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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 A, B, C, D, E, F, G, and H. The following table shows the vials into which each patient’s blood sample is distributed.

PatientVialsPatientVials
1B, D, F, H9A, D, F, H
2B, D, F, G10A, D, F, G
3B, D, E, H11A, D, E, H
4B, D, E, G12A, D, E, G
5B, C, F, H13A, C, F, H
6B, C, F, G14A, C, F, G
7B, C, E, H15A, C, E, H
8B, C, E, G16A, 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.

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

This question was previously asked in
CAT 2020 Question Paper with Solution (29-Nov-2020) (Slot-3)
The correct answer is

Vials A and E positive, vials C and D negative

Every patient's sample goes into exactly one vial of each pair: A or B, C or D, E or F, G or H. Vial A holds patients 9 to 16, vial C holds patients 5 to 8 and 13 to 16, vial E holds patients 3, 4, 7, 8, 11, 12, 15, 16 and vial G holds the even-numbered patients.

So the patient with the disease makes exactly one vial of each pair positive, and those four positive vials point to one patient only.

So in each pair (A, B), (C, D), (E, F), (G, H) exactly one vial is positive and the other is negative.

B positive, C, F, H negative: vials B, D, E, G = patient 4, possible.
B, D positive, F, H negative: vials B, D, E, G = patient 4, possible.
A, G positive, D, E negative: vials A, C, F, G = patient 14, possible.

A and E positive with C and D both negative leaves the pair (C, D) with no positive vial, which cannot happen.

Hence, Vials A and E positive, vials C and D negative.

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Similar Questions

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

  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?

  3. 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?


Important Questions from Analytical Reasoning

  1. The main idea of the passage is-
  2. The narrator and his kinsman's initial impression of the "unusual man" highlights which theme most strongly?
  3. Deduction and Contradictory Evidence

    If the theft was committed by Bharat, which established fact must be incorrect, based on the provided information?

  4. Analyzing Accessory Evidence 

    The discovery of the silver button near the display case is the most incriminating evidence against which suspect, and why? 

    (A) Bharat, because he had the technical expertise to get close to the case 

    (B) Chitra, because she was near the museum late that night 

    (C) Anjali, because she is known to wear a coat with similar buttons

     (D) Mr. Hemant, as he was the last person to check the area

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

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