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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 11 through 1616, 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.

PatientVialsPatientVials
1B, D, F, H9A, D, F, H
2B, D, F, G10A, D, F, G
3B, D, E, H11A, D, E, H
4B, D, E, G12A, D, E, G
5B, C, F, H13A, C, F, H
6B, C, F, G14A, C, F, G
7B, C, E, H15A, C, E, H
8B, C, E, G16A, C, E, G

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.

Which of the following combinations of test results is NOT possible?

Solution

✅ Correct Option: 3
Slide 1/2

Understanding the Set:

  1. This is a question-based set. In this set, you are told that there are 16 patients and 8 vials — labeled A, B, C, D, E, F, G, and H.

(Vials are simply the containers in which blood samples are stored.)

  1. It is also given that only one person has the disease.
  1. If a patient has the disease, then every vial containing his/her blood sample will test positive.

a) If a vial tests positive, at least one of the patients whose blood samples were mixed in that vial has the disease.

b) If a vial tests negative, then none of the patients whose samples were mixed in that vial has the disease.

This set might initially seem a bit confusing, but it was actually one of the simplest sets asked.

The key was to understand the passage correctly — once that was done, the questions were softballs.

PatientVialsPatientVials
1B, D, F, H9A, D, F, H
2B, D, F, G10A, D, F, G
3B, D, E, H11A, D, E, H
4B, D, E, G12A, D, E, G
5B, C, F, H13A, C, F, H
6B, C, F, G14A, C, F, G
7B, C, E, H15A, C, E, H
8B, C, E, G16A, C, E, G

Going by options,

  1. 1st option is possible and it will result into patient 4 being diseased.
  1. 2nd option is possible and it will result into patient 4, 8 or 12 being diseased
  1. 3rd option is not possible is not possible as it will result into making all the patients free from disease.
  1. 4th option is possible as it will result into patient 14 being diseased.

So, 3rd option is the correct answer.

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