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

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Bunuel
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In the table above, what is the least number of table entries that are [#permalink] New post   24 Jan 2014, 03:51
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A
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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


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Bunuel
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Re: In the table above, what is the least number of table entries that are [#permalink] New post   24 Jan 2014, 03:52
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SOLUTION


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
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Re: In the table above, what is the least number of table entries that are [#permalink] New post   01 Aug 2014, 00:26
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Just count the colored boxes below the diagonal

= 5 + 4 + 3 + 2 + 1

= 15

Answer = A
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Re: In the table above, what is the least number of table entries that are [#permalink] New post   20 Jul 2014, 02:59
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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 !
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Re: In the table above, what is the least number of table entries that are [#permalink] New post   01 Apr 2015, 03:09
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Attachment:
The attachment Untitled.png is no longer available
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

Problem Solving
Question: 56
Category: Arithmetic Interpretation of tables
Page: 69
Difficulty: 600


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Answer 15 A
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Re: In the table above, what is the least number of table entries that are [#permalink] New post   12 Oct 2015, 08:39
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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
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Re: In the table above, what is the least number of table entries that are [#permalink] New post   12 Oct 2015, 10:50
5+4+3+2+1=15
AB,AC,AD,AE,AF
BC,BD,BE,BF
CD,CE,CF
DE.DF
EF
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Re: In the table above, what is the least number of table entries that are [#permalink] New post   04 Apr 2017, 16:20
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Bunuel wrote:

Attachment:
Untitled.png
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


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. [For example, if Team A plays Team B, the pairing of (Team A vs. Team B) is identical to (Team B vs. Team A)]. 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
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Re: In the table above, what is the least number of table entries that are [#permalink] New post   29 Sep 2018, 05:59
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eybrj2 wrote:
Attachment:
Table.png
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


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
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Re: In the table above, what is the least number of table entries that are [#permalink] New post   05 Oct 2020, 08:41
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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
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Re: In the table above, what is the least number of table entries that are [#permalink] New post   23 Jun 2021, 03:33
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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
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Re: In the table above, what is the least number of table entries that are [#permalink] New post   18 Sep 2021, 10:25
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
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In the table above, what is the least number of table entries that are [#permalink] New post   26 Aug 2022, 05:51
Bunuel wrote:

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


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Attachment:
Untitled.png


Hi,
AndrewN
avigutman
Bunuel

What does the below sentence mean ?
Quote:
needed to show the mileage between each city


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.
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Re: In the table above, what is the least number of table entries that are [#permalink] New post   12 Sep 2022, 03:56
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PriyamRathor wrote:
What does the below sentence mean ?
Quote:
needed to show the mileage between each city


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

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:
Quote:
the mileage between each city and each of the other five cities

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.
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Re: In the table above, what is the least number of table entries that are [#permalink] New post   18 Oct 2022, 10:22
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
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Re: In the table above, what is the least number of table entries that are [#permalink] New post   18 Oct 2022, 11:15
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760Abhi wrote:
Hi

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

Is it mean "distance"?

Yes, 760Abhi. mileage means "number of miles".
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Re: In the table above, what is the least number of table entries that are [#permalink] New post   18 Oct 2022, 22:05
avigutman wrote:
760Abhi wrote:
Hi

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

Is it mean "distance"?

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



Thank you so much for your prompt response avigutman
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Re: In the table above, what is the least number of table entries that are [#permalink] New post   25 Oct 2023, 07:56
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