Example Case 4

Read the following and answer the questions that follow

Prof. Singh has been tracking the number of visitors to his homepage. His service provider has provided him with the following data on the country of origin of the visitors and the university they belong to:

[CAT 2004]

4) To which country does University 5 belong?

(1) India or Netherlands but not USA
(2) India or USA but not Netherlands
(3) Netherlands or USA but not India
(4) India or USA but not UK

5) University 1 can belong to

(1) UK
(2) Canada
(3) Netherlands
(4) USA

6) Which among the listed countries can possibly host three of the eight listed universities?

(1) None
(2) Only UK
(3) Only India
(4) Both India and UK

7) Visitors from how many universities from UK visited Prof. Singh's homepage in the three days?

(1) 1
(2) 2
(3) 3
(4) 4

Case Solution

4)
We can infer that we won’t be able to definitely determine the countries for some of the universities. As there are very few numbers in days 2 and 3, let's start with those.
On Day 3, there are only 2 visitors from UK, 1 visitor from USA only. So we can conclude that University 4 is in UK and University 6 is in USA based on the data given.

Likewise, if we look at day 2, there is 1 visitor from Netherlands and 2 visitors from India only. So we can conclude that University 3 is in Netherlands and University 8 is in India.

Universities 1, 2, 5 and 7 are left. We have to match them using Day 1.
Every University must be present in exactly one country. Considering Day 1, there are four universities for four countries. There are 2 visitors from Canada and UK. Therefore Universities 2 and 7 must be UK/Canada and Canada/UK respectively. Likewise, there is 1 visitor from Netherlands and India. Therefore Universities 1 and 5 must be India/Netherlands and Netherlands/India respectively.

Answer: (1) India or Netherlands but not USA

5)
The table is as follows.

Based on this, the answer is Netherlands.

Answer: (3) Netherlands

6)
The table is as follows.

Based on this, no country can do this.

Answer: (1) None

7)
The table is as follows.

Based on this, the answer is 2.

Answer: (2) 2

Answer:
4) (1) India or Netherlands but not USA
5) (3) Netherlands
6) (1) None
7) (2) 2

Example Case 5

Read the following and answer the questions that follow

Five friends meet every morning at Sree Sagar restaurant for an idli-vada breakfast. Each consumes a different number of idlis and vadas. The number of idlis consumed are 1, 4, 5, 6, and 8, while the number of vadas consumed are 0, 1, 2, 4, and 6. Below are some more facts about who eats what and how much.

i. The number of vadas eaten by Ignesh is three times the number of vadas consumed by the person who eats four idlis.
ii. Three persons, including the one who eats four vadas eat without chutney.
iii. Sandeep does not take any chutney.
iv. The one who eats one idli a day does not eat any vadas or chutney. Further, he is not Mukesh.
v. Daljit eats idli with chutney and also eats vada.
vi. Mukesh, who does not take chutney, eats half as many vadas as the person who eats twice as many idlis as he does.
vii. Bimal eats two more idlis than Ignesh, but Ignesh eats two more vadas than Bimal.
[CAT 2003L]

8) Which one of the following statements is true?

(1) Daljit eats 5 idlis
(2) Ignesh eats 8 idlis
(3) Bimal eats 1 idli
(4) Bimal eats 6 idlis

9) Which of the following statements is true?

(1) Sandeep eats 2 vadas
(2) Mukesh eats 4 vadas
(3) Ignesh eats 6 vadas
(4) Bimal eats 2 vadas

10) Which of the following statements is true?

(1) Mukesh eats 8 idlis and 4 vadas but no chutney
(2) The person who eats 5 idlis and 1 vada does not take chutney
(3) The person who eats equal number of vadas and idlis also takes chutney
(4) The person who eats 4 idlis and 2 vadas also takes chutney

Case Solution

8)

We need to match the number of Idlis and Vadas consumed by the five friends and we also need to find whether they take chutney or not. We will make a note of number of Idlis and Vadas consumed by the five friends.

Idlis – 1, 4, 5, 6, 8
Vadas – 0, 1, 2, 4, 6

We can form a table with each friend in a different row and we’ll match them to the number of Idlis and Vadas they consume.

Statement 1 says that the number of Vadas eaten by Ignesh is three times the number of vadas consumed by the person who eats four idlis. Therefore the number of Vadas eaten by Ignesh must be a multiple of 3. The only 3 multiple in Vadas is 6. So the number of Vadas eaten by Ignesh is 6. So we can conclude that the person eats 4 Idlis eats 2 Vadas (6/3).

From this, we can say that the person who eat 4 Idlis eats 2 Vadas.
From statement 3, we can mark no Chutney for Sandeep.
From statement 5, we can mark yes for Chutney for Daljit.
From statement 6, we can mark no Chutney for Mukesh and as it is given that Mukesh eats half as many vadas as the who eats twice as many idlis as he does. So we can take x and y for the number of Vadas and Idlis eaten by Mukesh. So the other person eats 2x and 2y number of Vadas and Idlis respectively. Based on the number of Idlis, we can see that 4 and 8 are the only numbers possible. So we conclude that Mukesh eats 4 Idlis and the other person eats 8 idlis. As we have already noted that the person eats 4 Idlis eats 2 Vadas, we can conclude that Mukesh eats 2 Vadas. As Mukesh eats 2 Vadas, the other person eats 4 Vadas. So we can say that the other person eats 8 Idlis and 4 Vadas.

From statement 7, we can conclude that Bimal eats 4 Vadas. As we have already noted that the person eats 4 Vadas eats 8 Idlis we can say that Bimal eats 8 Idlis. As Ignesh eats 2 Idlis less than Bimal, Ignesh eats 6 Idlis. As statement 2 says that the person who eats 4 Vadas eats without Chutney, we can mark no Chutney for Bimal.

Statement 2 says that 3 people don't eat Chutney. As we already have 3 No's for Chutney, we can conclude that Ignesh eats with Chutney.
The person who eats 1 Idli and 0 Vadas cannot be Daljit according to statement 5. So we can conclude that Sandeep is the one who eats 1 Idli and 0 Vadas.

Now Daljit is the only person left.The leftover number of Idlis and Vadas are 5 and 1 respectively. So we can put 5 Idlis and 1 Vada for Daljit.

Answer: (1) Daljit eats 5 idlis

9)
The table is as follows.

Based on this, only option (3) is true.
Answer: (3) Ignesh eats 6 vadas

10)
The table is as follows.

Based on this, only option (3) is true.

Answer: (3) The person who eats equal number of vadas and idlis also takes chutney

Answer:
8) (1) Daljit eats 5 idlis
9) (3) Ignesh eats 6 vadas
10) (3) The person who eats equal number of vadas and idlis also takes chutney.