GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
On Elm Street there are 6 houses on one side
[#permalink]
Updated on: 13 Dec 2019, 11:47
Updated on: 13 Dec 2019, 11:47
1
Expert Reply
1
Bookmarks
00:00
Question Stats:
72% (01:05) correct
27% (01:05) wrong based on 87 sessions
Hide Show timer Statistics
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
[#permalink]
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
[#permalink]
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
RELATED VIDEOS
