In a certain board examination, students were to appear for examination in five subjects: English, Hindi, Mathematics, Science and Social Science. Due to a certain emergency situation, a few of the examinations could not be conducted for some students. Hence, some students missed one examination and some others missed two examinations. Nobody missed more than two examinations. The board adopted the following policy for awarding marks to students. If a student appeared in all five examinations, then the marks awarded in each of the examinations were on the basis of the scores obtained by them in those examinations. If a student missed only one examination, then the marks awarded in that examination was the average of the best three among the four scores in the examinations they appeared for. If a student missed two examinations, then the marks awarded in each of these examinations was the average of the best two among the three scores in the examinations they appeared for. The marks obtained by six students in the examination are given in the table below. Each of them missed either one or two examinations. The following facts are also known. I. Four of these students appeared in each of the English, Hindi, Science, and Social Science examinations. II. The student who missed the Mathematics examination did not miss any other examination. III. One of the students who missed the Hindi examination did not miss any other examination. The other student who missed the Hindi examination also missed the Science examination.
Question for CAT Previous Year Questions: Caselets- 2
Try yourself:Who among the following did not appear for the Mathematics examination?
Explanation
From the fourth paragraph, it is very clear that if the student miss exactly two exams, them his / her marks in those two subjects would be the average of best two scores and would also be “EQUAL”
By properly analysing the table, we can conclude that Esha is the only student who do not score equal marks in any two subjects. Hence, Esha is one of the student who missed exactly one subject.
Marks obtained by the student in the missed examination is the average of Best three scores, and the average/mean cannot be lowest or highest value.
Considering this concept of averages, Isha can miss examination of English, Hindi or Science.
If Esha missed English Exam, then her marks in that exam would be
Eventually she scored 80 only in English. Hence Esha could miss examination of English If Esha missed Hindi Exam, then her marks would be
This contradicts with value given the table if Esha missed science Exam, then her marks in science exam would be Again contradiction
In conclusion, Esha missed the exam of exactly subject that is English
From the second fact, we can infer that one of student missed exam of only Mathematics. If Alva missed Maths exam, then her scored would be
This value contradicts with value given the table Hence Alva did not miss the Math Exam
If Bithi missed the Maths Exam, then her score would not be the lowest score (55)
If Carl missed the Maths exam, then his score would be Carl could be the student who missed the maths exam.
If Deep missed the Maths exam then he can’t score the highest marks of 100
If Foni missed the Maths exam then her score in that exam would be
This contradicts with value given in the table. In conclusion, Carl is the student who missed the exam of only mathematics.
From the third fact, we can conclude that one student missed only Hindi exam. Another student missed two exams one Hindi and one more. Two students among Alva, Bithi, Deep and Foni would be in this category.
If Alva missed only Hindi exam, then her score would be marks score. If Alva missed two exams, then her score in both the exam would be equal.
Alva can miss Hindi and science, and her score in both these exam in the average of marks scored
In conclusion, Alva can miss only Hindi exam or Hindi and science both
If Bithi missed Hindi exam, then the score would be 90 + 85+ 85 or 86.6. The contradicts with value in the table
If Deep missed Hindi exam, then his score would be Makes score
If Deep missed Hindi and science, then his score would be Again marks score
In conclusion Deep missed the exam of only Hindi or Hindi and science If Foni missed Hindi, then her score would be . This contradicts with value of given that table After analysing the third fact, we can conclude that one among Alwa and deep missed only Hindi and the other missed Hindi and science.
So far we have analysed missed exams as Alwa, Carl. Deep and Foni.
Only Bithi and Foni left
From the first fact, we can conclude that
Exactly two students missed English exam.
Exactly two students missed Hindi exam.
Exactly two students missed Science and Exactly two students missed Social, Science Social Science was missed by two students and those 2 students must be Bithi and Foni
We need to make sure apart from Esha, one more student missed English exam. Between Bithi and Foni, the scores are equal in Social score and English. In conclusion, Foni missed the exams of English and Social.
