Logic

(CAT 2020) 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? Patient 8 Patient 14 Patient 6 Patient 2 2)  Suppose vial A tests positive and vials D and G test negative. Which of the follo...

(CAT 2020) A survey of 600 schools in India was conducted to gather information about their online teaching learning processes (OTLP). The following four facilities were studied. F1: Own software for OTLP F2: Trained teachers for OTLP F3: Training materials for OTLP F4: All students having Laptops The following observations were summarized from the survey. 1. 80 schools did not have any of the four facilities – F1, F2, F3, F4. 2. 40 schools had all four facilities. 3. The number of schools with only F1, only F2, only F3, and only F4 was 25, 30, 26 and 20 respectively. 4. The number of schools with exactly three of the facilities was the same irrespective of which three were considered. 5. 313 schools had F2. 6. 26 schools had only F2 and F3 (but neither F1 nor F4). 7. Among the schools having F4, 24 had only F3, and 45 had only F2. 8. 162 schools had both F1 and F2. 9. The number of schools having F1 was the same as the number of schools having F4. 1)  What was the total numbe...

(CAT 2020) XYZ organization got into the business of delivering groceries to home at the beginning of the last month. They have a two-day delivery promise. However, their deliveries are unreliable. An order booked on a particular day may be delivered the next day or the day after. If the order is not delivered at the end of two days, then the order is declared as lost at the end of the second day. XYZ then does not deliver the order, but informs the customer, marks the order as lost, returns the payment and pays a penalty for non-delivery. The following table provides details about the operations of XYZ for a week of the last month. The first column gives the date, the second gives the cumulative number of orders that were booked up to and including that day. The third column represents the number of orders delivered on that day. The last column gives the cumulative number of orders that were lost up to and including that day. It is known that the numbers of orders that were booked on...

(CAT 2020) The Hi-Lo game is a four-player game played in six rounds. In every round, each player chooses to bid Hi or Lo. The bids are made simultaneously. If all four bid Hi, then all four lose 1 point each. If three players bid Hi and one bids Lo, then the players bidding Hi gain 1 point each and the player bidding Lo loses 3 points. If two players bid Hi and two bid Lo, then the players bidding Hi gain 2 points each and the players bidding Lo lose 2 points each. If one player bids Hi and three bid Lo, then the player bidding Hi gains 3 points and the players bidding Lo lose 1 point each. If all four bid Lo, then all four gain 1 point each. Four players Arun, Bankim, Charu, and Dipak played the Hi-Lo game. The following facts are known about their game: 1. At the end of three rounds, Arun had scored 6 points, Dipak had scored 2 points, Bankim and Charu had scored -2 points each. 2. At the end of six rounds, Arun had scored 7 points, Bankim and Dipak had scored -1 point each, and C...

(CAT 2020) A farmer had a rectangular land containing 205 trees. He distributed that land among his four daughters – Abha, Bina, Chitra and Dipti by dividing the land into twelve plots along three rows (X,Y,Z) and four  Columns (1,2,3,4) as shown in the figure below: The plots in rows X, Y, Z contained mango, teak and pine trees respectively. Each plot had trees in non-zero multiples of 3 or 4 and none of the plots had the same number of trees. Each daughter got an even number of plots. In the figure, the number mentioned in top left corner of a plot is the number of trees in that plot, while the letter in the bottom right corner is the first letter of the name of the daughter who got that plot (For example, Abha got the plot in row Y and column 1 containing 21 trees). Some information in the figure got erased, but the following is known: 1. Abha got 20 trees more than Chitra but 6 trees less than Dipti. 2. The largest number of trees in a plot was 32, but it was not with Abha. 3....

