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GRE Math Challenge #117-On Elm Street there are 6 houses on

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GRE Math Challenge #117-On Elm Street there are 6 houses on [#permalink]  15 May 2015, 11:21
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Question Stats:

75% (00:49) correct 25% (00:32) wrong based on 4 sessions
On Elm Street there are 6 houses on one side of the street and 4 houses on the other. Each pair of houses on Elm Street is connected by exactly one telephone line.

Quantity A: The total number of such lines that connect houses on opposite sides of Elm Street
Quantity B: 12

• Quantity A is greater.
• Quantity B is greater.
• Both Quantities are Equal
• Cannot be determined
[Reveal] Spoiler: OA

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Sandy
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Re: GRE Math Challenge #117 [#permalink]  17 May 2015, 16:30
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sandy wrote:
On Elm Street there are 6 houses on one side of the street and 4 houses on the other. Each pair of houses on Elm Street is connected by exactly one telephone line.

Quantity A: The total number of such lines that connect houses on opposite sides of Elm Street
Quantity B: 12

Let A, B, C, D, E and F be the houses on one side of the street
Let W, X, Y and Z be the houses on other side of the street

How many lines does house A have that go ACROSS the street?
It has 4 lines that go to houses W, X, Y and Z

How many lines does house B have that go ACROSS the street?
It has 4 lines that go to houses W, X, Y and Z

How many lines does house C have that go ACROSS the street?
It has 4 lines that go to houses W, X, Y and Z

.
.
.
How many lines does house F have that go ACROSS the street?
It has 4 lines that go to houses W, X, Y and Z

NOTE: All other lines stay on the same side of the street, so we don't care about those lines.

So, the TOTAL number of lines that go ACROSS the street = 4 + 4 + 4 + 4 + 4 + 4
= 24

So, we get:
Quantity A: 24
Quantity B: 12

[Reveal] Spoiler:
A

Cheers,
Brent
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GRE Instructor
Joined: 10 Apr 2015
Posts: 1978
Followers: 60

Kudos [?]: 1798 [1] , given: 9

Re: GRE Math Challenge #117-On Elm Street there are 6 houses on [#permalink]  02 Sep 2017, 10:36
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Expert's post
sandy wrote:
On Elm Street there are 6 houses on one side of the street and 4 houses on the other. Each pair of houses on Elm Street is connected by exactly one telephone line.

Quantity A: The total number of such lines that connect houses on opposite sides of Elm Street
Quantity B: 12

• Quantity A is greater.
• Quantity B is greater.
• Both Quantities are Equal
• Cannot be determined

Here's a solution that uses the Fundamental Counting Principle.

Let A, B, C, D, E and F be the houses on the NORTH side of the street
Let W, X, Y and Z be the houses on the SOUTH side of the street

Take the task of connecting houses (on opposite sides of the street) and break it into stages.

Stage 1: Select a house on the NORTH side of the street
There are 6 houses to choose from (A, B, C, D, E and F), so we can complete stage 1 in 6 ways

Stage 2: Select a house SOUTH side of the street to connect with the house selected in stage 1
There are 4 houses to choose from (W, X, Y and Z), so we can complete stage 2 in 4 ways

By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus connect house on opposite sides of the street) in (6)(4)ways (= [color=#ff0000]24 ways)

We get
Quantity A: 24
Quantity B: 12

[Reveal] Spoiler:
A

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Re: GRE Math Challenge #117-On Elm Street there are 6 houses on   [#permalink] 02 Sep 2017, 10:36
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