# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-8/17

Exercises: Try Out - Set 8: Real exam simulation to sharpen your skills and build confidence. - Question 17

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## Exercise 17

### Question

export const metadata = {
  title: "Question 17",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

The decimal value closest to the largest value among the fractions <InlineMath math="\frac{34}{33}, \frac{6.1}{6}, \frac{56}{55}, \frac{12.5}{12.4}, \frac{26}{25}" /> is...


### Choices

- [ ] $$1.181$$
- [ ] $$1.030$$
- [ ] $$1.124$$
- [x] $$1.040$$
- [ ] $$1.110$$

### Answer & Explanation

export const metadata = {
  title: "Solution to Question 17",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

The fractions can be rewritten in the form <InlineMath math="1 + \frac{1}{x}" /> as follows:

<MathContainer>
  <BlockMath math="\frac{34}{33} = 1 \frac{1}{33} = 1 + \frac{1}{33}" />
  <BlockMath math="\frac{6.1}{6} = \frac{61}{60} = 1 \frac{1}{60} = 1 + \frac{1}{60}" />
  <BlockMath math="\frac{56}{55} = 1 \frac{1}{55} = 1 + \frac{1}{55}" />
  <BlockMath math="\frac{12.5}{12.4} = \frac{125}{124} = 1 \frac{1}{124} = 1 + \frac{1}{124}" />
  <BlockMath math="\frac{26}{25} = 1 \frac{1}{25} = 1 + \frac{1}{25}" />
</MathContainer>

So, all numbers have the form <InlineMath math="1 + \frac{1}{x}" />. To find the largest value, we need to find the fraction where <InlineMath math="\frac{1}{x}" /> is largest. The value of <InlineMath math="\frac{1}{x}" /> increases as the denominator <InlineMath math="x" /> decreases.

From the five fractions above, the values of <InlineMath math="x" /> are <InlineMath math="33, 60, 55, 124," /> and <InlineMath math="25" /> respectively. The smallest <InlineMath math="x" /> is <InlineMath math="25" />.

Therefore, the largest value is <InlineMath math="\frac{26}{25}" />.

Let's calculate its decimal value:

<BlockMath math="\frac{26}{25} = \frac{26 \times 4}{25 \times 4} = \frac{104}{100} = 1.04" />

The decimal value is <InlineMath math="1.040" />.


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