CAT 2025 Lesson : Ranking - Case 4

Read the following and answer the questions that follow
A tea taster was assigned to rate teas from six different locations - Munnar, Wayanad, Ooty, Darjeeling, Assam and Himachal. These teas were placed in six cups, numbered 1 to 6, not necessarily in the same order. The tea taster was asked to rate these teas on the strength of their flavour on a scale of 1 to 10. He gave a unique integer rating to each tea. Some other information is given below:

1. Cup 6 contained tea from Himachal.
2. Tea from Ooty got the highest rating, but it was not in Cup 3.
3. The rating of tea in Cup 3 was double the rating of the tea in Cup 5.
4. Only two cups got ratings in even numbers.
5. Cup 2 got the minimum rating and this rating was an even number.
6. Tea in Cup 3 got a higher rating than that in Cup 1.
7. The rating of tea from Wayanad was more than the rating of tea from Munnar, but less than that from Assam.
[CAT 2017 S2]

5) What was the second highest rating given?

Answer:

6) What was the number of the cup that contained tea from Ooty?

Answer:

7) If the tea from Munnar did not get the minimum rating, what was the rating of the tea from Wayanad?

(1) 3
(2) 5
(3) 1
(4) 6

8) If cups containing teas from Wayanad and Ooty had consecutive numbers, which of the following statements may be true?

(1) Cup 5 contains tea from Assam
(2) Cup 1 contains tea from Darjeeling
(3) Tea from Wayanad has got a rating of 6
(4) Tea from Darjeeling got the minimum rating

Solution

Let's use letters to represent the children for convenience and short notes. Ranks assigned are 1 for the better flavour and 10 for the least flavour.

Munnar - M; Wayanad - W; Ooty - O; Darjeeling - D; Assam - A; Himachal - H.



- We have a direct clue in statement (1), H being in Cup 6.
- From statement (2), We know that Cup 3 cannot be Ooty.
- From statement (5), We know that Cup 2 should be minimum and even number. Least even number is 2.



- From statement (3), We know that cup 3 is double of the cup 5.



The least value a and odd number can take is 3. If a = 3 then cup 3 is 6. If a = 5 then cup 3 is 10. The condition doesn't satisfy since Ooty has to be Maximum. The only possible case being cup 5 = 3 and cup 3 = 6.

- Even number cups are 2, 6 and odd cups are 3, 5, 7, 9



- From statement (6), Cup 3 > Cup 1. The only possible number for cup 1 being is 5.



Only place for Ooty being max and 9 is cup 4. Since Cup 6 is occupied with H. Therefore H has a rating of 7.



5)

The 2nd highest rating was given to H with 7.

Answer: 7

6)

The Cup which belongs to Ooty is 4.

Answer: 4

7)

If M ≠ 2, then M = 3, W = 5, and A = 6.

Answer: (2) 5

8)

Since W and O have consecutive Cupa. If W = Cup 3 with rating of 6 (A > W > M) then A should have max the W which is not possible. The only possibility is where W = Cup 5 with a rating of 3.



W has rating of 3, which means that M has to be rating of 2.



The only possible rating left for A/D = 5/6.



Let us consider the options.
Option (1): False.
Option (2): True.
Option (3): False.
Option (4): False.

Answer: (2) Cup 1 contains tea from Darjeeling

Answer:
5) 7
6) 4
7) (2) 5
8) (2) Cup 1 contains tea from Darjeeling