Tree Plantation 1) C 2) A 3) B 4) C 5) A 6) D HI-LO Game 1) C 2) 4 3) 4 4) 2 5) 1 6) A Grocery Delivery 1) A 2) D 3) D 4) D OTLP 1) C 2) A 3) 42 4) 20 16 Patients 1) C 2) B 3) D 4) B

(CAT 2020) The Humanities department of a college is planning to organize eight seminars, one for each of the eight doctoral students - A, B, C, D, E, F, G and H. Four of them are from Economics, three from Sociology and one from Anthropology department. Each student is guided by one among P, Q, R, S and T. Two students are guided by each of P, R and T, while one student is guided by each of Q and S. Each student is guided by a guide belonging to their department. Each seminar is to be scheduled in one of four consecutive 30-minute slots starting at 9:00 am, 9:30 am, 10:00 am and 10:30 am on the same day. More than one seminars can be scheduled in a slot, provided the guide is free. Only three rooms are available and hence at the most three seminars can be scheduled in a slot. Students who are guided by the same guide must be scheduled in consecutive slots. The following additional facts are also known. 1. Seminars by students from Economics are scheduled in each of the four slots. ...

(CAT 2020) In an election several candidates contested for a constituency. In any constituency, the winning candidate was the one who polled the highest number of votes, the first runner up was the one who polled the second highest number of votes, the second runner up was the one who polled the third highest number of votes, and so on. There were no ties (in terms of number of votes polled by the candidates) in any of the constituencies in this election. In an electoral system, a security deposit is the sum of money that a candidate is required to pay to the election commission before he or she is permitted to contest. Only the defeated candidates (i.e., one who is not the winning candidate) who fail to secure more than one sixth of the valid votes polled in the constituency, lose their security deposits. The following table provides some incomplete information about votes polled in four constituencies: A, B, C and D, in this election.   Constituency   A B C D No. of candidat...

(CAT 2020) A chain of departmental stores has outlets in Delhi, Mumbai, Bengaluru and Kolkata. The sales are categorized by its three departments – ‘Apparel’, ‘Electronics’, and ‘HomeDecor’. An Accountant has been asked to prepare a summary of the 2018 and 2019 sales amounts for an internal report. He has collated partial information and prepared the following table. The following additional information is known. 1. The sales amounts in the Apparel departments were the same for Delhi and Kolkata in 2018. 2. The sales amounts in the Apparel departments were the same for Mumbai and Bengaluru in 2018. This sales amount matched the sales amount in the Apparel department for Delhi in 2019. 3. The sales amounts in the HomeDecor departments were the same for Mumbai and Kolkata in 2018. 4. The sum of the sales amounts of four Electronics departments increased by the same amount as the sum of the sales amounts of four Apparel departments from 2018 to 2019. 5. The total sales amounts of the f...

(CAT 2020) A shopping mall has a large basement parking lot with parking slots painted in it along a single row. These slots are quite narrow; a compact car can fit in a single slot but an SUV requires two slots. When a car arrives, the parking attendant guides the car to the first available slot from the beginning of the row into which the car can fit. For our purpose, cars are numbered according to the order in which they arrive at the lot. For example, the first car to arrive is given a number 1, the second a number 2, and so on. This numbering does not indicate whether a car is a compact or an SUV. The configuration of a parking lot is a sequence of the car numbers in each slot. Each single vacant slot is represented by letter V. For instance, suppose cars numbered 1 through 5 arrive and park, where cars 1, 3 and 5 are compact cars and 2 and 4 are SUVs. At this point, the parking lot would be described by the sequence 1, 2, 3, 4, 5. If cars 2 and 5 now vacate their slots, the parki...

(CAT 2020) Twenty five coloured beads are to be arranged in a grid comprising of five rows and five columns. Each cell in the grid must contain exactly one bead. Each bead is coloured either Red, Blue or Green. While arranging the beads along any of the five rows or along any of the five columns, the rules given below are to be followed: 1. Two adjacent beads along the same row or column are always of different colours. 2. There is at least one Green bead between any two Blue beads along the same row or column. 3. There is at least one Blue and at least one Green bead between any two Red beads along the same row or column. Every unique, complete arrangement of twenty five beads is called a configuration. 1) The total number of possible configurations using beads of only two colours is: 2) What is the maximum possible number of Red beads that can appear in any configuration? 3) What is the minimum number of Blue beads in any configuration? 4)  Two Red beads have been placed in ‘...

