Download Arrangement Questions for CAT<\/a><\/p>\n CAT Online Coaching<\/a><\/p>\n Instructions<\/b><\/p>\n A shopping mall has a large basement parking lot with parking slots painted in it along a\u00a0single row. These slots are quite narrow; a compact car can fit in a single slot but an SUV\u00a0requires two slots. When a car arrives, the parking attendant guides the car to the first\u00a0available slot from the beginning of the row into which the car can fit.<\/p>\n For our purpose, cars are numbered according to the order in which they arrive at the lot. For\u00a0example, the first car to arrive is given a number 1, the second a number 2, and so on. This\u00a0numbering does not indicate whether a car is a compact or an SUV. The configuration of a\u00a0parking lot is a sequence of the car numbers in each slot. Each single vacant slot is\u00a0represented by letter V.<\/p>\n For instance, suppose cars numbered 1 through 5 arrive and park, where cars 1, 3 and 5 are\u00a0compact cars and 2 and 4 are SUVs. At this point, the parking lot would be described by the\u00a0sequence 1, 2, 3, 4, 5. If cars 2 and 5 now vacate their slots, the parking lot would now be\u00a0described as 1, V, V, 3, 4. If a compact car (numbered 6) arrives subsequently followed by an\u00a0SUV (numbered 7), the parking lot would be described by the sequence 1, 6, V, 3, 4, 7.<\/p>\n Answer the following questions INDEPENDENTLY of each other.<\/p>\n Question 1:\u00a0<\/b>Initially cars numbered 1, 2, 3, and 4 arrive among which 1 and 4 are SUVs while 2 and\u00a03 are compact cars. Car 1 then leaves, followed by the arrivals of car 5 (a compact car)\u00a0and car 6 (an SUV). Car 4 then leaves. Then car 7 (an SUV) and car 8 (a compact car)\u00a0arrive. At this moment, which among the following numbered car is parked next to car\u00a03?<\/p>\n a)\u00a08<\/p>\n b)\u00a05<\/p>\n c)\u00a06<\/p>\n d)\u00a07<\/p>\n 1)\u00a0Answer\u00a0(D)<\/strong><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n following is the order of arrival and departure of cars<\/p>\n As we can see that car 2 and car 7 are parked next to car 3<\/p>\n Question 2:\u00a0<\/b>Suppose eight cars have arrived, of which two have left. Also suppose that car 4 is a\u00a0compact and car 7 is an SUV. Which of the following is a POSSIBLE current\u00a0configuration of the parking lot?<\/p>\n a)\u00a08, 2, 3, V, 6, 5, 7<\/p>\n b)\u00a0V, 2, 3, 7, 5, 6, 8<\/p>\n c)\u00a08, 2, 3, V, 5, 7, 6<\/p>\n d)\u00a08, 2, 3, V, 5, 6, 7<\/p>\n 2)\u00a0Answer\u00a0(D)<\/strong><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n Let’s look at option 4.<\/p>\n Order of cars is 8,2,3,V,5,6,7. This sequence is easily possible.<\/p>\n Let’s say cars 1,2,3,4,5,6,7 arrive one after the another.<\/p>\n Now Car 1 leaves and Car 8 takes that place.<\/p>\n Finally Car 4 leaves. Hence we can see that this combination of cars is possible<\/p>\n Question 3:\u00a0<\/b>Suppose the sequence at some point of time is 4, 5, 6, V, 3. Which of the following is\u00a0NOT necessarily true?<\/p>\n a)\u00a0Car 4 is a compact.<\/p>\n b)\u00a0Car 1 is an SUV.<\/p>\n c)\u00a0Car 3 is an SUV<\/p>\n d)\u00a0Car 5 is a compact.<\/p>\n 3)\u00a0Answer\u00a0(C)<\/strong><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n The original sequence as given in the question is 4,5,6,V,3<\/p>\n This is possible when cars 1,2,3 arrived and then cars 1 and 2 leave. After that cars 4,5 and 6 arrive.<\/p>\n Now there are 4 slots to the left of car 3. This is only possible when cars 1 and 2 were SUVs. Now out of these 4 slots,<\/p>\n 3 slots are occupied by cars 4,5 and 6. As a result these are compact cars . Car 3 can be a SUV or a Compact car and it won’t impact the final solution.<\/p>\n Question 4:\u00a0<\/b>Suppose that car 4 is not the first car to leave and that the sequence at a time between\u00a0the arrival of the car 7 and car 8 is V, 7, 3, 6, 5. Then which of the following statements\u00a0MUST be false?