In a coaching class, some students register online, and some others register offline. No student registers both online and offline; hence the total registration number is the sum of online and offline registrations. The following facts and table pertain to these registration numbers for the five months – January to May of 2023. The table shows the minimum, maximum, median registration numbers of these five months, separately for online, offline and total number of registrations. The following additional facts are known.

1. In every month, both online and offline registration numbers were multiples of 10.
2. In January, the number of offline registrations was twice that of online registrations.
3. In April, the number of online registrations was twice that of offline registrations.
4. The number of online registrations in March was the same as the number of offline registrations in February.
5. The number of online registrations was the largest in May.

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1743775593/aptidude_questions/wkmjhzv0v1kexn3x9gr0.png)

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Which of the following statements can be true?
I. The number of offline registrations was the smallest in May.
II. The total number of registrations was the smallest in February.

Question

In a coaching class, some students register online, and some others register offline. No student registers both online and offline; hence the total registration number is the sum of online and offline registrations. The following facts and table pertain to these registration numbers for the five months – January to May of 2023. The table shows the minimum, maximum, median registration numbers of these five months, separately for online, offline and total number of registrations. The following additional facts are known.

1. In every month, both online and offline registration numbers were multiples of 10.
2. In January, the number of offline registrations was twice that of online registrations.
3. In April, the number of online registrations was twice that of offline registrations.
4. The number of online registrations in March was the same as the number of offline registrations in February.
5. The number of online registrations was the largest in May.

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1743775593/aptidude_questions/wkmjhzv0v1kexn3x9gr0.png)

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Which of the following statements can be true?
I. The number of offline registrations was the smallest in May.
II. The total number of registrations was the smallest in February.

Accepted Answer

**Correct Answer:**  
**B. Only II**

### Explanation:

To determine which statements can be true, we analyze the given data and constraints step by step.

### Step-by-Step Analysis:

#### Key Observations from the Table
- **Online registrations (minimum = 40, maximum = 100, median = 80):**
  - The median indicates that **80** was one of the middle values for online registrations.
- **Offline registrations (minimum = 30, maximum = 80, median = 50):**
  - The median indicates that **50** was one of the middle values for offline registrations.
- **Total registrations (minimum = 110, maximum = 130, median = 120):**
  - The median indicates that **120** was one of the middle values for total registrations.

#### Verify Statement I: *The number of offline registrations was the smallest in May.*
- From Fact 5: May had the largest online registrations (**100**, as per maximum value).
- For May:
  $$
  	ext{Offline} = 	ext{Total} - 	ext{Online}.
  $$
- If Total = **110** (minimum possible), then Offline:
$$
	ext{Offline} = 110 - 100 = \mathbf{10}.
$$

However, the minimum offline registration number is explicitly stated as **30** in the table. Thus, **Offline registrations cannot be smaller than 30**, making Statement I **false**.

#### Verify Statement II: *The total number of registrations was the smallest in February.*
- From Fact 4: Online (March) = Offline (February).
- If February had the smallest total registration (**110**, minimum possible):
  - Assign Online + Offline to satisfy this condition:
    - Possible values: Offline = **50** (median), Online = $$110 - 50 = \mathbf{60}$$.
- This satisfies the condition that total registrations were smallest in February.

Thus, Statement II is **true**.

### Conclusion:
Only Statement II is true, making option **B (Only II)** correct.

![Screenshot 2025-04-02 190658.png](https://res.cloudinary.com/aptidude/image/upload/v1743602748/aptidude_questions/peecpuddlx3m5eeooyro.png)![Screenshot 2025-04-02 190652.png](https://res.cloudinary.com/aptidude/image/upload/v1743602741/aptidude_questions/htdacmv2dhhn5n1wjsnw.png)![Screenshot 2025-04-02 190641.png](https://res.cloudinary.com/aptidude/image/upload/v1743602735/aptidude_questions/dmiwpfxl9qqmye0dt4sg.png)![Screenshot 2025-04-02 190634.png](https://res.cloudinary.com/aptidude/image/upload/v1743602727/aptidude_questions/ye3kpc3iltjhwiavyzvw.png)![Screenshot 2025-04-02 190625.png](https://res.cloudinary.com/aptidude/image/upload/v1743602707/aptidude_questions/ekul0kmrnhaytnvavvdm.png)![Screenshot 2025-04-02 190616.png](https://res.cloudinary.com/aptidude/image/upload/v1743602696/aptidude_questions/ziqst1lsbzirrwwlplzj.png)![Screenshot 2025-04-02 190610.png](https://res.cloudinary.com/aptidude/image/upload/v1743602688/aptidude_questions/wygea09k2j3hqhoi3f3c.png)

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