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adkhanz: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Tue Dec 15, 2009 9:21 am; GMAT Score:620

by adkhanz » Mon Dec 28, 2009 11:52 pm

Several friends in a dinner group decide to contribute equally to the purchase of a $36 gift. How many people are in the group?

(1) The number of people in the group is equal to the size of each person's contribution, in dollars.
(2) If three more people joined the group, each person's individual contribution would fall by $2.

I worked through the problem and think the answer is A. Any takers?

Thanks,

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Source: Beat The GMAT — Data Sufficiency | Mon Dec 28, 2009 11:52 pm

papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

by papgust » Tue Dec 29, 2009 1:27 am

Isn't it D?

Let n be no. of people.

(1) The number of people in the group is equal to the size of each person's contribution, in dollars
n = 36/n
n^2 = 36
Sufficient.

(2) If three more people joined the group, each person's individual contribution would fall by $2.
n+3 = (36/n)-2
n^2+5n-36=0
Sufficient.

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adkhanz: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Tue Dec 15, 2009 9:21 am; GMAT Score:620

by adkhanz » Tue Dec 29, 2009 11:52 am

Think your initial setup from the given question stem is incorrect, especially no (2). That is, I think it should be:

Let n be no. of people; Let m be the contribution per person. Therefore,
initial equation is:
m = 36/n

1) Given is n = m
so then the initial equation becomes n = 36/n => n= +-6 => 6
{sufficient}

2) Given is if n is increased by 3 (n+3), then m is decreased by 2 (m = m-2)
so then the initial equation becomes (36/(n+3)) = m-2

Therefore we have two equations:
36 = (n+3)(m-2) and
36/n = m

substituting the value of m in the equation 36 = (n+3)(m-2) will yield 6 and -9 and 6 would be the answer.

{sufficient}

Therefore it would be D.

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mmslf75: Legendary Member; Posts: 503; Joined: Sun Aug 09, 2009 9:53 pmFollowed by: 2 members; Thanked: 31 times

by mmslf75 » Tue Dec 29, 2009 11:59 am

papgust wrote:Isn't it D?

Let n be no. of people.

(1) The number of people in the group is equal to the size of each person's contribution, in dollars
n = 36/n
n^2 = 36
Sufficient.

(2) If three more people joined the group, each person's individual contribution would fall by $2.
n+3 = (36/n)-2
n^2+5n-36=0
Sufficient.

D it is... same approach me too

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adkhanz: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Tue Dec 15, 2009 9:21 am; GMAT Score:620

by adkhanz » Tue Dec 29, 2009 12:36 pm

Using information from statement 2 alone, how can you derive the equation 36/n = n?

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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

by papgust » Tue Dec 29, 2009 7:09 pm

Sorry. I think i solved this prob in a hurry.

Ok. Let's assume that m is the contribution of a member in group.

We know that m = 36/n from the question.

(2) m - 2 = 36/n+3

Sub. m=36/n,

36/n - 2 = 36/n+3

Now, you can solve to find out n (no. of people). Its sufficient.

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adkhanz: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Tue Dec 15, 2009 9:21 am; GMAT Score:620

by adkhanz » Thu Dec 31, 2009 12:41 pm

Yeah think now you have it correct. However, duly note that in statement 2, the "n" on both side of the equation will like yield an "n^2" quad equation, which will require you to factor and hence will lead to two answers. If the two solutions for the n^2 yields two different positive values, then statement 2 will be "insufficient" and answer to the problem would have been A.

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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

by papgust » Thu Dec 31, 2009 6:05 pm

How do you get n^2 in statement II? Can you pls explain?

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adkhanz: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Tue Dec 15, 2009 9:21 am; GMAT Score:620

by adkhanz » Thu Dec 31, 2009 11:58 pm

Sure, see my second post above under statement 2:

2) Given is if n is increased by 3 (n+3), then m is decreased by 2 (m = m-2)
so then the initial equation becomes (36/(n+3)) = m-2

Therefore we have two equations:
36 = (n+3)(m-2) and
36/n = m

substituting the value of m in the equation 36 = (n+3)(m-2) will yield 6 and -9 and 6 would be the answer.

{sufficient}

In your post you listed statement 2 as:
(2) m - 2 = 36/n+3

Sub. m=36/n,

36/n - 2 = 36/n+3 --> This means, (36/2) - (2/1) = (36/(n+3)). Hope this helps.

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