CAT 2020 Slot 3 — DILR Question 2
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 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?
Answer & solution
- A
Vial B
- B
Vial C
Vial E
- D
Vial H
Since vial A tests positive one of patient 9 to 16 will have the disease.
Now, vials D and G test negative hence, patients 9, 10, 11, 12, 14 and 16 cannot have the disease.
⇒ One of patients 13 or 15 will have the disease.
To check which one of patients 13 or 15 have the disease we need to check a vial which does not have both the samples.
∴ We can check either vial E or F.
Hence, option (c).