BackALL MODULES
CAT 2025 Lesson : DILR: Jul '25 to Aug '25 - Live Solving - 29 Aug 2025
Read the following and answer the questions that follow
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.
1) Suppose vial C tests positive and vials A, E and H test negative. Which patient has the disease?
(1) Patient 2
(2) Patient 6
(3) Patient 14
(4) Patient 8
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 C
(2) Vial H
(3) Vial B
(4) Vial E
3) Which of the following combinations of test results is NOT possible?
(1) Vial B positive, vials C, F and H negative
(2) Vials B and D positive, vials F and H negative
(3) Vials A and G positive, vials D and E negative
(4) Vials A and E positive, vials C and D negative
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}
(4) {4,5,6,7,8}
Read the following and answer the Questions that follow
Three reviewers Amal, Bimal, and Komal are tasked with selecting questions from a pool of 13 questions (Q01 to Q13). Questions can be created by external “subject matter experts” (SMEs) or by one of the three reviewers. Each of the reviewers either approves or disapproves a question that is shown to them. Their decisions lead to eventual acceptance or rejection of the question in the manner described below.
If a question is created by an SME, it is reviewed first by Amal, and then by Bimal. If both of them approve the question, then the question is accepted and is not reviewed by Komal. If both disapprove the question, it is rejected and is not reviewed by Komal. If one of them approves the question and the other disapproves it, then the question is reviewed by Komal. Then the question is accepted only if she approves it.
A question created by one of the reviewers is decided upon by the other two. If a question is created by Amal, then it is first reviewed by Bimal. If Bimal approves the question, then it is accepted. Otherwise, it is reviewed by Komal. The question is then accepted only if Komal approves it. A similar process is followed for questions created by Bimal, whose questions are first reviewed by Komal, and then by Amal only if Komal disapproves it. Questions created by Komal are first reviewed by Amal, and then, if required, by Bimal.
The following facts are known about the review process after its completion.
1. Q02, Q06, Q09, Q11, and Q12 were rejected and the other questions were accepted.
2. Amal reviewed only Q02, Q03, Q04, Q06, Q08, Q10, Q11, and Q13.
3. Bimal reviewed only Q02, Q04, Q06 through Q09, Q12, and Q13.
4. Komal reviewed only Q01 through Q05, Q07, Q08, Q09, Q11, and Q12.
5) How many questions were DEFINITELY created by Amal?
Answer:
6) How many questions were DEFINITELY created by Komal?
Answer:
7) How many questions were DEFINITELY created by the SMEs?
Answer:
8) How many questions were DEFINITELY disapproved by Bimal?
(1) 5
(2) 7
(3) 4
(4) 3
9) The approval ratio of a reviewer is the ratio of the number of questions (s)he approved to the number of questions (s)he reviewed. Which option best describes Amal’s approval ratio?
(1) lies between 0.25 and 0.50
(2) lies between 0.25 and 0.75
(3) either 0.25 or 0.75
(4) 0.25
10) How many questions created by Amal or Bimal were disapproved by at least one of the other reviewers?
(1) 5
(2) 7
(3) 2
(4) 4
Details for Questions 11 to 14 are provided below
Each of the bottles mentioned in this question contains 50 ml of liquid. The liquid in any bottle can be 100% pure content (P) or can have certain amount of impurity (I). Visually it is not possible to distinguish between P and I. There is a testing device which detects impurity, as long as the percentage of impurity in the content tested is 10% or more.
For example, suppose bottle 1 contains only P, and bottle 2 contains 80% P and 20% I. If content from bottle 1 is tested, it will be found out that it contains only P. If content of bottle 2 is tested, the test will reveal that it contains some amount of I. If 10 ml of content from bottle 1 is mixed with 20 ml content from bottle 2, the test will show that the mixture has impurity, and hence we can conclude that at least one of the two bottles has I. However, if 10 ml of content from bottle 1 is mixed with 5 ml of content from bottle 2. the test will not detect any impurity in the resultant mixture.
11) 5 ml of content from bottle A is mixed with 5 ml of content from bottle B. The resultant mixture, when tested, detects the presence of I. If it is known that bottle A contains only P, what BEST can be concluded about the volume of I in bottle B?
(1) 1 ml
(2) 10 ml
(3) 10 ml or more
(4) Less than 1 ml
12) There are four bottles. Each bottle is known to contain only P or only I. They will be considered to be “collectively ready for despatch” if all of them contain only P. In minimum how many tests, is it possible to ascertain whether these four bottles are “collectively ready for despatch”?
Answer:
13) There are four bottles. It is known that three of these bottles contain only P, while the remaining one contains 80% P and 20% I. What is the minimum number of tests required to definitely identify the bottle containing some amount of I?
Answer:
14) There are four bottles. It is known that either one or two of these bottles contain(s) only P, while the remaining ones contain 85% P and 15% I. What is the minimum number of tests required to ascertain the exact number of bottles containing only P?
