There are 15 girls and some boys among the graduating students in a class. They are planning a get-together, which can be either a 1-day event, or a 2-day event, or a 3-day event. There are 6 singers in the class, 4 of them are boys. There are 10 dancers in the class, 4 of them are girls. No dancer in the class is a singer.

Some students are not interested in attending the get-together. Those students who are interested in attending a 3-day event are also interested in attending a 2-day event; those who are interested in attending a 2-day event are also interested in attending a 1-day event.

The following facts are also known:

1. All the girls and 80% of the boys are interested in attending a 1-day event. 60% of the boys are interested in attending a 2-day event.
2. Some of the girls are interested in attending a 1-day event, but not a 2-day event; some of the other girls are interested in attending both.
3. 70% of the boys who are interested in attending a 2-day event are neither singers nor dancers. 60% of the girls who are interested in attending a 2-day event are neither singers nor dancers.
4. No girl is interested in attending a 3-day event. All male singers and 2 of the dancers are interested in attending a 3-day event.
5. The number of singers interested in attending a 2-day event is one more than the number of dancers interested in attending a 2-day event.

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What fraction of the class are interested in attending a 2-day event?

Question

There are 15 girls and some boys among the graduating students in a class. They are planning a get-together, which can be either a 1-day event, or a 2-day event, or a 3-day event. There are 6 singers in the class, 4 of them are boys. There are 10 dancers in the class, 4 of them are girls. No dancer in the class is a singer.

Some students are not interested in attending the get-together. Those students who are interested in attending a 3-day event are also interested in attending a 2-day event; those who are interested in attending a 2-day event are also interested in attending a 1-day event.

The following facts are also known:

1. All the girls and 80% of the boys are interested in attending a 1-day event. 60% of the boys are interested in attending a 2-day event.
2. Some of the girls are interested in attending a 1-day event, but not a 2-day event; some of the other girls are interested in attending both.
3. 70% of the boys who are interested in attending a 2-day event are neither singers nor dancers. 60% of the girls who are interested in attending a 2-day event are neither singers nor dancers.
4. No girl is interested in attending a 3-day event. All male singers and 2 of the dancers are interested in attending a 3-day event.
5. The number of singers interested in attending a 2-day event is one more than the number of dancers interested in attending a 2-day event.

----

What fraction of the class are interested in attending a 2-day event?

Accepted Answer

To determine the fraction of the class interested in attending a **2-day event**, we analyze the problem step by step using the given data.

---

### Step-by-Step Analysis:

#### Key Information Recap:
1. **Total number of girls = 15.**
2. **Total number of boys = 50.**
3. **60% of boys are interested in attending a 2-day event:**
   $$
   	ext{Boys (2-day)} = 0.6 	imes 50 = 30.
   $$
4. **60% of girls interested in a 2-day event are neither singers nor dancers (Fact 3).**
5. **All girls are interested in attending a 1-day event, and some overlap with the 2-day event (Fact 1).**
6. **No girl is interested in attending a 3-day event (Fact 4).**

---

#### Step 2: Determine Students Interested in a 2-Day Event

##### Boys Interested:
- Total boys interested in a **2-day event** = **30**.

##### Girls Interested:
- Total girls = **15**.
- Since no girl attends a **3-day event**, all girls who attend the **1-day event** can also attend the **2-day event**:
$$
	ext{Girls (2-day)} = \mathbf{15}.
$$

##### Total Students Interested:
$$
	ext{Total Students (2-day)} = 	ext{Boys (2-day)} + 	ext{Girls (2-day)} = 30 + 15 = \mathbf{45}.
$$

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#### Step 3: Fraction of Class Interested
The total number of students in the class is:
$$
	ext{Total Class} = 	ext{Boys} + 	ext{Girls} = 50 + 15 = \mathbf{65}.
$$

The fraction of students interested in attending a **2-day event** is:
$$
\frac{	ext{Students Interested}}{	ext{Total Class}} = \frac{45}{65}.
$$

Simplify:
$$
\frac{45}{65} = \frac{\mathbf{7}}{\mathbf{13}}.
$$

---

### Conclusion:
The fraction of the class interested in attending a **2-day event** is **7/13**, making option **C** correct.

![Screenshot 2025-04-05 015146.png](https://res.cloudinary.com/aptidude/image/upload/v1743799801/aptidude_questions/e7zit6phc2qjptgbrtys.png)![Screenshot 2025-04-05 015154.png](https://res.cloudinary.com/aptidude/image/upload/v1743799819/aptidude_questions/awk02lbsmkdlop3ksnou.png)![Screenshot 2025-04-05 015201.png](https://res.cloudinary.com/aptidude/image/upload/v1743799830/aptidude_questions/oysire2zqsmq0eayjq2i.png)![Screenshot 2025-04-05 015206.png](https://res.cloudinary.com/aptidude/image/upload/v1743799843/aptidude_questions/hmatmmlkx1cqjzxxlctq.png)![Screenshot 2025-04-05 015211.png](https://res.cloudinary.com/aptidude/image/upload/v1743799854/aptidude_questions/xd0hfxobmkukism5n1zp.png)![Screenshot 2025-04-05 015215.png](https://res.cloudinary.com/aptidude/image/upload/v1743799861/aptidude_questions/wpg5njtvqjdmrqwxgwuh.png)

Answer

Answer

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