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)

• A. 40 Registrations
• B. 30 Registrations
• C. 60 Registrations
• D. 50 Registrations

Answer 1

The Correct Option is A

Multiples of 10:

• Monthly online and offline registration figures are all divisible by 10.

January Registrations:

• Offline registrations were double the online registrations.
• Let \(x\) represent the number of online registrations.
• Consequently, offline registrations equal \(2x\), making the total registrations \(3x\).
• Based on the table data, \(3x\) must fall within the specified total registration range.
• Given that \(x\) is a multiple of 10, we determine \(x=40\).
• Therefore, January recorded 40 online and 80 offline registrations.

April Registrations:

• In April, there were 80 online and 40 offline registrations.

May Registrations:

• May saw the highest number of online registrations at 100.
• The minimum number of offline registrations in May was 30, resulting in a total of 130.
• Thus, May had 100 online and 30 offline registrations.

Assumption for March:

• We assume that \(x\) (the number of offline registrations in May) is equivalent to the number of online registrations in March.
• This assumption facilitates data organization within the table.

Median Calculation:

• From the table, the median for offline data is 50.
• This indicates that \(x\) should be between 50 and 80, inclusive.
• For 80 to be the median of the online data, \(y\) must be between 80 and 100, inclusive.

February Registrations:

• Considering February:
  • The minimum value for \(y+x\) is \(80+50=130\), which is also the maximum possible total registrations.
  • Therefore, \(x=50\) and \(y=80\).

March Registrations:

• Given the minimum total registrations is 110, and using \(x=50\) (offline registrations in February) for the calculation:
  • \(50 + z=110\), which means \(z=60\).
  • Consequently, March had 50 online and 60 offline registrations.

The following table summarizes the data:

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 clearly presents all registration data.
January's online registrations totaled 40.