CAT 2020 Slot 3 DILR Set 5 Q21–Q24

A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2020 Slot 3, with 4 questions (Venn & Set Puzzles). 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.

Sixteen patients in a hospital must undergo a blood test for a disease. It is known that exactly one of them has the disease. The hospital has only eight testing kits and has decided to pool blood samples of patients into eight vials for the tests. The patients are numbered 1 through 16, and the vials are labelled A, B, C, D, E, F, G, and H. The following table shows the vials into which each patient’s blood sample is distributed.
[Figure in the original paper]
If a patient has the disease, then each vial containing his/her blood sample will test positive. If a vial tests positive, one of the patients whose blood samples were mixed in the vial has the disease. If a vial tests negative, then none of the patients whose blood samples were mixed in the vial has the disease.

Question 21

Suppose vial C tests positive and vials A, E and H test negative. Which patient has the disease?
  1. A
    Patient 8
  2. B
    Patient 14
  3. C
    Patient 6
  4. D
    Patient 2

Answer: (C) Patient 6 Venn & Set Puzzles MCQ

A worked solution for this question is being written. Meanwhile, practise it in a timed mock and see how other aspirants did.

Question 22

Suppose vial A tests positive and vials D and G test negative. Which of the following vials should we test next to identify the patient with the disease?
  1. A
    Vial H
  2. B
    Vial E
  3. C
    Vial B
  4. D
    Vial C

Answer: (B) Vial E Venn & Set Puzzles MCQ

A worked solution for this question is being written. Meanwhile, practise it in a timed mock and see how other aspirants did.

Question 23

Which of the following combinations of test results is NOT possible?
  1. A
    Vial B positive, vials C, F and H negative
  2. B
    Vials A and G positive, vials D and E negative
  3. C
    Vials B and D positive, vials F and H negative
  4. D
    Vials A and E positive, vials C and D negative

Answer: (D) Vials A and E positive, vials C and D negative Venn & Set Puzzles MCQ

A worked solution for this question is being written. Meanwhile, practise it in a timed mock and see how other aspirants did.

Question 24

Suppose one of the lab assistants accidentally mixed two patients' blood samples before they were distributed to the vials. Which of the following correctly represents the set of all possible numbers of positive test results out of the eight vials?
  1. A
    {4,5,6,7}
  2. B
    {4,5,6,7,8}
  3. C
    {4,5}
  4. D
    {5,6,7,8}

Answer: (B) 4,5,6,7,8 Venn & Set Puzzles MCQ

A worked solution for this question is being written. Meanwhile, practise it in a timed mock and see how other aspirants did.

Same concept in other years

See every question on Pooled testing: mix samples to identify the defective one.

More Venn & Set Puzzles questions from CAT

All 60 Venn & Set Puzzles questions asked since 2017.