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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.

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?

Solution

✅ Correct Option: 4
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

Since vial A tests positive and vials D and G test negative so from the given table the only possible patients with the disease can be 13 or 15.

To eliminate between 13 and 15 numbered patients vial E or F can be tested as they both have vials A, C and H, as common vials.

So answer is 4th option

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