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. Minimum Maximum Median online 40 100 80 Offline 30 80 50 Total 110 130 120
What was the number of online registrations in January? (This Question was asked as TITA)
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.
What was the number of online registrations in January? (This Question was asked as TITA)
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.
| Minimum | Maximum | Median | |
|---|---|---|---|
| online | 40 | 100 | 80 |
| Offline | 30 | 80 | 50 |
| Total | 110 | 130 | 120 |
Updated On: Sep 17, 2024
- 40 Registrations
- 30 Registrations
- 60 Registrations
- 50 Registrations
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The Correct Option is A
Solution and Explanation
Multiples of 10:
- Each month's online and offline registration numbers are multiples of 10.
January Registrations:
- Offline registrations were twice the online registrations.
- Let π₯x be the number of online registrations.
- Then, offline registrations are 2π₯2x, making total registrations 3π₯3x.
- From the table data, 3π₯3x must fit within the given range of total registrations.
- Given π₯x is a multiple of 10, we determine π₯=40x=40.
- So, January had 40 online and 80 offline registrations.
April Registrations:
- In April, there were 80 online and 40 offline registrations.
May Registrations:
- May had the highest number of online registrations, which is 100.
- The lowest possible number of offline registrations in May is 30, making the total 130.
- Therefore, May had 100 online and 30 offline registrations.
Assumption for March:
- Assume π₯x (offline registrations in May) equals the number of online registrations in March.
- This helps us organize the data in a table.
Median Calculation:
- From the table, 50 is the median for offline data.
- This implies π₯x should be between 50 and 80, inclusive.
- For 80 to be the median for the online data, π¦y should be between 80 and 100, inclusive.
February Registrations:
- Considering February:
- Minimum value of π¦+π₯=80+50=130y+x=80+50=130 (which is the maximum possible total registrations).
- So, π₯=50x=50 and π¦=80y=80.
March Registrations:
- Since the minimum number of total registrations is 110, and considering π₯=50x=50 (offline registrations in February) and the remaining value:
- 50 + π§=110z=110, so π§=60z=60.
- Thus, March had 50 online and 60 offline registrations.
Let's summarize the data in a table:
| Month | Online Registrations | Offline Registrations | Total Registrations |
|---|---|---|---|
| January | 40 | 80 | 120 |
| February | 80 | 50 | 130 |
| March | 50 | 60 | 110 |
| April | 80 | 40 | 120 |
| May | 100 | 30 | 130 |
This table captures all the registration data clearly.
The number of online registrations in Jan is 40.
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