We also need to make sure apart from Alva or Deep, one more student missed Science exam and the only possibility is Bithi.
Alwa → Only Hindi or Hindi + Science
Bithi → Science and Social Science
Carl → Only mathematics
Deep → Only Hindi or Hindi and Science
Foni → English and social science
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Question for CAT Previous Year Questions: Caselets- 2
Try yourself:What BEST can be concluded about the students who did not appear for the Hindi examination?
Explanation
From the fourth paragraph, it is very clear that if the student miss exactly two exams, them his / her marks in those two subjects would be the average of best two scores and would also be “EQUAL”
By properly analysing the table, we can conclude that Esha is the only student who do not score equal marks in any two subjects. Hence, Esha is one of the student who missed exactly one subject.
Marks obtained by the student in the missed examination is the average of Best three scores, and the average/mean cannot be lowest or highest value.
Considering this concept of averages, Isha can miss examination of English, Hindi or Science.
If Esha missed English Exam, then her marks in that exam would be
Eventually she scored 80 only in English. Hence Esha could miss examination of English If Esha missed Hindi Exam, then her marks would be
This contradicts with value given the table if Esha missed science Exam, then her marks in science exam would be Again contradiction
In conclusion, Esha missed the exam of exactly subject that is English
From the second fact, we can infer that one of student missed exam of only Mathematics. If Alva missed Maths exam, then her scored would be
This value contradicts with value given the table Hence Alva did not miss the Math Exam
If Bithi missed the Maths Exam, then her score would not be the lowest score (55)
If Carl missed the Maths exam, then his score would be Carl could be the student who missed the maths exam.
If Deep missed the Maths exam then he can’t score the highest marks of 100
If Foni missed the Maths exam then her score in that exam would be
This contradicts with value given in the table. In conclusion, Carl is the student who missed the exam of only mathematics.
From the third fact, we can conclude that one student missed only Hindi exam. Another student missed two exams one Hindi and one more. Two students among Alva, Bithi, Deep and Foni would be in this category.
If Alva missed only Hindi exam, then her score would be marks score. If Alva missed two exams, then her score in both the exam would be equal.
Alva can miss Hindi and science, and her score in both these exam in the average of marks scored
In conclusion, Alva can miss only Hindi exam or Hindi and science both
If Bithi missed Hindi exam, then the score would be 90 + 85+ 85 or 86.6. The contradicts with value in the table
If Deep missed Hindi exam, then his score would be Makes score
If Deep missed Hindi and science, then his score would be Again marks score
In conclusion Deep missed the exam of only Hindi or Hindi and science If Foni missed Hindi, then her score would be . This contradicts with value of given that table After analysing the third fact, we can conclude that one among Alwa and deep missed only Hindi and the other missed Hindi and science.
So far we have analysed missed exams as Alwa, Carl. Deep and Foni.
Only Bithi and Foni left
From the first fact, we can conclude that
Exactly two students missed English exam.
Exactly two students missed Hindi exam.
Exactly two students missed Science and Exactly two students missed Social, Science Social Science was missed by two students and those 2 students must be Bithi and Foni
We need to make sure apart from Esha, one more student missed English exam. Between Bithi and Foni, the scores are equal in Social score and English. In conclusion, Foni missed the exams of English and Social.
We also need to make sure apart from Alva or Deep, one more student missed Science exam and the only possibility is Bithi.
Alwa → Only Hindi or Hindi + Science
Bithi → Science and Social Science
Carl → Only mathematics
Deep → Only Hindi or Hindi and Science
Foni → English and social science
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*Answer can only contain numeric values
Question for CAT Previous Year Questions: Caselets- 2
Try yourself:How many out of these six students missed exactly one examination?
