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Each • in the mileage table above represents an entry indicating the distance between a pair of the five cities. If the table were extended to represent the distances between all pairs of 30 cities and each distance were to be represented by only one entry, how many entries would the table then have?
Each • in the mileage table above represents an entry indica
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02 Jun 2010, 10:54
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snkrhed wrote:
Each dot in the mileage table above represents an entry indicating the distance between a pair of the five cities. If the table were extended to represent the distances of 30 cities and each distance were to be represented by only one entry, how many entries would the table then have?
(A) 60 (B) 435 (C) 450 (D) 465 (E) 900
We are told that there should be one entry for each pair. How many entries would the table then have? Or how many different pairs can 30 cities give?
Re: Each • in the mileage table above represents an entry indica
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27 Jan 2020, 15:09
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Top Contributor
snkrhed wrote:
Each • in the mileage table above represents an entry indicating the distance between a pair of the five cities. If the table were extended to represent the distances between all pairs of 30 cities and each distance were to be represented by only one entry, how many entries would the table then have?
APPROACH #1: Each entry in the mileage table denotes a distinct pair of cities. We can determine the total number of distinct pairs of cities by using combinations. When there are 5 cities, the total number of distinct pairs of cities = 5C2 = 10 Noticed that in the given table there are 10 entries. Perfect!
Likewise, if we have a mileage table consisting of 30 cities, the total number of distinct pairs of cities = 30C2 [to learn how to mentally calculate combinations like 30C2, watch the video below] = (30)(29)/(2)(1) = 435 Answer: B
APPROACH #2: Notice that, when there are 5 cities in the mileage table, the number of entries = 1 + 2 + 3 + 4 Likewise, if we have a mileage table consisting of 30 cities, the number of entries = 1 + 2 + 3 + . . . . + 28 + 29
One way to calculate this is to apply the following formula: The sum of the integers from 1 to n inclusive = (n)(n+1)/2
So, 1+2+...........+28+29 = (29)(29+1)/2 = (29)(30)/2 = (29)(15) = 435 Answer: B
Re: Each • in the mileage table above represents an entry indica
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02 Jun 2010, 10:42
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snkrhed wrote:
So there's a chart that looks a lot like this:
-E D C B A A * * * * B * * * C * * D * E
Each * in the mileage table above represents an entry indicating the distance between all pairs of 30 cities and each distance were to be represented by only one entry, how many entries would the table then have?
(A) 60 (B) 435 (C) 450 (D) 465 (E) 900
City B, the second city has 1 point City C the third city has 2 points City D, the fourth city has 3 points
What's the pattern?
Number of cities minus 1 so the 30th city is going to have 29 points
Then it becomes a matter of adding the consecutive integers from 1 to 29 The sum is the average * number of terms average = 15 number of terms = 29 29*15 = 435
Re: Each • in the mileage table above represents an entry indica
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10 Nov 2013, 22:42
How would this question be solved using a consecutive integer format? Can you find the average on the consecutive integers and then multiply by the number of terms? I ask because this question is listed as a consecutive integer question in the MGAMT quant guide.
Re: Each • in the mileage table above represents an entry indica
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16 Feb 2014, 01:47
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stevennu wrote:
How would this question be solved using a consecutive integer format? Can you find the average on the consecutive integers and then multiply by the number of terms? I ask because this question is listed as a consecutive integer question in the MGAMT quant guide.
If second entry =1 third entry = 2 30th entry = 29 etc
Thus S(n)=n/2(2a+(n-1)d) where a=1, d=1, n=29 plug in and you get the answer. _________________
learn the rules of the game, then play better than anyone else.
Re: Each • in the mileage table above represents an entry indica
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13 Apr 2014, 11:30
Bunuel wrote:
snkrhed wrote:
Attachment:
img.jpg
Each dot in the mileage table above represents an entry indicating the distance between a pair of the five cities. If the table were extended to represent the distances of 30 cities and each distance were to be represented by only one entry, how many entries would the table then have?
(A) 60 (B) 435 (C) 450 (D) 465 (E) 900
We are there told that there should be one entry for each pair. How many entries would the table then have? Or how many different pairs can 30 cities give?
\(C^2_{30}=435\)
Answer: B.
Hi Bunuel,
Can you please elaborate on how this formula works?
Thanks!
EDIT: I did it via the table method but i've seen your formula pop up quite often and I'm failing miserably at it. That might explain the horrible score in NP.
