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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 $\text{A, B, C, D, E, F, G,}$ and $\text{H}.$ 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 $\text{A}$ tests positive and vials $\text{D}$ and $\text{G}$ test negative. Which of the following vials should we test next to identify the patient with the disease $?$

  1. Vial $\text{E}$
  2. Vial $\text{H}$
  3. Vial $\text{C}$
  4. Vial $\text{B}$
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