Correct Answer : 3
Explanation
From the fourth paragraph, it is very clear that if the student miss exactly two exams, them his / her marks in those two subjects would be the average of best two scores and would also be “EQUAL”
By properly analysing the table, we can conclude that Esha is the only student who do not score equal marks in any two subjects. Hence, Esha is one of the student who missed exactly one subject.
Marks obtained by the student in the missed examination is the average of Best three scores, and the average/mean cannot be lowest or highest value.
Considering this concept of averages, Isha can miss examination of English, Hindi or Science.
If Esha missed English Exam, then her marks in that exam would be
Eventually she scored 80 only in English. Hence Esha could miss examination of English If Esha missed Hindi Exam, then her marks would be
This contradicts with value given the table if Esha missed science Exam, then her marks in science exam would be Again contradiction
In conclusion, Esha missed the exam of exactly subject that is English
From the second fact, we can infer that one of student missed exam of only Mathematics. If Alva missed Maths exam, then her scored would be
This value contradicts with value given the table Hence Alva did not miss the Math Exam
If Bithi missed the Maths Exam, then her score would not be the lowest score (55)
If Carl missed the Maths exam, then his score would be Carl could be the student who missed the maths exam.
If Deep missed the Maths exam then he can’t score the highest marks of 100
If Foni missed the Maths exam then her score in that exam would be
This contradicts with value given in the table. In conclusion, Carl is the student who missed the exam of only mathematics.
From the third fact, we can conclude that one student missed only Hindi exam. Another student missed two exams one Hindi and one more. Two students among Alva, Bithi, Deep and Foni would be in this category.
If Alva missed only Hindi exam, then her score would be marks score. If Alva missed two exams, then her score in both the exam would be equal.
Alva can miss Hindi and science, and her score in both these exam in the average of marks scored
In conclusion, Alva can miss only Hindi exam or Hindi and science both
If Bithi missed Hindi exam, then the score would be 90 + 85+ 85 or 86.6. The contradicts with value in the table
If Deep missed Hindi exam, then his score would be Makes score
If Deep missed Hindi and science, then his score would be Again marks score
In conclusion Deep missed the exam of only Hindi or Hindi and science If Foni missed Hindi, then her score would be . This contradicts with value of given that table After analysing the third fact, we can conclude that one among Alwa and deep missed only Hindi and the other missed Hindi and science.
So far we have analysed missed exams as Alwa, Carl. Deep and Foni.
Only Bithi and Foni left
From the first fact, we can conclude that
Exactly two students missed English exam.
Exactly two students missed Hindi exam.
Exactly two students missed Science and Exactly two students missed Social, Science Social Science was missed by two students and those 2 students must be Bithi and Foni
We need to make sure apart from Esha, one more student missed English exam. Between Bithi and Foni, the scores are equal in Social score and English. In conclusion, Foni missed the exams of English and Social.
We also need to make sure apart from Alva or Deep, one more student missed Science exam and the only possibility is Bithi.
Alwa → Only Hindi or Hindi + Science
Bithi → Science and Social Science
Carl → Only mathematics
Deep → Only Hindi or Hindi and Science
Foni → English and social science
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Question for CAT Previous Year Questions: Caselets- 2
Try yourself:Which students did not appear for the English examination?
Explanation
From the fourth paragraph, it is very clear that if the student miss exactly two exams, them his / her marks in those two subjects would be the average of best two scores and would also be “EQUAL”
By properly analysing the table, we can conclude that Esha is the only student who do not score equal marks in any two subjects. Hence, Esha is one of the student who missed exactly one subject.
Marks obtained by the student in the missed examination is the average of Best three scores, and the average/mean cannot be lowest or highest value.
Considering this concept of averages, Isha can miss examination of English, Hindi or Science.