<\/p>\n a)\u00a0Car 2 is a compact.<\/p>\n b)\u00a0Car 7 is a compact.<\/p>\n c)\u00a0Car 4 is an SUV.<\/p>\n d)\u00a0Car 6 is a compact.<\/p>\n 4)\u00a0Answer\u00a0(D)<\/strong><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n Here we can see that cars 3 and 5 are still in their position. Thus car 4 was not the first car to leave, either 1 or 2 left before 4. Let’s say only car 2 left before car 4. Now supposingly if car 2 is an SUV, car 6 was parked in that lot. Thus car 2 and car 7 are compact cars. Option 4 is correct.<\/p>\n Instructions<\/b><\/p>\n Twenty five coloured beads are to be arranged in a grid comprising of five rows and five\u00a0columns. Each cell in the grid must contain exactly one bead. Each bead is coloured either\u00a0Red, Blue or Green.\u00a0While arranging the beads along any of the five rows or along any of the five columns, the\u00a0rules given below are to be followed:<\/p>\n 1. Two adjacent beads along the same row or column are always of different colours. Every unique, complete arrangement of twenty five beads is called a configuration.<\/p>\n Question 5:\u00a0<\/b>The total number of possible configurations using beads of only two colours is:<\/p>\n 5)\u00a0Answer:\u00a02<\/b><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n There are only 2 configurations possible<\/p>\n Question 6:\u00a0<\/b>What is the maximum possible number of Red beads that\u00a0can appear in any configuration?<\/p>\n 6)\u00a0Answer:\u00a09<\/b><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n Maximum 9 red beads are possible as shown here<\/p>\n Question 7:\u00a0<\/b>What is the minimum number of Blue beads in any\u00a0configuration?<\/p>\n 7)\u00a0Answer:\u00a06<\/b><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n To solve this question we can use the answer of the previous question, since maximum 9 red beads are possible, filling the remaining space with green and blue beads, in such a way that number of blue beads is minimised<\/p>\n Hence number of blue beads is 6<\/p>\n Question 8:\u00a0<\/b>Two Red beads have been placed in \u2018second row, third column\u2019 and \u2018third row,\u00a0second column\u2019. How many more Red beads can be placed so as to maximise the\u00a0number of Red beads used in the configuration?<\/p>\n 8)\u00a0Answer:\u00a06<\/b><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n 6 more beads can be placed as shown<\/p>\n Instructions<\/b><\/p>\n Princess, Queen, Rani and Samragni were the four finalists in a dance competition. Ashman, Badal, Gagan and Dyu were the four music composers who individually assigned items to the dancers. Each dancer had to individually perform in two dance items assigned by the different composers. The first items performed by the four dancers were all assigned by different music composers. No dancer performed her second item before the performance of the first item by any other dancers. The dancers performed their second items in the same sequence of their performance of their first items.<\/p>\n The following additional facts are known. Question 9:\u00a0<\/b>Which of the following is true?<\/p>\n a)\u00a0The second performance was composed by Dyu.<\/p>\n b)\u00a0The third performance was composed by Dyu.<\/p>\n c)\u00a0The third performance was composed by Ashman.<\/p>\n d)\u00a0The second performance was composed by Gagan.<\/p>\n 9)\u00a0Answer\u00a0(A)<\/strong><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n Since\u00a0the dancers performed their second items in the same sequence of their performance of their first items. The table will be as follows:<\/p>\n The items assigned by Ashman were performed consecutively. The number of performances between items assigned by each of the remaining composers was the same.<\/p>\n Also,\u00a0the first items performed by the four dancers were all assigned by different music composers. Badal can come only at the place as shown in the table.