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An airline serving n cities has 2 nonstop flights per day, one in each

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guddo
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An airline serving n cities has 2 nonstop flights per day, one in each [#permalink] New post   27 Jan 2024, 10:03
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An airline serving n cities has 2 nonstop flights per day, one in each direction, between each pair of these cities. How many nonstop flights does the airline have among these n cities each day?

A. 2n(n-1)
B. n(n-1)
C. 2n^2
D. n^2
E. 2n


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Bunuel
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Re: An airline serving n cities has 2 nonstop flights per day, one in each [#permalink] New post   27 Jan 2024, 10:11
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guddo wrote:
An airline serving n cities has 2 nonstop flights per day, one in each direction, between each pair of these cities. How many nonstop flights does the airline have among these n cities each day?

A. 2n(n-1)
B. n(n-1)
C. 2n^2
D. n^2
E. 2n


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Attachment:
2024-01-27_20-58-23.png


From n cities, we can form \(C^2_n=\frac{n!}{2!(n-2)!}=\frac{(n-2)!(n-1)n}{2!(n-2)!}=\frac{(n-1)n}{2}\) pairs. Since there are 2 flights between each pair of cities, the total number of flights among n cities is \(2*\frac{(n-1)n}{2}=(n-1)n\).

Answer: B.
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gmatophobia
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Re: An airline serving n cities has 2 nonstop flights per day, one in each [#permalink] New post   27 Jan 2024, 11:24
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guddo wrote:
An airline serving n cities has 2 nonstop flights per day, one in each direction, between each pair of these cities. How many nonstop flights does the airline have among these n cities each day?

A. 2n(n-1)
B. n(n-1)
C. 2n^2
D. n^2
E. 2n


Show Spoiler
Attachment:
2024-01-27_20-58-23.png


One way to solve this question is by using the concept of Permutations and Combinations as Bunuel has depicted.

Another way is to assume a value of n and then eliminate the options.

Assume n = 2

The number of flights nonstop flights the airline has among these 2 cities ⇒ is 2 (one flight from City 1 to City 2 and another from City 2 to City 1

Answer choice elimination

A. 2n(n-1) ⇒ 2 * 2 (1) = 4

B. n(n-1) ⇒ 2 * 1 = 2

C. 2n^2 ⇒ 2*2^2 = 8

D. n^2 ⇒ 2^2 = 4

E. 2n ⇒ 2 * 2 = 4

Option B
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Re: An airline serving n cities has 2 nonstop flights per day, one in each [#permalink] New post   24 Mar 2024, 05:56
gmatophobia wrote:
guddo wrote:
An airline serving n cities has 2 nonstop flights per day, one in each direction, between each pair of these cities. How many nonstop flights does the airline have among these n cities each day?

A. 2n(n-1)
B. n(n-1)
C. 2n^2
D. n^2
E. 2n


Show Spoiler
Attachment:
2024-01-27_20-58-23.png

One way to solve this question is by using the concept of Permutations and Combinations as Bunuel has depicted.

Another way is to assume a value of n and then eliminate the options.

Assume n = 2

The number of flights nonstop flights the airline has among these 2 cities ⇒ is 2 (one flight from City 1 to City 2 and another from City 2 to City 1

Answer choice elimination

A. 2n(n-1) ⇒ 2 * 2 (1) = 4

B. n(n-1) ⇒ 2 * 1 = 2

C. 2n^2 ⇒ 2*2^2 = 8

D. n^2 ⇒ 2^2 = 4

E. 2n ⇒ 2 * 2 = 4

Option B

­I tried this is the same way but picked 3 and ended up being confused between E and B. solved again with 4 and got it.
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Re: An airline serving n cities has 2 nonstop flights per day, one in each [#permalink] New post   24 Mar 2024, 07:32
Method 1:
Select 2 cities. For each selection we have 2 flights

NC2*2=n(n-1)

Method 2:
Take n=2 . Say you travel b/w Mumbai and New York.
There are 2 flights (Mumbai to NY & back)

Only option B works

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Re: An airline serving n cities has 2 nonstop flights per day, one in each [#permalink] New post   25 Apr 2024, 11:36
Start with two cities. It can have two flights between them. 2*1 = 2
Then , with three cities ; They can have 6 flights among them ; 3*2 = 6

Then with , four cities ; They can 12 flights among them ; 4*3 = 12

Hence using this analogy , we can say that for n cities , we can have n*(n-1) flights.
B is the answer.

KarishmaB , MartyMurray Is my approach correct ?­
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Re: An airline serving n cities has 2 nonstop flights per day, one in each [#permalink]
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