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Virtusa - Sample Analytical Paper
Posted Date: 04 Mar 2008 Resource Type: Articles/Knowledge Sharing Category: Placement Papers
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Posted By: Deepu Member Level: Diamond
Rating:  Points: 5
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Analytical Section
Answer the following question on the basis of the information given below:
Mathematicians are assigned a number called Erdos number (named after the famous mathematician, Paul Erdos). Only Paul Erdos himself has an Erdos number of zero. Any mathematician who has written a research paper with Erdos has an Erdos number of 1. For other mathematicians, the calculation of his/her Erdos number is illustrated below:
Suppose that a mathematicians X has co-authored papers with several other mathematicians. From among them, mathematician Y has the smallest Erdos number. Let the Erdos number of Y be y. Then X has an Erdos number y +1.Hence any mathematician with no co-authorship chain connected to Erdos has an Erdos number of infinity.
In a seven day long mini-conference organised in memory of Paul Erdos, a close group of eight mathematicians, call them A,B,C,D,E,F,G,and H, discussed some research problems. At the beginning of the conference, A was the only participant who has an infinite Erdos number. Nobody had an Erdos number less than that of F.
· On the third day of the conference F co-authored a paper jointly with A and C. This reduced the average Erdos number of the group of eight mathematicians to 3.The Erdos numbers of B, D, E, G, and H remained unchanged with the writing of this paper. Further, no other co-authorship among any three members would have reduced the average Erdos number of the group of eight to as low as 3.
· At the end of the third day, five members of this group had identical Erdos numbers while the other three had Erdos numbers distinct from each other.
· On the fifth day, Eco-authored a paper with F which reduced the group’s average Erdos number by 0.5.The Erdos numbers of the remaining six were unchanged with the writing of this paper.
· No other paper was written during the conference.
1. How many participants in the conference did not change their Erdos number during the conference?
(1) 2 (2) 3 (3) 4 (4) 5
2. The person having the largest Erdos number at the end of the conference must have had Erdos number (at that time) :
(1) 5 (2) 7 (3) 9 (4) 14 (5) 15
3. How many participants had the same Erdos number at the beginning of the conference?
(1) 2 (2) 3 (3) 4 (4) 5 (5) cannot be determined
4. The Erdos number of C at the end of the conference was:
(1) 1 (2) 2 (3) 3 (4) 4 (5) 5
5. The Erdos number of E at the beginning of the conference was:
(1) 2 (2) 5 (3) 6 (4) 7 (5) 8
Answers:
1.(4)
2.(2)
3.(2)
4.(2)
5.(3)
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