skills and build confidence. - Problem 13

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## Exercise 13

### Question

export const metadata = {
  title: "Problem 13",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

A set of data has an average of <InlineMath math="24" /> and a range of <InlineMath math="12" />. If each data value is subtracted by <InlineMath math="a" /> and then the result is divided by <InlineMath math="b" />, it produces new data with an average of <InlineMath math="10" /> and a range of <InlineMath math="6" />. The values of <InlineMath math="a" /> and <InlineMath math="b" /> are...


### Choices

- [ ] $$14 \text{ and } 2$$
- [ ] $$12 \text{ and } 2$$
- [ ] $$8 \text{ and } 2$$
- [x] $$4 \text{ and } 2$$
- [ ] $$2 \text{ and } 2$$

### Answer & Explanation

export const metadata = {
  title: "Solution for Problem 13",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

#### Properties of Average and Range

-   **Average**: Its value changes if each data point is added, subtracted, multiplied, or divided.
-   **Range**: Its value **only** changes if each data point is multiplied or divided (it does not change if added or subtracted).

#### Finding the Value of <InlineMath math="b" />

The initial range is <InlineMath math="12" />. Then, each data value is subtracted by <InlineMath math="a" /> and divided by <InlineMath math="b" />. Since the range only changes when multiplied or divided, the new range becomes:

<MathContainer>
  <BlockMath math="j_{new} = \frac{j_{initial}}{b}" />
  <BlockMath math="6 = \frac{12}{b}" />
  <BlockMath math="b = \frac{12}{6}" />
  <BlockMath math="b = 2" />
</MathContainer>

#### Finding the Value of <InlineMath math="a" />

The initial average is <InlineMath math="24" />. Then, each data value is subtracted by <InlineMath math="a" /> and divided by <InlineMath math="b" />, so the new average becomes:

<MathContainer>
  <BlockMath math="\bar{x}_{new} = \frac{\bar{x}_{initial} - a}{b}" />
  <BlockMath math="10 = \frac{24 - a}{b}" />
</MathContainer>

Substitute the value <InlineMath math="b = 2" />:

<MathContainer>
  <BlockMath math="10 = \frac{24 - a}{2}" />
  <BlockMath math="20 = 24 - a" />
  <BlockMath math="a = 24 - 20" />
  <BlockMath math="a = 4" />
</MathContainer>

Thus, the values are <InlineMath math="a = 4" /> and <InlineMath math="b = 2" />.


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