I understand what formula to use but i'm having a hard time connecting the formula to the problem "\(C^n_k = \frac{n!}{k!(n-k)!}\)"
Re: Each • in the mileage table above represents an entry indica
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14 Apr 2014, 00:04
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russ9 wrote:
Bunuel wrote:
snkrhed wrote:
Attachment:
img.jpg
Each dot in the mileage table above represents an entry indicating the distance between a pair of the five cities. If the table were extended to represent the distances of 30 cities and each distance were to be represented by only one entry, how many entries would the table then have?
(A) 60 (B) 435 (C) 450 (D) 465 (E) 900
We are there told that there should be one entry for each pair. How many entries would the table then have? Or how many different pairs can 30 cities give?
\(C^2_{30}=435\)
Answer: B.
Hi Bunuel,
Can you please elaborate on how this formula works?
Thanks!
EDIT: I did it via the table method but i've seen your formula pop up quite often and I'm failing miserably at it. That might explain the horrible score in NP.
I understand what formula to use but i'm having a hard time connecting the formula to the problem "\(C^n_k = \frac{n!}{k!(n-k)!}\)"
\(C^2_{30}\) is choosing 2 out of 30. There are 30 cities and each pair of cities need an entry, hence 30 cites need \(C^2_{30}\) entries.
Re: Each • in the mileage table above represents an entry indica
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10 May 2014, 04:06
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russ9 wrote:
Bunuel wrote:
\(C^2_30\) is choosing 2 out of 30. There are 30 cities and each pair of cities need an entry, hence 30 cites need \(C^2_30\) entries.
Hope it's clear.
Hi Bunuel,
Unfortunately, still not clear. Why are we choosing 2 out of 30?
Consider the table given in the original post:
A and B have 1 entry; A and C have 1 entry; A and D have 1 entry; A and E have 1 entry; B and C have 1 entry; B and D have 1 entry; B and E have 1 entry; C and D have 1 entry; C and E have 1 entry; D and E have 1 entry.
So, each pair of letters from {A, B, C, D, E} has 1 entry, total of 10 entries. How many pairs can we have? \(C^2_5=10\).
Re: Each • in the mileage table above represents an entry indica
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13 Oct 2014, 02:08
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Combination formula is no doubt easiest and fastest. But other method is
Imagine it was an excel spreadsheet. Remove Cells A1, B2, C3, D4 etc, basically a diagonal across. Total will be 30 such cells. So now we have 900 - 30 = 870.
On both sides of the diagonal distance (between cities) is shown twice.
Re: Each • in the mileage table above represents an entry indica
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15 Apr 2015, 09:32
The distance from each city to its own is not represented in the table. So in the case of 5 cities, each city can have a distance w.r.t another 4 cities. ( A-B,A-C,A-D,A-E; BUT NOT A-A) Hence these 5 cities can have 5*4 = 20 distances. However we are representing each distance (to and fro) only once instead of twice. e.g A-B is same as B-A. Hence divide 20/2 = 10 dots
Similarly, in case of 30 cities, total distances will be 30*29 = 870 But we want to represent each distance only once instead of twice, so 870/2= 435 dots
Re: Each • in the mileage table above represents an entry indica
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18 Apr 2015, 11:05
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Expert Reply
Hi kirtivardhan,
The prompt gives us a 5x5 table, then tells us that it will be EXTENDED to a 30x30 table. From the table, you can see the 'pattern' involving the dots - as you go 'to the right', each column has one more dot in it than the column before. This means the final column will have 29 dots in it.
There are actually several different ways to answer this question. Noticing that LESS than HALF of the squares have dots in them and using the "spread" of the answer choices can help you to avoid most of the "math" involved in this question.
Re: Each • in the mileage table above represents an entry indica
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18 Apr 2015, 21:15
kirtivardhan wrote:
Hi Mates,
How are we getting this 29 for 30 cities?
The distance from a city to itself is not measured. If there are 5 cities A,B,C,D,E, THEN we measure A-B, A-C,A-D, A-E but not A-A. This for 5 cities, we get 4 distances.
When there are total 30 cities, we measure 29 distances for each city. Hope its clear.
Re: Each • in the mileage table above represents an entry indica
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18 Jun 2015, 13:44
Expert Reply
Hi stephyw,
Your approach absolutely works. If you read the other posts in this thread, you'll see that there are several ways to approach this prompt (and most of the questions that you'll see on Test Day will also be approachable in multiple ways). This goes to show that just because you got a question correct doesn't necessarily mean that you can't improve on your process. There might be a faster, more strategic way to approach the prompt; there might be a way that requires less 'work', etc. As you continue to study, you should commit some of your time to improving your overall tactical knowledge - those other methods can help you to increase your scores, improve your pacing and get "unstuck" when dealing with a question in which "your" approach doesn't seem to get you to the solution.
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