Arrangements of Beads 1) 2 2) 9 3) 6 4) 6 Parking Slots 1) D 2) C 3) C 4) A Sales Account 1) A 2) A 3) B 4) A Election 1) 9 2) 11 3) B 4) A 5) D 6) D Departmental Seminars 1) D 2) C 3) B 4) B 5) A 6) D

(CAT 2020) 1000 patients currently suffering from a disease were selected to study the effectiveness of treatment of four types of medicines — A, B, C and D. These patients were first randomly assigned into two groups of equal size, called treatment group and control group. The patients in the control group were not treated with any of these medicines; instead they were given a dummy medicine, called placebo, containing only sugar and starch. The following information is known about the patients in the treatment group. a. A total of 250 patients were treated with type A medicine and a total of 210 patients were treated with type C medicine. b. 25 patients were treated with type A medicine only. 20 patients were treated with type C medicine only. 10 patients were treated with type D medicine only. c. 35 patients were treated with type A and type D medicines only. 20 patients were treated with type A and type B medicines only. 30 patients were treated with type A and type C medicines on...

(CAT 2020) Ten musicians (A, B, C, D, E, F, G, H, I and J) are experts in at least one of the following three percussion instruments: tabla, mridangam, and ghatam. Among them, three are experts in tabla but not in mridangam or ghatam, another three are experts in mridangam but not in tabla or ghatam, and one is an expert in ghatam but not in tabla or mridangam. Further, two are experts in tabla and mridangam but not in ghatam, and one is an expert in tabla and ghatam but not in mridangam. The following facts are known about these ten musicians. Both A and B are experts in mridangam, but only one of them is also an expert in tabla. D is an expert in both tabla and ghatam. Both F and G are experts in tabla, but only one of them is also an expert in mridangam. Neither I nor J is an expert in tabla. Neither H nor I is an expert in mridangam, but only one of them is an expert in ghatam. 1) Who among the following is DEFINITELY an expert in tabla but not in either mridangam or ghatam? A F H...

(CAT 2020) 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. Th...

(CAT 2020) Four institutes, A, B, C, and D, had contracts with four vendors W, X, Y, and Z during the ten calendar years from 2010 to 2019. The contracts were either multi-year contracts running for several consecutive years or single-year contracts. No institute had more than one contract with the same vendor. However, in a calendar year, an institute may have had contracts with multiple vendors, and a vendor may have had contracts with multiple institutes. It is known that over the decade, the institutes each got into two contracts with two of these vendors, and each vendor got into two contracts with two of these institutes. The following facts are also known about these contracts. I. Vendor Z had at least one contract in every year. II. Vendor X had one or more contracts in every year up to 2015, but no contract in any year after that. III. Vendor Y had contracts in 2010 and 2019. Vendor W had contracts only in 2012. IV. There were five contracts in 2012. V. There were exactly fou...

(CAT 2020) The local office of the APP-CAB company evaluates the performance of five cab drivers, Arun, Barun, Chandan, Damodaran, and Eman for their monthly payment based on ratings in five different parameters (P1 to P5) as given below:P1: timely arrival P2: behaviour P3: comfortable ride P4: driver's familiarity with the route P5: value for money Based on feedback from the customers, the office assigns a rating from 1 to 5 in each of these parameters. Each rating is an integer from a low value of 1 to a high value of 5. The final rating of a driver is the average of his ratings in these five parameters. The monthly payment of the drivers has two parts – a fixed payment and final rating-based bonus. If a driver gets a rating of 1 in any of the parameters, he is not eligible to get bonus. To be eligible for bonus a driver also needs to get a rating of five in at least one of the parameters. The partial information related to the ratings of the drivers in different parameters and ...

Driver Rating 1) B 2) C 3) B 4) A Contracts 1) D 2) D 3) A 4) A 5) D 6) C Board Exams 1) A 2) D 3) C 4) D 5) 3 6) 4 Ten Musicians 1) C 2) B 3) C 4) A 1000 Patients 1) 340 2) 10 3) 150 4) 325