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Question:

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

Explanation:

Given, if a patient has the disease, then each vial containing his/her blood sample will test positive.

E.g., suppose patient 5 has the disease. Then vials B, C, F and H will definitely test positive.

Or if vial B tests positive, it means one of patient 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10 has the disease.

If vial C tests positive, it means one of patient 5, 6, 7, 8, 13, 14, 15 or 16 has the disease.

Now, since vial A tests negative, it means that patient 9 to 16 don’t have the disease.

Now, we are left with patient 5, 6, 7 and 8 who can have the disease.

Vial E tests negative, it means patients 7 and 8 cannot have the disease.

Now, we are left with patient 5 and 6 who can have the disease.

Vial H tests negative, it means patient 5 cannot have the disease.

∴ Only patient who can have the disease is patient 6.

Hence, option (c).