CAT 2004 | Question: 04

Question

Answer the questions based on the information given below:

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:

Number of Visitors
Countries	Day
	1	2	3
Canada	2	0	0
Netherlands	1	1	0
India	1	2	0
UK	2	0	2
USA	1	0	1

 

Number of Visitors
UNIVERSITY	Day
	1	2	3
University 1	1	0	0
University 2	2	0	0
University 3	0	1	0
University 4	0	0	2
University 5	1	0	0
University 6	1	0	1
University 7	2	0	0
University 8	0	2	0

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

• A. None
• B. Only UK
• C. Only India
• D. Both India and UK

Answer 1

I think it will be option $2^{nd}$ ONLY UK

Because India can't able to handle $3$ request.

University request for UK will be

University 1	1 0 0
University 4	0 0 2
University 5	1 0 0

 

This will fulfill $2 \; 0 \; 2$ max request by UK.

Answer 2

Both India and UK

Option 4

Comments

How India will handle the users? I can't make any combination that makes 1 for day1 and 2 for day2 and 0 for 3^rd day.

Answer 3

only india

Answer 4

Answer is $\text{D}.$ Both India and UK
Here's How :
Total number of visitors from India are $3$ and $4$ are from UK.
India on Day $1$ has $1$ visitor which could be from University $1,2,5,6$ and $7$. On the second day India has two visitors, one could be from University $3$ and other from University $8.$ So three distinct universities can be covered.
UK has $2$ visitors on Day $1$ which could be from Universities $1,2,5,6$ and $7$ and $2$ visitors on Day $3$ who could be from University $4$ and $6.$ Even if Visitor from University $6$ is common, the other three must be distinct because University $6$ makes only one visit on Day $1.$
Other countries cannot host three distinct Universities because they have less than $3$ visitors.