If Esha missed English Exam, then her marks in that exam would be
Eventually she scored 80 only in English. Hence Esha could miss examination of English If Esha missed Hindi Exam, then her marks would be
This contradicts with value given the table if Esha missed science Exam, then her marks in science exam would be Again contradiction
In conclusion, Esha missed the exam of exactly subject that is English
From the second fact, we can infer that one of student missed exam of only Mathematics. If Alva missed Maths exam, then her scored would be
This value contradicts with value given the table Hence Alva did not miss the Math Exam
If Bithi missed the Maths Exam, then her score would not be the lowest score (55)
If Carl missed the Maths exam, then his score would be Carl could be the student who missed the maths exam.
If Deep missed the Maths exam then he can’t score the highest marks of 100
If Foni missed the Maths exam then her score in that exam would be
This contradicts with value given in the table. In conclusion, Carl is the student who missed the exam of only mathematics.
From the third fact, we can conclude that one student missed only Hindi exam. Another student missed two exams one Hindi and one more. Two students among Alva, Bithi, Deep and Foni would be in this category.
If Alva missed only Hindi exam, then her score would be marks score. If Alva missed two exams, then her score in both the exam would be equal.
Alva can miss Hindi and science, and her score in both these exam in the average of marks scored
In conclusion, Alva can miss only Hindi exam or Hindi and science both
If Bithi missed Hindi exam, then the score would be 90 + 85+ 85 or 86.6. The contradicts with value in the table
If Deep missed Hindi exam, then his score would be Makes score
If Deep missed Hindi and science, then his score would be Again marks score
In conclusion Deep missed the exam of only Hindi or Hindi and science If Foni missed Hindi, then her score would be . This contradicts with value of given that table After analysing the third fact, we can conclude that one among Alwa and deep missed only Hindi and the other missed Hindi and science.
So far we have analysed missed exams as Alwa, Carl. Deep and Foni.
Only Bithi and Foni left
From the first fact, we can conclude that
Exactly two students missed English exam.
Exactly two students missed Hindi exam.
Exactly two students missed Science and Exactly two students missed Social, Science Social Science was missed by two students and those 2 students must be Bithi and Foni
We need to make sure apart from Esha, one more student missed English exam. Between Bithi and Foni, the scores are equal in Social score and English. In conclusion, Foni missed the exams of English and Social.
We also need to make sure apart from Alva or Deep, one more student missed Science exam and the only possibility is Bithi.
Alwa → Only Hindi or Hindi + Science
Bithi → Science and Social Science
Carl → Only mathematics
Deep → Only Hindi or Hindi and Science
Foni → English and social science
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Question for CAT Previous Year Questions: Caselets- 2
Try yourself:What BEST can be concluded about the students who missed the Science examination?
Explanation
From the fourth paragraph, it is very clear that if the student miss exactly two exams, them his / her marks in those two subjects would be the average of best two scores and would also be “EQUAL”
By properly analysing the table, we can conclude that Esha is the only student who do not score equal marks in any two subjects. Hence, Esha is one of the student who missed exactly one subject.
Marks obtained by the student in the missed examination is the average of Best three scores, and the average/mean cannot be lowest or highest value.
Considering this concept of averages, Isha can miss examination of English, Hindi or Science.
If Esha missed English Exam, then her marks in that exam would be
Eventually she scored 80 only in English. Hence Esha could miss examination of English If Esha missed Hindi Exam, then her marks would be
This contradicts with value given the table if Esha missed science Exam, then her marks in science exam would be Again contradiction
In conclusion, Esha missed the exam of exactly subject that is English
From the second fact, we can infer that one of student missed exam of only Mathematics. If Alva missed Maths exam, then her scored would be
This value contradicts with value given the table Hence Alva did not miss the Math Exam
If Bithi missed the Maths Exam, then her score would not be the lowest score (55)
If Carl missed the Maths exam, then his score would be Carl could be the student who missed the maths exam.
If Deep missed the Maths exam then he can’t score the highest marks of 100
If Foni missed the Maths exam then her score in that exam would be
This contradicts with value given in the table. In conclusion, Carl is the student who missed the exam of only mathematics.
