Question

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

• A. Patient 14
• B. Patient 2
• C. Patient 6
• D. Patient 8
• A. Vial E
• B. Vial H
• C. Vial C
• D. Vial B
• A. Vials A and G positive, vials D and E negative
• B. Vials B and D positive, vials F and H negative
• C. Vial B positive, vials C, F and H negative
• D. Vials A and E positive, vials C and D negative
• A. {4,5}
• B. {5,6,7,8}
• C. {4,5,6,7,8}
• D. {4,5,6,7}

Answer 1

The Correct Option is C

The correct answer is (C): Patient 6

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 

⇒ following patients can’t have disease

Patients who can’t have disease are :

Patient No. 5, 7, 8, 13, 14, 15 & 16 

⇒ Patient 6 must have disease

Answer 2

Patients in Vial A: \(9, 10, 11, 12, 13, 14, 15, 16\)
Patients in Vial B: \(1, 2, 3, 4, 5, 6, 7, 8\)
Patients in Vial C: \(5, 6, 7, 8, 13, 14, 15, 16\)
Patients in Vial D: \(1, 2, 3, 4, 9, 10, 11, 12\)
Patients in Vial E: \(3, 4, 7, 8, 11, 12, 15, 16\)
Patients in Vial F: \(1, 2, 5, 6, 9, 10, 13, 14\)
Patients in Vial G: \(2, 4, 6, 8, 10, 12, 14, 16\)
Patients in Vial H: \(1, 3, 5, 7, 9, 11, 13, 15\)

If Vial C tests positive and Vials A, E, and H test negative, then Patient 6 must have the disease, as all other patients in Vial C except Patient 6 are present in at least one of Vials A, E, or H.

So, the correct option is (C): Patient 6.

Answer 3

The correct answer is (A): Vial E

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

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

Vials D & G test negative

⇒ Following patients, can't have disease patients

No : -1,2,3,4,6,8,9,10,11,12,14,16 → (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.

Answer 4

The patients distributed across vials are as follows:
Vial A: \(9, 10, 11, 12, 13, 14, 15, 16\)
Vial B: \(1, 2, 3, 4, 5, 6, 7, 8\)
Vial C: \(5, 6, 7, 8, 13, 14, 15, 16\)
Vial D: \(1, 2, 3, 4, 9, 10, 11, 12\)
Vial E: \(3, 4, 7, 8, 11, 12, 15, 16\)
Vial F: \(1, 2, 5, 6, 9, 10, 13, 14\)
Vial G: \(2, 4, 6, 8, 10, 12, 14, 16\)
Vial H: \(1, 3, 5, 7, 9, 11, 13, 15\)

Given that Vial A tests positive and Vials D and G test negative, the positive patient must be either Patient \(13\) or Patient \(15\).
Neither Patient \(13\) nor Patient \(15\) is present in Vial B, ruling out Option D.
Both patients are present in Vial C, but their disease status cannot be determined regardless of the test result, eliminating Option C.
Similarly, both patients are present in Vial H, but their disease status remains uncertain, dismissing Option B.
Only Patient \(15\) is present in Vial E. If tested positive, Patient \(15\) has the disease; otherwise, it's Patient \(13\).

So, the correct option is (A): Vial E

Answer 5

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.

So, the correct answer is (D): Vials A and E positive, vials C and D negative.

Answer 6

The patients in,
Vial A: \(9, 10, 11, 12, 13, 14, 15, 16\)
Vial B: \(1, 2, 3, 4, 5, 6, 7, 8\)
Vial C: \(5,6,7,8,13,14,15,16\)
Vial D: \(1,2,3,4,9,10,11,12\)
Vial E: \(3,4,7,8,11,12,15,16\)
Vial F: \(1,2,5,6,9,10,13,14\)
Vial G: \(2,4,6,8,10,12,14,16\)
Vial H: \(1,3,5,7,9,11,13,15\)
If vials C and D negative then no patient could test negative.

So, the correct option is (D): Vials A and E positive, vials C and D negative.

Answer 7

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. ⇒ 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.

So, the correct answer is (C): {4,5,6,7,8}

Answer 8

If either Patient 1 or Patient 16 has the disease and their blood is mixed with others, all 8 vials will test positive, making 8 a necessary option.
When the blood of Patient 2 or Patient 16, one of whom may have the disease, is mixed, 7 out of the 8 vials will test positive, indicating that 7 must be included in the options.
If Patient 1 has the disease and is mixed with Patient 7, then 6 out of the 8 vials will test positive. Similarly, if Patient 1 has the disease and is mixed with Patient 9, then 5 out of the 8 vials will test positive.
Now, assuming Patient 1 has the disease and his blood remains unmixed, 4 vials will definitely show positive results.

Hence, the correct option is (C): {4,5,6,7,8}