(1) 4
(2) 2
(3) 1
(4) 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.
1) Suppose vial C tests positive and vials A, E and H test negative. Which patient has the disease?
(1) Patient 2
(2) Patient 6
(3) Patient 14
(4) Patient 8
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 C
(2) Vial H
(3) Vial B
(4) Vial E
3) Which of the following combinations of test results is NOT possible?
(1) Vial B positive, vials C, F and H negative
(2) Vials B and D positive, vials F and H negative
(3) Vials A and G positive, vials D and E negative
(4) Vials A and E positive, vials C and D negative
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}
(4) {4,5,6,7,8}
Read the following and answer the Questions that follow
Three reviewers Amal, Bimal, and Komal are tasked with selecting questions from a pool of 13 questions (Q01 to Q13). Questions can be created by external “subject matter experts” (SMEs) or by one of the three reviewers. Each of the reviewers either approves or disapproves a question that is shown to them. Their decisions lead to eventual acceptance or rejection of the question in the manner described below.
If a question is created by an SME, it is reviewed first by Amal, and then by Bimal. If both of them approve the question, then the question is accepted and is not reviewed by Komal. If both disapprove the question, it is rejected and is not reviewed by Komal. If one of them approves the question and the other disapproves it, then the question is reviewed by Komal. Then the question is accepted only if she approves it.
A question created by one of the reviewers is decided upon by the other two. If a question is created by Amal, then it is first reviewed by Bimal. If Bimal approves the question, then it is accepted. Otherwise, it is reviewed by Komal. The question is then accepted only if Komal approves it. A similar process is followed for questions created by Bimal, whose questions are first reviewed by Komal, and then by Amal only if Komal disapproves it. Questions created by Komal are first reviewed by Amal, and then, if required, by Bimal.
The following facts are known about the review process after its completion.
1. Q02, Q06, Q09, Q11, and Q12 were rejected and the other questions were accepted.
2. Amal reviewed only Q02, Q03, Q04, Q06, Q08, Q10, Q11, and Q13.
3. Bimal reviewed only Q02, Q04, Q06 through Q09, Q12, and Q13.
4. Komal reviewed only Q01 through Q05, Q07, Q08, Q09, Q11, and Q12.
5) How many questions were DEFINITELY created by Amal?
Answer:
6) How many questions were DEFINITELY created by Komal?
Answer:
7) How many questions were DEFINITELY created by the SMEs?
Answer:
8) How many questions were DEFINITELY disapproved by Bimal?
(1) 5
(2) 7
(3) 4
(4) 3
9) The approval ratio of a reviewer is the ratio of the number of questions (s)he approved to the number of questions (s)he reviewed. Which option best describes Amal’s approval ratio?
(1) lies between 0.25 and 0.50
(2) lies between 0.25 and 0.75
(3) either 0.25 or 0.75
(4) 0.25
10) How many questions created by Amal or Bimal were disapproved by at least one of the other reviewers?
(1) 5
(2) 7
(3) 2
(4) 4
Details for Questions 11 to 14 are provided below
Each of the bottles mentioned in this question contains 50 ml of liquid. The liquid in any bottle can be 100% pure content (P) or can have certain amount of impurity (I). Visually it is not possible to distinguish between P and I. There is a testing device which detects impurity, as long as the percentage of impurity in the content tested is 10% or more.
For example, suppose bottle 1 contains only P, and bottle 2 contains 80% P and 20% I. If content from bottle 1 is tested, it will be found out that it contains only P. If content of bottle 2 is tested, the test will reveal that it contains some amount of I. If 10 ml of content from bottle 1 is mixed with 20 ml content from bottle 2, the test will show that the mixture has impurity, and hence we can conclude that at least one of the two bottles has I. However, if 10 ml of content from bottle 1 is mixed with 5 ml of content from bottle 2. the test will not detect any impurity in the resultant mixture.
11) 5 ml of content from bottle A is mixed with 5 ml of content from bottle B. The resultant mixture, when tested, detects the presence of I. If it is known that bottle A contains only P, what BEST can be concluded about the volume of I in bottle B?
(1) 1 ml
(2) 10 ml
(3) 10 ml or more
(4) Less than 1 ml
12) There are four bottles. Each bottle is known to contain only P or only I. They will be considered to be “collectively ready for despatch” if all of them contain only P. In minimum how many tests, is it possible to ascertain whether these four bottles are “collectively ready for despatch”?
Answer:
13) There are four bottles. It is known that three of these bottles contain only P, while the remaining one contains 80% P and 20% I. What is the minimum number of tests required to definitely identify the bottle containing some amount of I?
Answer:
14) There are four bottles. It is known that either one or two of these bottles contain(s) only P, while the remaining ones contain 85% P and 15% I. What is the minimum number of tests required to ascertain the exact number of bottles containing only P?
(1) 4
(2) 2
(3) 1
(4) 3
Loading...Loading Video....