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On Elm Street there are 6 houses on one side
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Updated on: 13 Dec 2019, 11:47
Updated on: 13 Dec 2019, 11:47
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Question Stats:
72% (01:04) correct
27% (01:03) wrong based on 90 sessions
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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.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The total number of such lines that connect houses on opposite sides of Elm Street |
12 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: GRE Math Challenge #117
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17 May 2015, 16:30
17 May 2015, 16:30
1
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: 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
Answer:
Show: ::
A
Cheers,
Brent
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: GRE Math Challenge #117-On Elm Street there are 6 houses on
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02 Sep 2017, 10:36
02 Sep 2017, 10:36
1
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
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
Answer:
Show: ::
A
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