Seven friends, Abhay, Binny, Charu, Divya, Eshan, Fatima and Girish, are sitting on chairs in a straight line. All of them face the north direction. The chairs are numbered 1 to 7 from west to east. The following information is known about their relative positions :
1. Binny and Divya sit adjacent to each other with Divya's seat number being higher than Binny's.
2. Charu sits second to the left of Girish.
3. Fatima's seat number has the highest number of factors, and Binny's seat has the second highest.
4. Abhay does not sit at any end.
Based on the information provided, answer the following questions.
Solution
Given that there are 7 chairs numbered 1 to 7 east to west
Statement 3 states Fatima's seat number has the highest number of factors
From seat number 1 to 7, the number with the highest number of factors is 6, with four factors, i.e. 1, 2, 3 and 6.
So Fatima sits at seat number 6.
Similarly, the number with the second highest number of factors is 4, with three factors, i.e. 1, 2 and 4.
Hence, Binny sits at seat number 4.
Given Binny and Divya sit adjacent to each other with Divya's seat number being higher than Binny's
So, Divya sits at seat number 5.
As Charu sits second to the left of Girish, there is only two seats where they can be i.e. Seat 1 and 3
Hence, Charu sits at Seat 1 and Girish sits at Seat 3.
There are only two seats left, and given Abhay does not sit at the end seats.
So, Abhay sits at Seat 2 and Eshan sits at Seat 7.
So, the final arrangement is
The sum of the seat numbers of Binny and Fatima is 4+6 = 10.
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