CAT 2025 Lesson : Ranking - Case 6

Read the following and answer the questions that follow
Five friends - A, B, C, D and E - were ranked on the basis of 3 parameters - height, weight and marks scored in a test. The tallest, heaviest and highest scorer were ranked first in their respective parameters. The shortest, lightest and lowest scorer were ranked fifth in their respective parameters. No two students had the same height or the same weight or scored the same marks. None of the students got the same rank in two or more parameters.

1) While E weighed lower than D, E was taller and got more marks than D.
2) Neither A nor D got the first rank in any of the parameters.
3) A got a better rank than B and C in height, but a poorer rank than B and C in weight and marks scored.
4) E's rank in height and weight were numerically lower than her rank for marks scored.
5) C got the first rank in a parameter and the fifth rank in another parameter. Each of the other 4 friends got either the first rank or the last rank in at least one parameter.

13) Who was the third lightest student?

(1) A
(2) C
(3) E
(4) Cannot be determined

14) Who got the third rank in the test?

(1) A
(2) B
(3) E
(4) Cannot be determined

15) What was the numerical difference between the ranks secured by B and D in height?

(1) 1
(2) 2
(3) 3
(4) Cannot be determined

16) If MaxDiff(X) is a function that provides the maximum difference in the numerical value of the ranks secured by X in any two of the three parameters, then what is the smallest value of MaxDiff(X) that one of the friends could possibly have had?

Answer:

Solution

Case solution:

The rank assigned is 1 for the tallest/heaviest/highest scorer and 5 for the shortest/lightest/lowest scorer.



From (b) we can infer that A and D did not get the 1st rank in any of the three parameters, therefore the 1st position of three parameters must be occupied by C, B, and E. The last positions of Parameters are occupied by C, A, and D respectively.

B and C could not make it to the 1st rank in height, therefore E must be the tallest person. C's rank is better than A in both weight and marks, so C must have got the last rank in the height parameter. Based on (a), D is heavier than E, therefore D has to be ranked fifth in the marks, and A fifth in the weight parameter.



If E is ranked 4th in the weight parameter, then we cannot satisfy the condition in statement (d) – EH & EW is greater than EM . Hence, E and D must be ranked in the 3rd and 2nd positions in the weight parameter and E must be ranked 4th in marks because EW is greater than EM.

Statement (c) of marks parameter shows that B and C are better than A. This leaves 3rd rank of A in marks parameter.

A is taller than B in height, which means that A has to be ranked 2 in height parameter, as A already got the 3rd rank in the marks parameter.

Therefore, the table we have is:



13)

Based on the table, E is the 3rd lightest Student.

Answer: (3) E

14)

Based on the table, A got the 3rd rank in the test.

Answer: (1) A

15)

This is the table that we have created:



The rank of B and D in the height parameter is either 3 and 4 or 4 and 3. The numerical difference in the rank is 1

Answer: (1) 1

16)

This is the table that we have created:



Maximum difference:

A = 5 - 2 = 3
D = 5 - 2 = 3
E = 4 - 1 = 3

If we place C in rank 1 of weight and rank 2 of marks then the smallest value of MaxDiff cannot be achieved which is shown in the following table



In the above table the MaxDiff of
C = 5 – 1 = 4
B = 4 – 1 = 3
where B =3 is not the smallest value of MaxDiff.
When B occupies rank 1 of weight and rank 2 of marks, then the following table shows the maximum difference.



In the above table the MaxDiff of
C = 5 – 1 = 4
B = 3 – 1 = 2

B = 2 is the smallest value of MaxDiff.

Answer: 2

Answer:
13) (3) E
14) (1) A
15) (1) 1
16) 2