# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-6/15

Exercises: Try Out - Set 6: Real exam simulation to sharpen your skills and build confidence. - Problem 15

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## Exercise 15

### Question

export const metadata = {
  title: "Problem 15",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

The average of three numbers is <InlineMath math="24" />. If one of the numbers is replaced by the number <InlineMath math="14" />, the average of the three numbers decreases by <InlineMath math="3" />.

| <InlineMath math="P" /> | <InlineMath math="Q" /> |
| :---: | :---: |
| The number being replaced | <InlineMath math="42" /> |


### Choices

- [ ] $$P > Q$$
- [x] $$P < Q$$
- [ ] $$P = Q$$
- [ ] $$P = 2Q$$
- [ ] Cannot determine the relationship between P and Q

### Answer & Explanation

export const metadata = {
  title: "Solution to Problem 15",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

We will find the value of the replaced number (quantity <InlineMath math="P" />) first.

#### Analyzing Quantity P

Let the three numbers be <InlineMath math="a, b," /> and <InlineMath math="c" />.
The initial average is given as <InlineMath math="24" />:

<MathContainer>
  <BlockMath math="\frac{a + b + c}{3} = 24" />
  <BlockMath math="a + b + c = 72" />
</MathContainer>

Suppose the number <InlineMath math="c" /> is replaced by the number <InlineMath math="14" />.
The new average decreases by <InlineMath math="3" /> from the initial average, so the new average becomes <InlineMath math="24 - 3 = 21" />.

<MathContainer>
  <BlockMath math="\frac{a + b + 14}{3} = 21" />
  <BlockMath math="a + b + 14 = 63" />
  <BlockMath math="a + b = 63 - 14" />
  <BlockMath math="a + b = 49" />
</MathContainer>

We substitute the value <InlineMath math="a + b = 49" /> into the initial equation to find the value of <InlineMath math="c" />:

<MathContainer>
  <BlockMath math="(a + b) + c = 72" />
  <BlockMath math="49 + c = 72" />
  <BlockMath math="c = 72 - 49" />
  <BlockMath math="c = 23" />
</MathContainer>

Thus, the replaced number is <InlineMath math="23" />.
So, <InlineMath math="P = 23" />.

#### Comparing P and Q

Given <InlineMath math="Q = 42" />.

<MathContainer>
  <BlockMath math="P = 23" />
  <BlockMath math="Q = 42" />
</MathContainer>

It is clear that <InlineMath math="23 < 42" />.

Thus, <InlineMath math="P < Q" />.


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