<\/p>\n Then Ashman can only compose for the following performances.<\/p>\n Hence Dyu will compose for the following performances:<\/p>\n From (i) No composer who assigned item to Princess, assigned any item to Queen. Hence Dyu will compose for Samragni 1st Performance and Gagan will compose for\u00a0Queen\u00a01st Performance. Also, Badal will compose for Samragni 2nd Performance and Dyu will compose for Queens 2nd Performance.<\/p>\n Hence, the complete table is as follows:<\/p>\n The second performance was composed by Dyu. Hence A is the answer.<\/p>\n Question 10:\u00a0<\/b>Which of the following is FALSE?<\/p>\n a)\u00a0Samragni did not perform in any item composed by Ashman.<\/p>\n b)\u00a0Princess did not perform in any item composed by Dyu.<\/p>\n c)\u00a0Rani did not perform in any item composed by Badal.<\/p>\n d)\u00a0Queen did not perform in any item composed by Gagan.<\/p>\n 10)\u00a0Answer\u00a0(D)<\/strong><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n Since\u00a0the dancers performed their second items in the same sequence of their performance of their first items. The table will be as follows:<\/p>\n The items assigned by Ashman were performed consecutively. The number of performances between items assigned by each of the remaining composers was the same.<\/p>\n Also,\u00a0the first items performed by the four dancers were all assigned by different music composers. Badal can come only at the place as shown in the table.<\/p>\n Then Ashman can only compose for the following performances.<\/p>\n Hence Dyu will compose for the following performances:<\/p>\n From (i) No composer who assigned item to Princess, assigned any item to Queen. Hence Dyu will compose for Samragni 1st Performance and Gagan will compose for\u00a0Queen\u00a01st Performance. Also, Badal will compose for Samragni 2nd Performance and Dyu will compose for Queens 2nd Performance.<\/p>\n Hence, the complete table is as follows:<\/p>\n Option A:\u00a0Samragni did not perform in any item composed by Ashman. This statement is true.<\/p>\n Option B:\u00a0Princess did not perform in any item composed by Dyu. This is also true.<\/p>\n Option C:\u00a0Rani did not perform in any item composed by Badal. This statement is true.<\/p>\n Option D:\u00a0Queen did not perform in any item composed by Gagan. This statement is false.<\/p>\n Hence D is the answer.<\/p>\n Question 11:\u00a0<\/b>The sixth performance was composed by:<\/p>\n a)\u00a0Badal<\/p>\n b)\u00a0Dyu<\/p>\n c)\u00a0Ashman<\/p>\n d)\u00a0Gagan<\/p>\n![](\"https:\/\/cracku.in\/media\/uploads\/image_2020-12-31_200209.png\")
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\n2. There is at least one Green bead between any two Blue beads along the same row or\u00a0column.
\n3. There is at least one Blue and at least one Green bead between any two Red beads\u00a0along the same row or column.<\/p>\n![](\"https:\/\/cracku.in\/media\/uploads\/cracku1.PNG\")
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\ni) No composer who assigned item to Princess, assigned any item to Queen.
\nii) No composer who assigned item to Rani, assigned any item to Samragni.
\niii) The first performance was by Princess; this item was assigned by Badal.
\niv) The last performance was by Rani; this item was assigned by Gagan.
\nv) The items assigned by Ashman were performed consecutively. The number of performances between items assigned by each of the remaining composers was the same.<\/p>\n![](\"https:\/\/cracku.in\/media\/uploads\/image_tStlJVC.png\")
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\nFrom (ii)\u00a0No composer who assigned item to Rani, assigned any item to Samragni.<\/p>\n![](\"https:\/\/cracku.in\/media\/uploads\/image_lrFdRaP.png\")
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\nFrom (ii)\u00a0No composer who assigned item to Rani, assigned any item to Samragni.<\/p>\n<\/figure>\n