Contributions to gift certificate

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kobel51: Master | Next Rank: 500 Posts; Posts: 114; Joined: Tue Mar 24, 2009 9:19 am; Thanked: 1 times

by kobel51 » Sun Feb 16, 2014 9:58 am

Every member of a certain club volunteers to contribute equally to the purchase of a $60 gift certificate. How many members does the club have?

(1) Each member's contribution is to be $4.

(2) If 5 club members fail to contribute, the share of each contributing member will increase by $2

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Source: Beat The GMAT — Data Sufficiency | Sun Feb 16, 2014 9:58 am

Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members; Thanked: 335 times

by Patrick_GMATFix » Sun Feb 16, 2014 10:19 am

(1) is straightforward. everyone contributes $4 to pay for $60, so there must be 60/4 people contributing. Since "Every member" contributes, all members are accounted for.

(2) In general, whenever you deal with an equation of the form a*b=c with positive variables (eg: rate*time=distance, or principal*rate=interest), if you know by how much 2 of the variables will change while the 3rd stays fixed, AND if you know the value of any one of the variables, you will always have enough data to find the values of the other two variables

In this case, we have members * contribution = 60, we know by how much members and contribution would change, and we have the value 60, so we will have sufficiency. The full solution below is taken from the GMATFix App (answer D).

-Patrick

Last edited by Patrick_GMATFix on Sun Feb 16, 2014 2:05 pm, edited 1 time in total.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Feb 16, 2014 10:36 am

kobel51 wrote:Every member of a certain club volunteers to contribute equally to the purchase of a $60 gift certificate. How many members does the club have?

(1) Each member's contribution is to be $4.
(2) If 5 club members fail to contribute, the share of each contributing member will increase by $2

NOTE Let x = total number of club members

Target question: What is the value of x?

Given: The club members contributed equally to buy a $60 gift certificate

Statement 1: Each member's contribution is to be $4.
So, $60 divided among x members means each person pays $4
In other words, $60/x = $4
This tells us that x must equal 15
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: If 5 club members fail to contribute, the share of each contributing member will increase by $2
Patrick nicely explained why this statement is sufficient. Here's another approach:
With x members, each member's contribution = 60/x dollars
With x - 5 members, each member's contribution = 60/(x - 5) dollars
Statement 2 tells us that the DIFFERENCE in contributions is $2
So, we can write 60/(x - 5) - 60/x = 2
At this point, we need to determine whether or not this equation yields EXACTLY 1 possible value for x.
Let's find out.
First take 60/(x - 5) - 60/x = 2 and multiply both sides by (x)(x -5) to get: 60x - 60(x - 5) = 2(x)(x - 5)
Simplify left side to get: 300 = 2(x)(x - 5)
Divide both sides by 2 to get: 150 = (x)(x - 5)
Expand and rearrange to get: xÂ² - 5x - 150 = 0
Factor to get: (x - 15)(x + 5) = 0
So, x = 15 or x = -5
It APPEARS that we have 2 possible values for x. HOWEVER, this is a "real world" problem, and in the real world, we can't have -5 club members.
This means we can rule out the solution x = -5, which means x must equal 15
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Feb 16, 2014 11:58 am

kobel51 wrote:Every member of a certain club volunteers to contribute equally to the purchase of a $60 gift certificate. How many members does the club have?

(1) Each member's contribution is to be $4.

(2) If 5 club members fail to contribute, the share of each contributing member will increase by $2

Statement 1: Each member's contribution is to be $4.
Number of members = (total amount of the certificate)/(contribution per member) = 60/4 = 15.
SUFFICIENT.

Statement 2: If 5 club members fail to contribute, the share of each contributing member will increase by $2
Test whether the case implied by statement 1 -- 15 members, each contributing $4 -- is the ONLY case that will also satisfy statement 2.

Case 1: 15 members
If 5 members fail to contribute, the share for each of the 10 remaining members = 60/10 = 6.
Here, the share per member increases from $4 to $6, satisfying the constraint that the share of each contributing member increases by $2.

Case 2: 20 members
Share per member if all 20 members contribute = 60/20 = $3.
Share per member if only 15 members contribute = 60/15 = $4.
Here, the share per member increases from $3 to $4, VIOLATING the constraint that the share of each contributing member increases by $2.
Thus, Case 2 is not viable.

Implication:
For the share per member to increase by $2, only Case 1 is viable.
Thus, the number of members = 15.
SUFFICIENT.

The correct answer is D.

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