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 total number of registrations in April? (This Question was asked as TITA)

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)

Answer 1

The problem is solved by performing a monthly data analysis under specific constraints:

January: Online registrations are \( 2x \), offline registrations are \( 4x \), resulting in a total of \( 6x \).
March: Online registrations are equal to February's offline registrations, denoted as \( y \).
April: Online registrations are \( 2z \), offline registrations are \( z \), yielding a total of \( 3z \).
May: Online registrations are capped at 100.

The provided table indicates the following statistical ranges:

Online registrations: Minimum of 40, maximum of 100, median of 80.
Offline registrations: Minimum of 30, maximum of 80, median of 50.
Total registrations: Minimum of 110, maximum of 130, median of 120.

To meet April's requirement (online = 2 × offline), the following assumptions are made:

Total registrations in April are assumed to be 120.
Based on the total, \( 3z = 120 \), which implies \( z = 40 \).
Consequently, offline registrations are 40, and online registrations are 80.

These values are consistent with all provided statistics and constraints.

Answer: April registrations equal 120.

The Correct Option is C

Solution and Explanation

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