CAT 2023 Slot 3 DILR Set 2 Q6–Q10

A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2023 Slot 3, with 5 questions (Charts & Tables). Answers are CAT's official key.

The set

This set relies on a figure in the original paper, which is not reproduced here. The questions and answers are below.

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.

[Figure in the original paper]

Question 6

What was the total number of registrations in April?

TITA: type in the answer. There are no options and no negative marking.

Answer: 120 Charts & Tables TITA

Solution

  1. Jan: offline = 2 x online, total \(3x\) is a multiple of 10 in [110, 130], so \(3x=120\): online 40, offline 80. April likewise: online 80, offline 40, total 120.
  2. April total = 80 + 40 = 120.

Question 7

What was the number of online registrations in January?

TITA: type in the answer. There are no options and no negative marking.

Answer: 40 Charts & Tables TITA

Solution

  1. Jan: offline = 2 x online, total \(3x\) is a multiple of 10 in [110, 130], so \(3x=120\): online 40, offline 80. April likewise: online 80, offline 40, total 120.
  2. January online = 40.

Question 8

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.
  1. A
    Only II
  2. B
    Only I
  3. C
    Both I and II
  4. D
    Neither I nor II

Answer: (B) Only I Charts & Tables MCQ

Solution

  1. Jan: offline = 2 x online, total \(3x\) is a multiple of 10 in [110, 130], so \(3x=120\): online 40, offline 80. April likewise: online 80, offline 40, total 120.
  2. May online is the largest, so 100; total \(\le130\) forces offline \(\le30\), so May offline = 30 and total 130.
  3. Offline median 50 with values 80, 40, 30 known: Feb and Mar offline are 50 and z (z at least 50). Online median 80 with 40, 80, 100 known: one of Feb/Mar online is at least 80 and the other at most 80.
  4. If Mar offline = 50 then Feb offline = Mar online = z; Mar total = z+50 needs z at least 60, so Feb online is at least 80 and Feb total exceeds 130, a contradiction (z = 80 would make Feb online 30). So Feb offline = 50 = Mar online.
  5. Then Feb online is at least 80 but Feb total \(\le130\), so Feb = 80 + 50 = 130. The minimum total 110 must be March: offline 60. Final (online, offline, total): Jan 40, 80, 120; Feb 80, 50, 130; Mar 50, 60, 110; Apr 80, 40, 120; May 100, 30, 130.
  6. I: May offline 30 is the smallest, so I can be true. II: February total 130 is the largest, so II is false. Only I.

Question 9

What best can be concluded about the number of offline registrations in February?
  1. A
    30 or 50 or 80
  2. B
    80
  3. C
    50 or 80
  4. D
    50

Answer: (D) 50 Charts & Tables MCQ

Solution

  1. Jan: offline = 2 x online, total \(3x\) is a multiple of 10 in [110, 130], so \(3x=120\): online 40, offline 80. April likewise: online 80, offline 40, total 120.
  2. May online is the largest, so 100; total \(\le130\) forces offline \(\le30\), so May offline = 30 and total 130.
  3. Offline median 50 with values 80, 40, 30 known: Feb and Mar offline are 50 and z (z at least 50). Online median 80 with 40, 80, 100 known: one of Feb/Mar online is at least 80 and the other at most 80.
  4. If Mar offline = 50 then Feb offline = Mar online = z; Mar total = z+50 needs z at least 60, so Feb online is at least 80 and Feb total exceeds 130, a contradiction (z = 80 would make Feb online 30). So Feb offline = 50 = Mar online.
  5. Then Feb online is at least 80 but Feb total \(\le130\), so Feb = 80 + 50 = 130. The minimum total 110 must be March: offline 60. Final (online, offline, total): Jan 40, 80, 120; Feb 80, 50, 130; Mar 50, 60, 110; Apr 80, 40, 120; May 100, 30, 130.
  6. February offline is fixed at 50.

Question 10

Which pair of months definitely had the same total number of registrations?
I. January and April
II. February and May
  1. A
    Only I
  2. B
    Neither I nor II
  3. C
    Only II
  4. D
    Both I and II

Answer: (D) Both I and II Charts & Tables MCQ

Solution

  1. Jan: offline = 2 x online, total \(3x\) is a multiple of 10 in [110, 130], so \(3x=120\): online 40, offline 80. April likewise: online 80, offline 40, total 120.
  2. May online is the largest, so 100; total \(\le130\) forces offline \(\le30\), so May offline = 30 and total 130.
  3. Offline median 50 with values 80, 40, 30 known: Feb and Mar offline are 50 and z (z at least 50). Online median 80 with 40, 80, 100 known: one of Feb/Mar online is at least 80 and the other at most 80.
  4. If Mar offline = 50 then Feb offline = Mar online = z; Mar total = z+50 needs z at least 60, so Feb online is at least 80 and Feb total exceeds 130, a contradiction (z = 80 would make Feb online 30). So Feb offline = 50 = Mar online.
  5. Then Feb online is at least 80 but Feb total \(\le130\), so Feb = 80 + 50 = 130. The minimum total 110 must be March: offline 60. Final (online, offline, total): Jan 40, 80, 120; Feb 80, 50, 130; Mar 50, 60, 110; Apr 80, 40, 120; May 100, 30, 130.
  6. Jan = Apr = 120 and Feb = May = 130, so both pairs match.

Same concept in other years

See every question on Reconstruct individual values from mean, median, mode, range or min/max.

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