least no of table entries

[kishokbabu]

City A City B City C City D City E City F
City A
City B
City C
City D
City E
City F

For the above table, kindly refer the attachment.

In the table above, what is the least number of table entries that are needed to show the mileage between each city and each of the other five cities?

A) 15
B) 21
C) 25
D) 30
E) 36

[neelgandham]

From the table, total number of cells = 6*6 = 36. From the diagram attached The BLACK cell in the first row indicates the distance from City A to City A, which is 0. On similar lines, all the BLACK cells indicate distances from the same city(AtoA,BtoB,CtoC,DtoD,EtoE,FtoF), which is ZERO.
The GREEN cell in the first row indicates the distance from City B to City A and The GREEN cell in the second row indicates the distance from City A to City B. Since, Distance from City B to City A is EQUAL to Distance from City A to City B. If you know the value of the GREEN cell in the first row then you also know the value of the GREEN cell in the second row. So, If you fill all the cells located on one side of the diagonal(Black cells), you will also be able to fill the cells on the other side. The answer is equal to number of cells on one side of the diagonal(Black cells) = 15

Answer A

[pemdas]

6C2=15