CAT 2023 Slot 3 · DILR · Question 15

CAT 2023 Slot 3 previous year question on Tables, with the answer and a step-by-step solution.

TablesData InterpretationMultiple choiceMedium

Set 3: Online and Offline Registrations — this question belongs to a set. Read the full set with all 5 questions →

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

Which pair of months definitely had the same total number of registrations?

I. January and April

II. February and May

A
Both I and II
B
Only II
C
Only I
D
Neither I nor II

Pick an option, then check.

Answer & solution

Answer: Option A

Solving the set

Step 1 – Every month's total is 110, 120 or 130 (min 110, max 130, median 120 means the five totals are 110, x, 120, y, 130 with x, y between them, all multiples of 10).

Step 2 – January: offline = 2 × online, so the total is a multiple of 30 ⇒ 120: online 40, offline 80. April: online = 2 × offline ⇒ total 120: online 80, offline 40.

Step 3 – Online values are 40 (min), 100 (max), median 80. 100 is in May (largest). January has 40 and April 80, so the online numbers are 40, ?, 80, ?, 100 with February and March holding one value ≤ 80 and one = 80 (median).

Step 4 – Offline values: min 30, max 80 (January), median 50. April = 40. May's online is 100, so May's offline is 10, 20 or 30 to keep the total ≤ 130 ⇒ 30 (the minimum), total 130.

Step 5 – February and March. The offline numbers so far are 80 (Jan), 40 (Apr), 30 (May); the median 50 must be February's or March's. March's online = February's offline (fact 4).

• If February's offline = 50, March's online = 50, so February's online = 80 (median) ⇒ February total 130. March's total must then be 110 (we need one 110): March offline = 60. Offline list: 30, 40, 50, 60, 80 – median 50 ✓.

• If March's offline = 50 instead, February's offline f ≥ 50 and March's online = f. One of February/March must total 110. March total 110 ⇒ f = 60, and then February's online must be 80 or more (online median), giving February a total above 130 – impossible. February total 110 ⇒ either February's online ≥ 80 (so f ≤ 30, contradiction) or March's online f ≥ 80 (so February's online ≤ 30, below the online minimum 40) – impossible. So this case fails.

Month	Online	Offline	Total
January	40	80	120
February	80	50	130
March	50	60	110
April	80	40	120
May	100	30	130

This question

From the table: January 120 = April 120 and February 130 = May 130. Both pairs definitely match.

Hence, the answer is option 1.

CAT 2023 Slot 3 · DILR · Question 15

More Tables questions