Practice Question - 71 (Maxima Minima) | 100 DILR Questions for CAT Preparation PDF Download

Ans: (c)
Based on the given conditions, Damodaran misses out on the bonus if he gets a rating of 1 in any of the five parameters. He additionally needs to obtain a rating of 5 in at least one of the parameters. Thus, the maximum value of the range of ratings that he can acquire would be 1 + 3 (given) + 5 + 5 + 5. However, based on condition 2, he can have similar ratings in only two of the parameters. Thus, the maximum value of the final rating would be (1 + 3 + 5 + 5 + 4) / 5 = 18 / 5 = 3.6. Hence, Option C is the correct answer. 

Ans: (d)
Since Eman got a bonus, he must have obtained a rating of 5 in at least one of the parameters. To minimize his final rating we need to consider the following range of values: 5 (mandatory) + 2(given) + 2 + 3 + 3 = 15. The least value of his final rating is, therefore, 15 / 5 = 3. Hence, Option D is the correct answer. 

Ans: (d)
Our objective here is to minimize the final ratings in order to find the minimum value of the monthly payment. We cannot have a rating of 1 in any of the parameters since all the drives got the bonus and we need to have at least one parameter with a rating of 5. With this understanding, we obtain the following:
Arun:
Final rating = (5 + 4 + 2 + 2 + 3) / 5 = 16 / 5 = 3.2; Fixed payment = Rs.1000
Variable payment = 3.2 * Rs. 250 = Rs.800 ; Total = Rs. (1000 + 800) = Rs. 1800 
Barun:
Final rating = (5 + 3 + 2 + 2 + 3) / 5 = 15 / 5 = 3; Fixed payment = Rs.1200
Variable payment = 3 * Rs. 200 = Rs.600 ; Total = Rs.(1200 + 600) = Rs. 1800
Chandan: {rating of 5 in exactly two parameters based on condition 1}
Final rating = (5 + 5 + 2 + 2 + 3)/5 = 17/5 = 3.4; Fixed payment = Rs.1400
Variable payment = 3.4 * Rs. 100 = Rs.340 ; Total = Rs.(1400 + 340) = Rs. 1740
Damodaran:
Final rating = (5 + 3 + 2 + 2 + 3) / 5 = 15 / 5 = 3; Fixed payment = Rs.1300
Variable payment = 3 * Rs. 150 = Rs.450 ; Total = Rs.(1300 + 450) = Rs. 1750
Eman:
Final rating = (5 + 3 + 2 + 2 + 3 ) / 5 = 15 / 5 = 3; Fixed payment = Rs.1100
Variable payment = 3 * Rs. 200 = Rs.600 ; Total = Rs. (1100 + 600) = Rs. 1700

Hence, we observe that the minimum value of the monthly payment is Rs. 1700. Option D is the correct answer.

Ans: (a)
Our objective here is to maximize the final ratings in order to find the maximum possible value of the monthly payment. We cannot have a rating of 1 in any of the parameters since all the drives got the bonus and we need to have at least one parameter with a rating of 5. With this understanding, we obtain the following:

Arun: {can have only one rating of 5 based on condition 1}

Final rating = (5 + 4 + 4 + 3 + 3) / 5 = 19 / 5 = 3.8; Fixed payment = Rs.1000

Variable payment = 3.8 * Rs. 250 = Rs.950 ; Total = Rs.(1000 + 950) = Rs. 1950

Barun: {can have only one rating of 5 based on condition 1}

Final rating = (5 + 4 + 4 + 3 + 3) /5 = 19 / 5 = 3.8; Fixed payment = Rs.1200

Variable payment = 3.8 * Rs. 200 = Rs.760 ; Total = Rs.(1200 + 760) = Rs. 1960

Chandan:

Final rating = (5 + 5 + 2 + 4 + 4)/ 5 = 20 / 5 = 4; Fixed payment = Rs.1400

Variable payment = 4 * Rs. 100 = Rs. 400 ; Total = Rs. (1400 + 400) = Rs. 1800

Damodaran:

Final rating = (5 + 5 + 4 + 4 + 3) / 5 = 21 / 5 = 4.2; Fixed payment = Rs.1300

Variable payment = 4.2 * Rs. 150 = Rs.630 ; Total = Rs.(1300+630) = Rs. 1930

Eman:

Final rating = (5 + 5 + 2 + 4 + 4) / 5 = 20 /5 = 4; Fixed payment = Rs.1100

Variable payment = 4 * Rs. 200 = Rs.800 ; Total = Rs.(1100 + 800) = Rs. 1900

Hence, we observe that the maximum possible value of the monthly payment is Rs. 1960. Option (a) is the correct answer.