In the table above, what is the least number of table entries that are

Question

https://gmatclub.com/forum/download/file.php?id=22091 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 Untitled.png

Bunuel · Accepted Answer

SOLUTION https://gmatclub.com/forum/download/file.php?id=22091 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 The least number of table entries will be if we use only one entry for each pair of the cities. How many entries would the table then have? Or how many different pairs can be selected out of 6 cities? C^2_{6}=15 Answer: A. Similar question to practice: each-dot-in-the-mileage-table-above-represents-an-entry-95162.html

PareshGmat · Answer

Just count the colored boxes below the diagonal

= 5 + 4 + 3 + 2 + 1

= 15

Answer = A

BrainLab · Answer

Total possible pairs =6*6=36
Pairs with same letters=6
Pairs with same combinations (AB=BA etc)  \frac{36-6}{2} =15
Answer=36-6-15=15

BrainLab · Answer

For A horizontal: 5 entries (eliminate A to A)
For B horizontal: 4 entries (A to B = B to A / eliminate B to B ) 
For C horizontal: 3 entries (we had already A to C & B to C previously/ eliminate C to C)
For D horizontal: 2 entries (we had already A to D & B to D & C to D previously/ eliminate D to D)
For E horizontal: 1 entry (we had already A to E & B to E & C to E & D to E previously/ eliminate E to E)
For F horizontal: 0 entries (we had already A to F & B to F & C to F & D to F & E to F previously/ eliminate F to F)

Hope it helps !

abdulfmk · Answer

5+4+3+2+1=15
AB,AC,AD,AE,AF
BC,BD,BE,BF
CD,CE,CF
DE.DF
EF

JeffTargetTestPrep · Answer

This problem can be best solved using combinations.
 
This problem is similar to one in which 6 sports teams are playing in a tournament in which every team plays with each other team exactly once. No team plays itself, obviously, and the order of each pairing doesn't matter.  . We would calculate 6C2, or the number of combinations of 6 items taken 2 at a time:

6C2 =6!/2! (6 - 2)! = (6 x 5)/2! = 15
 
Answer A

GMATinsight · Answer

One entry must come between each pair of two cities

Two cities out of six cities (ABCDEF) can be chosen in 6C2 = 15 ways

Answer: Option C

MathRevolution · Answer

A - B, C, D, E, F = 5
B - C, D, E, F = 4
C - D, E, F = 3
D - E, F = 2
E - F = 1

Total: 5 + 4 + 3 + 2 + 1 = 15

Answer A

sahuanamika · Answer

I imagined cities with people where one person shakes hand with another person exactly once.
Now for 6 people , it will follow an arithmetic sequence i.e 5,4,3,2,1

Or Number of handshakes = (n-1)*n/2 
Given n = 6 => 6*5/2 = 15

Ans A

100mitra · Answer

Correct option :  A - 15

Method 1 - Counting Method : 5+4+3+2+1 =  15 
Method 2 - Combination - 6C2 =  15 
Method 3 - Mean - (6*5)/2 =  15

PriyamRathor · Answer

Hi,
 AndrewN 
 avigutman 
 Bunuel

What does the below sentence mean ?

Considering this sentence I thought we need to consider AA , BB ,CC ,DD ,EE and FF also .
Hence 15+6 = 21

Please guide how we cannot infer what I inferred.

avigutman · Answer

That's not a sentence,  PriyamRathor . The phrase "the mileage between" must be followed by the word "and" to get the structure:  the mileage between X and Y.  
If you just have  the mileage between X , there's no way to make sense of that.
So, the sentence is actually: 
That's using grammar to identify your mistake.
Using meaning: you don't need entries in a table to show the distance between a city and itself, because it's just zero.
AA, BB, CC, DD, EE and FF are all just equal to zero.

760Abhi · Answer

Hi

can any expert please tell me that what is the use of "mileage" word here?

Is it mean "distance"?

Actually I am not able to understand the question i.e. what we need to find in this question?

Thank you for helping me out.

Bunuel

avigutman · Answer

Yes,  760Abhi . mileage means "number of miles".

760Abhi · Answer

Thank you so much for your prompt response  avigutman

SatvikVedala · Answer

This is more similar to a shake hand problem

No.of outcomes = n(n-1)/2

6*5/2 = 15

Pixelm · Answer

another approach: half of the table will be filled.
there are 36 squares, so less than 18 will be filled.
the only answer choie that is less than 18 is 15.

In the table above, what is the least number of table entries that are

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In the table above, what is the least number of table entries that are

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