Logical 9 - Ranking

Passage 1:

Mr Bankatlal acted as a judge for the beauty contest. There were four participants, viz. Ms Andhra Pradesh, Ms Uttar Pradesh, Ms West Bengal and Ms Maharashtra. Mrs Bankatlal, who was very anxious about the result asked about it as soon as he was back home. Mr Bankatlal told her just that the one who was wearing the yellow saree won the contest. When Mrs Bankatlal pressed for further details, he elaborated as follows:

i. All of them were sitting in a row.  

ii. All of them wore sarees of different colours, viz. green, yellow, white, red.

iii. There was only one runner-up and she was sitting beside Ms Maharashtra.

iv. The runner-up was wearing the green saree.

v. Ms West Bengal was not sitting at the end and was not the runner-up.

vi. The winner and the runner up are not sitting adjacent to each other.

vii. Ms Maharashtra was wearing a white saree.

viii. Ms Andhra Pradesh was wearing a green saree.

ix. Participants wearing yellow saree and white saree were at the ends.

Solution: 

Practice Questions:

1. Who wore the red saree?

(a) Ms Andhra Pradesh

(b) Ms West Bengal

(c) Ms Uttar Pradesh

(d) Ms Maharashtra

2. Ms West Bengal was sitting adjacent to

(a) Ms Andhra Pradesh and Ms Maharashtra

(b) Ms Uttar Pradesh and Ms Maharashtra

(c) Ms Andhra Pradesh and Ms Uttar Pradesh

(d) Ms Uttar Pradesh only

3. Which saree was worn by Ms Andhra Pradesh?

(a) Yellow 

(b) Red

(c) Green 

(d) White

4. Who was the runner-up?

(a) Ms Andhra Pradesh

(b) Ms West Bengal

(c) Ms Uttar Pradesh

(d) Ms Maharashtra

Time to Think:

5. Who was the winner of the beauty contest?

(a) Ms Andhra Pradesh

(b) Ms West Bengal

(c) Ms Uttar Pradesh

(d) Ms Maharashtra

Passage 2:

Five geeks (enthusiasts) entered a comic book character costume contest held during the comic con festival. The contestants dressed up and were given two awards—one for being best in a particular category (i.e. strongest, smartest, most efficient, scariest and powerful) and one for being ranked (i.e. 1st, 2nd, 3rd, 4th and 5th). Determine who wore what costume and what two awards they received.

(i) The winner of the most efficient character’s costume was ranked just above Sacha’s character’s costume (which wasn’t the superman).

(ii) The winner of the strongest category (which wasn’t the Wonderwoman) was not worn by Billy.

(iii) The joker’s costume was ranked just above Sacha’s costume (which wasn’t the strongest costume winner).

(iv) The Wonderwoman costume ranked just above the scariest costume and just below Vladimirs’s costume.

(v) The Batman costume was placed just higher than the winner of the strongest costume and just lower than Catherine’s costume.

(vi) The Lex Luthor costume ranked just above Jelena’s (which wasn’t the Superman) and just below the smartest.

Solution:

On combining clues (i) and clues (iii) we would get the following Table 1:

We combine Clues (i) and (iii) because Clue (ii) is not usable at this stage, as it is what can be described as “a checking” clue, i.e. once we have multiple final figure possibilities in place, we use clues of the nature of clue (ii) and also clue (i) (Sacha was not the superman), to eliminate one of the possibilities. Clue (iv) will give us Table 2:

Clue (v) would give us Table 3:

Clue (vi) would give us Table 4:

From this point we need to focus on Sacha’s costume. We would realise that Sacha cannot wear Superman (given clue (i)); Cannot wear joker (as joker is above Sacha according to Table 1) and cannot wear Lex Luthor because we cannot superimpose Table 4 on Table 1 by making Sacha correspond to Lex Luthor as it leads to the joker being the smartest (but Table 1 has joker as most efficient). This leaves us with 2 possibilities for Sacha’s costume—Wonderwoman or Batman. Let us take a look at how possibility 1 rolls out: For Sacha to be Wonderwoman we would need to merge Tables 1 and 2 to get Table 5 below:

To this we need to merge Table 3, which would give us Table 6 below:

There is only one way from this point that Table 4 can get merged into Table 6. That would give us:

That leaves us with a final solution as below.

We can clearly see that this solution table contradicts clue (ii) – i.e. Billy was not the strongest. Thus, we reject Possibility 1 and move to a possibility which would give us that Sacha must be Batman. In this case the thinking pattern would go as follows: Combining Table 3 with Table 1:

To this we merge Table 3 and get:

To this we merge Table 4 and get:

This leaves us with the task of placing the remaining values in each column. When we do this we get:

6. Billy ranked fifth. Option (a)

7. Billy got the scariest costume. Option (a)

8. Sacha’s costume is Batman. Option (b) is correct.

9. Option (c) is the correct order.

10. Only (IV) and (V) are not properly matched. Hence, Option (a) is correct.

Practice Questions:

6. Who among the following ranked fifth?

(a) Billy 

(b) Jelena

(c) Vladimir 

(d) Can’t be determined

7. Who among the following got the award of the scariest costume?

(a) Billy 

(b) Catharine

(c) Sacha 

(d) Vladimir

8. Which of the following is the costume of Sacha?

(a) Joker 

(b) Batman

(c) Lex Luthor 

(d) Wonderwoman

9. Which of the following shows the correct order of ranks 1st, 2nd, 3rd, 4th and 5th respectively?

(a) Billy, Jelena, Vladimir, Sacha, Catherine

(b) Vladimir, Sacha, Catherine, Billy, Jelena

(c) Catherine, Sacha, Vladimir, Jelena, Billy

(d) Vladimir, Billy, Catherine, Sacha, Jelena

Time to Think:

10. Which of the following are not correctly matched?

Costume - Category

I. Joker - Most Efficient

II. Batman - Smartest

Ill. Lex Luthor - Strongest
IV. Wonderwoman - Scariest
V. Superman - Powerful

(a) Only IV and V 
(b) Only III and IV
(c) Only ll and III 
(d) Only I and II