DS: Installing Cable to Horace's family

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Sasha__K: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Mon Aug 25, 2008 8:53 pm

by Sasha__K » Tue Aug 26, 2008 2:00 pm

I have really hard time understanding this one:

To install cable television in a home, a certain cable company charges a basic fee of $30 plus a fee of $20 for each cable outlet installed in the home. How much did the cable company charge the Horace family for installing cable television in their home?

1. The cable company installed 3 cable outlets in Horace's home.
2. Tha amount that the cable company charge the Horace family for installing cable television in their home is equivalent to an average (arithmetic mean) charge of $30 per cable outlet installed)

correct answer is D, but I dont get why.
#1 is straight forward. Why is #2 sufficient?

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Source: Beat The GMAT — Data Sufficiency | Tue Aug 26, 2008 2:00 pm

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

Re: DS: Installing Cable to Horace's family

by Stuart@KaplanGMAT » Tue Aug 26, 2008 2:36 pm

Sasha__K wrote:I have really hard time understanding this one:

To install cable television in a home, a certain cable company charges a basic fee of $30 plus a fee of $20 for each cable outlet installed in the home. How much did the cable company charge the Horace family for installing cable television in their home?

2. Tha amount that the cable company charge the Horace family for installing cable television in their home is equivalent to an average (arithmetic mean) charge of $30 per cable outlet installed)

correct answer is D, but I dont get why.
#1 is straight forward. Why is #2 sufficient?

Average = sum of terms / # of terms

or, in slightly different terms:

Avg Cost = total cost / # of outlets

Let's call the number of outlets "n".

Total cost will therefore be $30 + $20(n)

So, we can write the formula as:

30 = (30 + 20n)/n
30n = 30 + 20n
30n - 20n = 30
10n = 30
n = 30/10 = 3

Of course, since this is data sufficiency, we should stop as soon as we see that we're going to get a single value for n (most likely after you write out the equation with numbers and "n"s).

You might also have decided that 2 was sufficient just using some common sense/logic. Since the total cost has a fixed amount ($30) plus a variable amount ($20/outlet), each number of outlets will give you a different average cost - so if we know the average cost, there must be some way of figuring out exactly how many outlets there are. Even if we have no clue how to calculate that number, we know that we have sufficient information to do so.

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Sasha__K: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Mon Aug 25, 2008 8:53 pm

Thanks

by Sasha__K » Tue Aug 26, 2008 3:31 pm

Thanks!

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Bens4vcobra: Senior | Next Rank: 100 Posts; Posts: 76; Joined: Thu Feb 19, 2009 12:10 pmFollowed by: 2 members; Thanked: 3 times

by Bens4vcobra » Fri Jun 24, 2011 5:50 am

Stuart Kovinsky wrote:
Sasha__K wrote:I have really hard time understanding this one:

To install cable television in a home, a certain cable company charges a basic fee of $30 plus a fee of $20 for each cable outlet installed in the home. How much did the cable company charge the Horace family for installing cable television in their home?

2. Tha amount that the cable company charge the Horace family for installing cable television in their home is equivalent to an average (arithmetic mean) charge of $30 per cable outlet installed)

correct answer is D, but I dont get why.
#1 is straight forward. Why is #2 sufficient?
Average = sum of terms / # of terms

or, in slightly different terms:

Avg Cost = total cost / # of outlets

Let's call the number of outlets "n".

Total cost will therefore be $30 + $20(n)

So, we can write the formula as:

30 = (30 + 20n)/n
30n = 30 + 20n
30n - 20n = 30
10n = 30
n = 30/10 = 3

Of course, since this is data sufficiency, we should stop as soon as we see that we're going to get a single value for n (most likely after you write out the equation with numbers and "n"s).

You might also have decided that 2 was sufficient just using some common sense/logic. Since the total cost has a fixed amount ($30) plus a variable amount ($20/outlet), each number of outlets will give you a different average cost - so if we know the average cost, there must be some way of figuring out exactly how many outlets there are. Even if we have no clue how to calculate that number, we know that we have sufficient information to do so.

I know this is a very old post, but could someone explain where it is indicated that $30 is the average cost? I'm just not seeing it. I got as far as A = 30 + 20n/n and only determined statement 1 was sufficient. I don't see how 30 can be used as the average, I don't see that indicated anywhere.

"It takes no ability to give effort. Toughness is not God-given; it's a choice. The discipline to execute is a habit." - Nick Saban

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himankk: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Wed Oct 27, 2010 1:56 am

by himankk » Sun Sep 11, 2011 3:17 am

Hi Nick,

Please read the Statement 2 again.

"The amount that the cable company charge the Horace family for installing cable television in their home is equivalent to an average (arithmetic mean) charge of $30 per cable outlet installed".

Its mentioned there.

Cheers,
HK

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