CAT 2020 Slot 3 — DILR Question 4
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 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?
Answer & solution
- A
{4,5,6,7}
{4,5,6,7,8}
- C
{4,5}
- D
{5,6,7,8}
Assuming patient 1 has the disease.
Case 1: Those patient’s blood is mixed which have no common vial.
∴ Patient 1 and 16’s samples are mixed.
In this case all 8 vials i.e., A to D will have the blood of diseased patient.
⇒ All 8 vials will test positive.
Case 2: Those patient’s blood is mixed which have exactly 1 common vial.
∴ Patient 1 and 15’s samples are mixed.
In this case 7 vials i.e., A to F and H will have the blood of diseased patient.
⇒ 7 vials will test positive.
Case 3: Those patient’s blood is mixed which have exactly 2 common vials.
∴ Patient 1 and 13’s samples are mixed.
In this case 6 vials i.e., A to D, F and H will have the blood of diseased patient.
⇒ 6 vials will test positive.
Case 4: Those patient’s blood is mixed which have exactly 3 common vials.
∴ Patient 1 and 9’s samples are mixed.
In this case 5 vials i.e., A, B, D, F and H will have the blood of diseased patient.
⇒ 5 vials will test positive.
Case 5: Those patient’s blood is mixed which don’t have the disease.
∴ Patient 2 and 3’s samples are mixed.
In this case 4 vials i.e., B, D, F and H will have the blood of diseased patient.
⇒ 4 vials will test positive.
∴ Either 4, 5, 6, 7 or 8 vials can test positive.
Hence, option (b).