CAT 2020 Slot 3 — DILR Question 1
Answer the next 4 questions based on the information given 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.
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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?
Answer & solution
- A
Patient 14
- B
Patient 2
Patient 6
- D
Patient 8
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).