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CAT 2020 [Slot 3] DILR set 3

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.

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.

Question 1:

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

  1. Patient 14
  2. Patient 2
  3. Patient 6
  4. Patient 8
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Question 2:

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?

  1. Vial E
  2. Vial H
  3. Vial C
  4. Vial B
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Question 3:

Which of the following combinations of test results is NOT possible?

  1. Vials A and G positive, vials D and E negative
  2. Vials B and D positive, vials F and H negative
  3. Vial B positive, vials C, F and H negative
  4. Vials A and E positive, vials C and D negative
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Question 4:

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?

  1. {4,5}
  2. {5,6,7,8}
  3. {4,5,6,7,8}
  4. {4,5,6,7}
Show Answer

This table helps to figure out that vials A & B, viable C & D, Vials E & F, Vials G & H cannot be negative simultaneously. As each group consists exclusive set of patients

Question 1:

If vial C tests positive vials A , E and H test negative . If vial C tests positive following patients can have disease.

Patient No. 5, 6, 7, 8, 13, 14, 15 & 16

If vials A, E & H test negative \(\Rightarrow\) following patients can’t have disease

Patients who can’t have disease are :

Patient No. 5, 7, 8, 13, 14, 15 & 16 \(\Rightarrow\) Patient 6 must have disease

Option: 3
Question 2:

If vial a tests positive, then following patients can have disease.

Patient No. \(9,10,11,12,13,14,15,16 \rightarrow(1)\)

Vials D \& G test negative

\(\Rightarrow\) Following patients, can't have disease patients

No :\(-1,2,3,4,6,8,9,10,11,12,14, \& 16 \rightarrow(2)\)

From both \(1 \& 2,\) we ca say that patient No .13 or patient No. 15 can have disease.

Now we have eliminate or find out who among patient 13 or patient 15 has disease. So we should test vials E or F

Option: 1
Question 3:

If vials C & D test negative, that means none of the patients through 16 have diseases. But its given in the questions, that exactly one of the patients has disease. This is not possible

Option: 4
Question 4:

i) Let’s assume one of the patients, patient 1 or patient 16 has disease and that patients blood is mixed with other them all 8 vials will test positive. \(\Rightarrow\) 8 has to be one of the answers.

ii) If patient 2 and patients 16’s blood is mixed of one of them has disease then 7 of the 8 vials will test positive. So 7 has to be there in the option.

iii) Let’s assume patient 1 has disease, if his blood is not mixed, then 4 vials will definitely show positive. So 4 also has to be there in answer. So the answer must definitely contain 4, 7 and 8

Option: 3

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