APP-CAB Company

CAT 2020 Slot 1 · DILR · Hard · Data Interpretation

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Passage / data set

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 the monthly payment structure (in rupees) is given in the table below:

DriverP1P2P3P4P5Fixed paymentBonus
Arun4Rs.1000Rs.250×Final Rating\text{Rs.}250 \times \text{Final Rating}
Barun3Rs.1200Rs.200×Final Rating\text{Rs.}200 \times \text{Final Rating}
Chandan2Rs.1400Rs.100×Final Rating\text{Rs.}100 \times \text{Final Rating}
Damodaran3Rs.1300Rs.150×Final Rating\text{Rs.}150 \times \text{Final Rating}
Eman2Rs.1100Rs.200×Final Rating\text{Rs.}200 \times \text{Final Rating}

The following additional facts are known:

  1. Arun and Barun have got a rating of 5 in exactly one of the parameters. Chandan has got a rating of 5 in exactly two parameters.
  2. None of drivers has got the same rating in three parameters.

Question 1 of 4

If Damodaran does not get a bonus, what is the maximum possible value of his final rating?

  1. A.

    3.4

  2. B.

    3.6

  3. C.

    3.8

  4. D.

    3.2

Answer

B

Explanation

Damodaran gets P2 = 3. If he does not get a bonus, he either gets a rating of 1 in at least one parameter or does not get any rating of 5. To maximize his final rating without getting a bonus, we should avoid 1s and maximize parameters up to 4 (since getting 5 might make him eligible if no 1 is present, or if we introduce a 1, the total score decreases). Without any 5 or 1, his highest ratings with no three same ratings can be 4, 4, 4, 3, 3, but no three ratings can be identical. So ratings can be 4, 4, 3, 4, 3 (values: 4, 4, 4, 3, 3 has three 4s, which is not allowed). To avoid three ratings being the same: ratings could be 4, 4, 3, 3, 4 (three 4s not allowed). Max ratings with at most two identical: two 4s, two 3s, one 5 (if he gets a 1 to negate bonus: 5, 5, 4, 3, 1 -> sum = 18 -> avg = 3.6). If no 1 and no 5: max ratings can be 4, 4, 3, 3, 2 -> sum = 16. With a 1 and two 5s: 5, 5, 4, 3, 1 -> sum = 18 -> avg = 3.6. Maximum possible final rating is 3.6.

Question 2 of 4

If Eman gets a bonus, what is the minimum possible value of his final rating?

  1. A.

    3.4

  2. B.

    3.2

  3. C.

    3.0

  4. D.

    2.8

Answer

C

Explanation

Eman has P5 = 2. To get a bonus, he must have at least one 5 and no 1s. To minimize his final rating, the other ratings should be as small as possible (min 2, since 1 is not allowed), with at most two parameters having the same rating. Ratings: 5, 2, 2, 3, 3 (sum = 15, average = 3.0). Thus, the minimum possible final rating is 3.0.

Question 3 of 4

If all five drivers get bonus, what is the minimum possible value of the monthly payment (in rupees) that a driver gets?

  1. A.

    1600

  2. B.

    1700

  3. C.

    1740

  4. D.

    1750

Answer

B

Explanation

Monthly payment = Fixed payment + Bonus coefficient * Final rating. For Eman: Fixed = 1100, bonus min final rating = 3.0. Total = 1100 + 200 * 3.0 = 1700. Checking all drivers' min payments when receiving bonus:

  • Arun: Fixed 1000 + 250 * R. Min R (P4=4, one 5, no 1s) = (5, 4, 2, 2, 3) => sum = 16 => R = 3.2. Total = 1000 + 250*3.2 = 1800.
  • Barun: Fixed 1200 + 200 * R. Min R (P1=3, one 5, no 1s) = (3, 5, 2, 2, 3) => sum = 15 => R = 3.0. Total = 1200 + 200*3.0 = 1800.
  • Chandan: Fixed 1400 + 100 * R. Min R = (5, 5, 2, 2, 3) => sum = 17 => R = 3.4. Total = 1400 + 100*3.4 = 1740.
  • Damodaran: Fixed 1300 + 150 * R. Min R = (5, 3, 2, 2, 3) => sum = 15 => R = 3.0. Total = 1300 + 150*3.0 = 1750.
  • Eman: Fixed 1100 + 200 * 3.0 = 1700. The minimum possible monthly payment among all drivers is Rs. 1700 (for Eman).

Question 4 of 4

If all five drivers get bonus, what is the maximum possible value of the monthly payment (in rupees) that a driver gets?

  1. A.

    1960

  2. B.

    1950

  3. C.

    1900

  4. D.

    2050

Answer

A

Explanation

To maximize payment for each driver under bonus conditions (at least one 5, no 1, max ratings with no three same ratings):

  • Arun: 5, 4, 4, 5 (only one 5 allowed for Arun) -> ratings: 5, 4, 4, 4 (not allowed 3 same) => 5, 4, 4, 3, 2 not max. Max for Arun (one 5, no 1s, at most two identical): ratings 5, 4, 4, 3, 3 -> sum = 19, avg = 3.8. Payment = 1000 + 250 * 3.8 = 1950.
  • Barun: (one 5 allowed) ratings 5, 4, 4, 3, 3 -> sum = 19, avg = 3.8. Payment = 1200 + 200 * 3.8 = 1960.
  • Chandan: (two 5s allowed) ratings 5, 5, 4, 4, 2 -> sum = 20, avg = 4.0. Payment = 1400 + 100 * 4.0 = 1800.
  • Damodaran: (at least one 5) ratings 5, 5, 4, 4, 3 -> sum = 21, avg = 4.2. Payment = 1300 + 150 * 4.2 = 1930.
  • Eman: ratings 5, 5, 4, 4, 2 -> sum = 20, avg = 4.0. Payment = 1100 + 200 * 4.0 = 1900. The maximum possible value of monthly payment is Rs. 1960 (for Barun).

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