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: x² - 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