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 total number of registrations in April? (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 total number of registrations in April? (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
- 90 Registration
- 110 Registration
- 120 Registration
- 100 Registration
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The Correct Option is C
Solution and Explanation
Given :
In every month,both online and offline registration numbers were multiples of 10.
From (2), in Jan, the number of offline registrations was double that of online registrations.
Let x be the number of online registrations
2x be the number of offline registrations
Total number of registrations be x + 2x = 3x
According to the table data :
3x should lie between the minimum and maximum total number of registrations.
x = 40 (as x should also be a multiple of 10)
In January, 40 and 80 are the online and offline registrations respectively.
From 5, we can say that the number of online registrations is highest in may.
In may, there are total 100 online registrations.
maximum possible total registrations is 130
lowest possible number of offline registrations is 30
Let x be the number of offline registrations in May which is equal to number of online registrations in March.
Let's arrange the data in table :
| Month | Online | Offline | Total |
|---|---|---|---|
| Jan | 40 | 80 | 120 |
| Feb | y | x | |
| Mar | x | z | |
| Apr | 80 | 140 | 120 |
| May | 100 | 30 | 130 |
From the table mentioned in question , 50 is the median for Offline data
Now x should lie between 50 and 80
For 80 to be the median for the online data
y should lie between 80 and 100
Now, let's consider the following :
Feb ⇒ Minimum value of y + x
= 80 + 50 = 130
Therefore , x = 50 and y = 80
Since,110 is the minimum number of total registrations, the only possibility is in March :
50 + z = 110
z = 60
Let's complete the table :
| Month | Online | Offline | Total |
|---|---|---|---|
| Jan | 40 | 80 | 120 |
| Feb | 80 | 50 | 130 |
| Mar | 50 | 60 | 130 |
| Apr | 80 | 140 | 120 |
| May | 100 | 30 | 130 |
So, total number of April's registrations is 120.
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