Data Interpretation – Sixteen patients in a hospital must undergo a blood



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.
di question 2 slot 3
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.

Q.1 Suppose vial C tests positive and vials A, E and H test negative. Which patient has the disease?
  1. Patient 8
  2. Patient 2
  3. Patient 14
  4. Patient 6

Answer: 4

Q.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

Answer: 1

Q.3 Which of the following combinations of test results is NOT possible?
  1. Vials B and D positive, vials F and H negative
  2. Vials A and G positive, vials D and E negative
  3. Vials A and E positive, vials C and D negative
  4. Vial B positive, vials C, F and H negative

Answer: 3

Q.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. {4,5,6,7,8}
  2. {4,5,6,7}
  3. {4,5}
  4. {5,6,7,8}

Answer: 1

Solutions:
Q.1 As C tests positive, so each vial containing his/her blood sample will test positive but it is given that A, E and H test negative. So we need to find out a vial which doesn’t include A, E and H but include C . From the table give , we can see patient 6 fit into this condition so it will be our answer.

Q.2 As A tests positive, so each vial containing his/her blood sample will test positive but it is given that D and G test negative. So to identify the patient which has the disease , we need to find out a vial which doesn’t include D and G but include A. From the table give , we can see patient 13 and patient 15 fit into this condition. Both have A, C and H in common . thus to identify the patient with disease we need to test one of the vial E or F. If we see the options , only vial E is there so this will be our answer.

Q.3 The option from which we will not be able to identify the patient with disease will be our correct option .
Option a) from this we can say patient 4 has disease. (see the solution of Q1 and 2 from this set)
Option b) from this we can say patient 14 has disease
Option c) from this we can say patient 4 has disease
Option d) from this information we can not identify the patient with disease so it will be the correct option.

Q.4 As we have seen in previous solutions of this set when one patient who had disease we get 4 positive test results.
So if the lab assistants accidentally mixed two patients’ blood samples before they were distributed to the vials, there there is a possibility that the patient whose the blood sample has been mixed have the disease and if we put these samples in different vials then all the test result will be positive .
For example if the sample A and B get mixed and patient 8 and 9 (due to same sample ) show the disease the all the 8 test will show positive results. Thus minimum 4 and maximum 8 positive results are possible.


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