Logical Reasoning

Grids

Easy

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.

Patient	Vials	Patient	Vials
1	B, D, F, H	9	A, D, F, H
2	B, D, F, G	10	A, D, F, G
3	B, D, E, H	11	A, D, E, H
4	B, D, E, G	12	A, D, E, G
5	B, C, F, H	13	A, C, F, H
6	B, C, F, G	14	A, C, F, G
7	B, C, E, H	15	A, C, E, H
8	B, C, E, G	16	A, 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 C tests positive and vials A, E and H test negative. Which patient has the disease?

Patient 2

Patient 6

Patient 14

Patient 8

✅ Correct Option: 2

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Understanding the Set:

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.)

It is also given that only one person has the disease.

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.

Since vial C tests positive so the patient who has the disease has to be one of the following:- $5, 6, 7, 8, 13, 14, 15, 16$ ,

But as vial E tests negative so patients $15, 16, 7$ and $8$ are ruled out,

Similarly as vial H tests negative so patients $5$ and $13$ are also ruled out.

Also as vial A tests negative so patients $13, 14, 15,16$ are ruled out.

Hence we are only left with patient $6$ who has the disease.

Question 2

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?

Question 3

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

Question 4

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?

Suppose vial C tests positive and vials A, E and H test negative. Which patient has the disease?

Solution

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