CAT 2014 DILR Slot 2 Question Paper(Available):Download Solutions with Answer Key

CAT Questions

• 1.

  
  The above is a schematic diagram of walkways (indicated by all the straight-lines) and lakes (3 of them, each in the shape of rectangles – shaded in the diagram) of a gated area. Different points on the walkway are indicated by letters (A through P) with distances being OP = 150 m, ON = MN = 300 m, ML = 400 m, EL = 200 m, DE = 400 m.
  The following additional information about the facilities in the area is known.
  1. The only entry/exit point is at C.
  2. There are many residences within the gated area; all of them are located on the path AH and ML with four of them being at A, H, M, and L.
  3. The post office is located at P and the bank is located at B.

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• 2.

  Out of 10 countries -- Country 1 through Country 10 -- Country 9 has the highest gross domestic product (GDP), and Country 10 has the highest GDP per capita. GDP per capita is the GDP of a country divided by its population. The table below provides the following data about Country 1 through Country 8 for the year 2024.
  Column 1 gives the country's identity.
  Column 2 gives the country's GDP as a fraction of the GDP of Country 9.
  Column 3 gives the country's GDP per capita as a fraction of the GDP per capita of Country 10.
  Column 4 gives the country's annual GDP growth rate.
  Column 5 gives the country's annual population growth rate.

  

  
  Assume that the GDP growth rates and population growth rates of the countries will remain constant for the next three years.

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• 3.

  The air-conditioner (AC) in a large room can be operated either in REGULAR mode or in POWER mode to reduce the temperature.
  If the AC operates in REGULAR mode, then it brings down the temperature inside the room (called inside temperature) at a constant rate to the set temperature in 1 hour. If it operates in POWER mode, then this is achieved in 30 minutes.
  If the AC is switched off, then the inside temperature rises at a constant rate so as to reach the temperature outside at the time of switching off in 1 hour.
  The temperature outside has been falling at a constant rate from 7 pm onward until 3 am on a particular night. The following graph shows the inside temperature between 11 pm (23:00) and 2 am (2:00) that night.

  

  
  The following facts are known about the AC operation that night.
  The AC was turned on for the first time that night at 11 pm (23:00).
  The AC setting was changed (including turning it on/off, and/or setting different temperatures) only at the beginning of the hour or at 30 minutes after the hour.
  The AC was used in POWER mode for longer duration than in REGULAR mode during this 3-hour period.

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• 4.

  The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are placed in ten slots of the following grid based on the conditions below
  
  1. Numbers in any row appear in an increasing order from left to right.
  2. Numbers in any column appear in a decreasing order from top to bottom.
  3. 1 is placed either in the same row or in the same column as 10.
  4. Neither 2 nor 3 is placed in the same row or in the same column as 10.
  5. Neither 7 nor 8 is placed in the same row or in the same column as 9.
  6. 4 and 6 are placed in the same row.

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• 5.

  Two students, Amiya and Ramya are the only candidates in an election for the position of class representative. Students will vote based on the intensity level of Amiya’s and Ramya’s campaigns and the type of campaigns they run. Each campaign is said to have a level of 1 if it is a staid campaign and a level of 2 if it is a vigorous campaign. Campaigns can be of two types, they can either focus on issues, or on attacking the other candidate.
  If Amiya and Ramya both run campaigns focusing on issues, then
  • The percentage of students voting in the election will be 20 times the sum of the levels of campaigning of the two students. For example, if Amiya and Ramya both run vigorous campaigns, then $20 × (2+2)\%$, that is, $80\%$ of the students will vote in the election.
  • Among voting students, the percentage of votes for each candidate will be proportional to the levels of their campaigns. For example, if Amiya runs a staid (i.e., level 1) campaign while Ramya runs a vigorous (i.e., level 2) campaign, then Amiya will receive \(\frac{1}{3}\) of the votes cast, and Ramya will receive the other \(\frac{2}{3}\).
  The above-mentioned percentages change as follows if at least one of them runs a campaign attacking their opponent.
  • If Amiya runs a campaign attacking Ramya and Ramya runs a campaign focusing on issues, then $10\%$ of the students who would have otherwise voted for Amiya will vote for Ramya, and another $10\%$ who would have otherwise voted for Amiya, will not vote at all.
  • If Ramya runs a campaign attacking Amiya and Amiya runs a campaign focusing on issues, then $20\%$ of the students who would have otherwise voted for Ramya will vote for Amiya, and another $5\%$ who would have otherwise voted for Ramya, will not vote at all.
  • If both run campaigns attacking each other, then $10\%$ of the students who would have otherwise voted for them had they run campaigns focusing on issues, will not vote at all.

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• 6.

  An online e-commerce firm receives daily integer product ratings from 1 through 5 given by buyers. The daily average is the average of the ratings given on that day. The cumulative average is the average of all ratings given on or before that day. The rating system began on Day 1, and the cumulative averages were 3 and 3.1 at the end of Day 1 and Day 2, respectively. The distribution of ratings on Day 2 is given in the figure below
  
  The following information is known about ratings on Day 3.
  1. 100 buyers gave product ratings on Day 3.
  2. The modes of the product ratings were 4 and 5.
  3. The numbers of buyers giving each product rating are non-zero multiples of 10.
  4. The same number of buyers gave product ratings of 1 and 2, and that number is half the number of buyers who gave a rating of 3.