From the third fact, we can conclude that one student missed only Hindi exam. Another student missed two exams one Hindi and one more. Two students among Alva, Bithi, Deep and Foni would be in this category.
If Alva missed only Hindi exam, then her score would be marks score. If Alva missed two exams, then her score in both the exam would be equal.
Alva can miss Hindi and science, and her score in both these exam in the average of marks scored
In conclusion, Alva can miss only Hindi exam or Hindi and science both
If Bithi missed Hindi exam, then the score would be 90 + 85+ 85 or 86.6. The contradicts with value in the table
If Deep missed Hindi exam, then his score would be Makes score
If Deep missed Hindi and science, then his score would be Again marks score
In conclusion Deep missed the exam of only Hindi or Hindi and science If Foni missed Hindi, then her score would be . This contradicts with value of given that table After analysing the third fact, we can conclude that one among Alwa and deep missed only Hindi and the other missed Hindi and science.
So far we have analysed missed exams as Alwa, Carl. Deep and Foni.
Only Bithi and Foni left
From the first fact, we can conclude that
Exactly two students missed English exam.
Exactly two students missed Hindi exam.
Exactly two students missed Science and Exactly two students missed Social, Science Social Science was missed by two students and those 2 students must be Bithi and Foni
We need to make sure apart from Esha, one more student missed English exam. Between Bithi and Foni, the scores are equal in Social score and English. In conclusion, Foni missed the exams of English and Social.
We also need to make sure apart from Alva or Deep, one more student missed Science exam and the only possibility is Bithi.
Alwa → Only Hindi or Hindi + Science
Bithi → Science and Social Science
Carl → Only mathematics
Deep → Only Hindi or Hindi and Science
Foni → English and social science
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*Answer can only contain numeric values
Question for CAT Previous Year Questions: Caselets- 2
Try yourself:For how many students can we be definite about which examinations they missed?
Correct Answer : 4
Explanation
From the fourth paragraph, it is very clear that if the student miss exactly two exams, them his / her marks in those two subjects would be the average of best two scores and would also be “EQUAL”
By properly analysing the table, we can conclude that Esha is the only student who do not score equal marks in any two subjects. Hence, Esha is one of the student who missed exactly one subject.
Marks obtained by the student in the missed examination is the average of Best three scores, and the average/mean cannot be lowest or highest value.
Considering this concept of averages, Isha can miss examination of English, Hindi or Science.
If Esha missed English Exam, then her marks in that exam would be
Eventually she scored 80 only in English. Hence Esha could miss examination of English If Esha missed Hindi Exam, then her marks would be
This contradicts with value given the table if Esha missed science Exam, then her marks in science exam would be Again contradiction
In conclusion, Esha missed the exam of exactly subject that is English
From the second fact, we can infer that one of student missed exam of only Mathematics. If Alva missed Maths exam, then her scored would be
This value contradicts with value given the table Hence Alva did not miss the Math Exam
If Bithi missed the Maths Exam, then her score would not be the lowest score (55)
If Carl missed the Maths exam, then his score would be Carl could be the student who missed the maths exam.
If Deep missed the Maths exam then he can’t score the highest marks of 100
If Foni missed the Maths exam then her score in that exam would be
This contradicts with value given in the table. In conclusion, Carl is the student who missed the exam of only mathematics.
From the third fact, we can conclude that one student missed only Hindi exam. Another student missed two exams one Hindi and one more. Two students among Alva, Bithi, Deep and Foni would be in this category.
If Alva missed only Hindi exam, then her score would be marks score. If Alva missed two exams, then her score in both the exam would be equal.
