Blood Test

CAT 2020 Slot 3 · DILR · Hard · Logical Reasoning

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Passage / data set

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.

Question 1 of 4

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

  1. A.

    Patient 8

  2. B.

    Patient 14

  3. C.

    Patient 6

  4. D.

    Patient 2

Answer

C

Explanation

Since A, E, and H are negative, the positive vials must be B, C, F, G. The unique patient assigned to B, C, F, G is Patient 6.

Question 2 of 4

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. A.

    Vial H

  2. B.

    Vial E

  3. C.

    Vial B

  4. D.

    Vial C

Answer

B

Explanation

Testing Vial E gives the required distinction among the remaining candidate patients.

Question 3 of 4

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

  1. A.

    Vial B positive, vials C, F and H negative

  2. B.

    Vials A and G positive, vials D and E negative

  3. C.

    Vials B and D positive, vials F and H negative

  4. D.

    Vials A and E positive, vials C and D negative

Answer

D

Explanation

Combination D cannot be formed by any single diseased patient's sample matrix.

Question 4 of 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. A.

    {4,5,6,7}

  2. B.

    {4,5,6,7,8}

  3. C.

    {4,5}

  4. D.

    {5,6,7,8}

Answer

A

Explanation

Mixing two patients' samples can produce 4, 5, 6, or 7 positive vials depending on how many vials they share.

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