Online and Offline Coaching Registrations
CAT 2023 Slot 3 · DILR · Medium · Data Interpretation
Passage / data set
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.
- In every month, both online and offline registration numbers were multiples of 10.
- In January, the number of offline registrations was twice that of online registrations.
- In April, the number of online registrations was twice that of offline registrations.
- The number of online registrations in March was the same as the number of offline registrations in February.
- 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 |
Question 1 of 5
What was the total number of registrations in April?
120
Explanation
In April, Online = 2 * Offline, so Total = 3 * Offline (a multiple of 30). The possible totals are 110, 120, 130. The only multiple of 30 among these is 120. Therefore, total registrations in April = 120.
Question 2 of 5
What was the number of online registrations in January?
40
Explanation
In January, Offline = 2 * Online, so Total = 3 * Online (a multiple of 30). Since the total must be a multiple of 30, it is 120. Thus Online = 120 / 3 = 40.
Question 3 of 5
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.
- A.
Only II
- B.
Only I
- C.
Both I and II
- D.
Neither I nor II
C
Explanation
Analyzing the cases for May and February shows both scenarios are consistent with all given bounds (Online max in May = 100, offline = 30; total in Feb = 110). Hence, both statements I and II can be true.
Question 4 of 5
What best can be concluded about the number of offline registrations in February?
- A.
30 or 50 or 80
- B.
80
- C.
50 or 80
- D.
50
C
Explanation
By evaluating the constraints across all 5 months, the number of offline registrations in February can be either 50 or 80.
Question 5 of 5
Which pair of months definitely had the same total number of registrations? I. January and April II. February and May
- A.
Only I
- B.
Neither I nor II
- C.
Only II
- D.
Both I and II
A
Explanation
Both January and April must have total registrations equal to 120 (since total is a multiple of 30). Hence, January and April definitely have the same total number of registrations.
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