Alva can miss Hindi and science, and her score in both these exam in the average of marks scored
In conclusion, Alva can miss only Hindi exam or Hindi and science both
If Bithi missed Hindi exam, then the score would be 90 + 85+ 85 or 86.6. The contradicts with value in the table
If Deep missed Hindi exam, then his score would be Makes score
If Deep missed Hindi and science, then his score would be Again marks score
In conclusion Deep missed the exam of only Hindi or Hindi and science If Foni missed Hindi, then her score would be . This contradicts with value of given that table After analysing the third fact, we can conclude that one among Alwa and deep missed only Hindi and the other missed Hindi and science.
So far we have analysed missed exams as Alwa, Carl. Deep and Foni.
Only Bithi and Foni left
From the first fact, we can conclude that
Exactly two students missed English exam.
Exactly two students missed Hindi exam.
Exactly two students missed Science and Exactly two students missed Social, Science Social Science was missed by two students and those 2 students must be Bithi and Foni
We need to make sure apart from Esha, one more student missed English exam. Between Bithi and Foni, the scores are equal in Social score and English. In conclusion, Foni missed the exams of English and Social.
We also need to make sure apart from Alva or Deep, one more student missed Science exam and the only possibility is Bithi.
Alwa → Only Hindi or Hindi + Science
Bithi → Science and Social Science
Carl → Only mathematics
Deep → Only Hindi or Hindi and Science
Foni → English and social science
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Passage - 2
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.
Question for CAT Previous Year Questions: Caselets- 2
Try yourself:Suppose vial C tests positive and vials A, E and H test negative. Which patient has the disease?
Explanation
This table helps to figure out that vials A & B, viable C & D, Vials E & F, Vials G & H cannot be negative simultaneously. As each group consists exclusive set of patients
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
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Question for CAT Previous Year Questions: Caselets- 2
Try yourself:Which of the following combinations of test results is NOT possible?
Explanation
This table helps to figure out that vials A & B, viable C & D, Vials E & F, Vials G & H cannot be negative simultaneously. As each group consists exclusive set of patients
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.
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Question for CAT Previous Year Questions: Caselets- 2
Try yourself: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?
Explanation
This table helps to figure out that vials A & B, viable C & D, Vials E & F, Vials G & H cannot be negative simultaneously. As each group consists exclusive set of patients
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
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Question for CAT Previous Year Questions: Caselets- 2
Try yourself: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?
Explanation
This table helps to figure out that vials A & B, viable C & D, Vials E & F, Vials G & H cannot be negative simultaneously. As each group consists exclusive set of patients 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
FAQs on Caselets- 2 CAT Previous Year Questions with Answer PDF
1. What is CAT 2020?
Ans. CAT 2020 refers to the Common Admission Test conducted by the Indian Institutes of Management (IIMs) for admission into their various management programs. It is a national-level entrance exam conducted annually.
2. What are the Caselets in CAT?
Ans. Caselets in CAT are a type of question format where a small passage or case study is provided, followed by a set of questions. These questions are based on the information given in the caselet and test the candidate's ability to analyze and solve problems.
3. How can I prepare for the Caselets in CAT 2020?
Ans. To prepare for the Caselets in CAT 2020, it is important to practice solving case-based questions regularly. This will help you develop your analytical and problem-solving skills. Additionally, reading and understanding different types of case studies will enhance your ability to comprehend and interpret the information given in the caselets.
4. What is the difficulty level of the Caselets in CAT?
Ans. The difficulty level of the Caselets in CAT can vary from moderate to high. The questions are designed to assess the candidate's ability to analyze data, draw conclusions, and make decisions based on the given information. It is important to practice solving case-based questions of varying difficulty levels to be well-prepared for the actual exam.
5. How can I improve my performance in the Caselets section of CAT?
Ans. To improve your performance in the Caselets section of CAT, it is crucial to practice solving case-based questions regularly. This will help you become familiar with the question format and develop your analytical and problem-solving skills. Additionally, time management is essential, so practice solving questions within the given time limit. Reviewing and analyzing your performance in mock tests will also help identify areas of improvement and strategize accordingly.