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URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/2026/set-2/5

Exercises: Try Out 2026 - Set 2: Real exam simulation to sharpen your skills and build confidence. - Question 5

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## Exercise 5

### Question

export const metadata = {
  title: "Question 5",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "11/22/2025",
};

The following table presents data on the number of students related to their favorite subjects.

| Class | Math | Science | Social Studies |
| :---: | :---: | :---: | :---: |
| A | <InlineMath math="2a" /> | <InlineMath math="10" /> | <InlineMath math="20" /> |
| B | <InlineMath math="5" /> | <InlineMath math="15" /> | <InlineMath math="3a" /> |
| C | <InlineMath math="15" /> | <InlineMath math="10" /> | <InlineMath math="25" /> |

The total number of students from all classes is <InlineMath math="150" />.

Based on the information provided, which of the following relationships between quantity <InlineMath math="P" /> and <InlineMath math="Q" /> is correct?

| <InlineMath math="P" /> | <InlineMath math="Q" /> |
| :---: | :---: |
| Percentage of total students with Social Studies as their favorite subject | <InlineMath math="50\%" /> |



### Choices

- [ ] $$P > Q$$
- [ ] $$Q > P$$
- [x] $$P = Q$$
- [ ] $$P = 2Q$$
- [ ] The information provided is not sufficient to decide one of the three options above

### Answer & Explanation

export const metadata = {
  title: "Explanation 5",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "11/22/2025",
};

The first step is to find the value of <InlineMath math="a" /> by summing up all students and equating it to the known total students, which is <InlineMath math="150" />.

#### Calculating the Unknown Value

The total number of students is the sum of students from all subjects in all classes:

<MathContainer>
  <BlockMath math="\text{Total} = (2a + 10 + 20) + (5 + 15 + 3a) + (15 + 10 + 25)" />
  <BlockMath math="150 = 2a + 30 + 20 + 3a + 50" />
  <BlockMath math="150 = 5a + 100" />
</MathContainer>

Solve the equation:

<MathContainer>
  <BlockMath math="5a = 150 - 100" />
  <BlockMath math="5a = 50" />
  <BlockMath math="a = 10" />
</MathContainer>

#### Calculating Total Social Studies Students

Now we calculate the number of students who like Social Studies (IPS):

<MathContainer>
  <BlockMath math="\text{Total Social Studies} = 20 + 3a + 25" />
  <BlockMath math="= 45 + 3(10)" />
  <BlockMath math="= 45 + 30" />
  <BlockMath math="= 75" />
</MathContainer>

#### Calculating the First Quantity

Quantity <InlineMath math="P" /> is the percentage of total students with Social Studies as their favorite subject out of the total students:

<MathContainer>
  <BlockMath math="P = \frac{\text{Total Social Studies}}{\text{Total Students}} \times 100\%" />
  <BlockMath math="P = \frac{75}{150} \times 100\%" />
  <BlockMath math="P = 50\%" />
</MathContainer>

#### Comparing the Quantities

Given <InlineMath math="Q = 50\%" />.

Thus:

<BlockMath math="50\% = 50\% \Rightarrow P = Q" />


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