## Is the number of members of…

## Solution:

We need to determine whether the number of members of club X is greater than the number of members of club Y.

An easy way to solve the problem is to set up a double set matrix. In our matrix we have two main categories: Club X and Club Y. More specifically, our table will be labeled with:

1) Number of members in Club X (Club X)

2) Number of members not in Club X (No Club X)

3) Number of members in Club Y (Club Y)

4) Number of members not in Club Y (No Club Y)

(To save room on our table headings we will use the abbreviations for these categories)

**Statement One Alone: **

Of the members of club X, 20% are also members of club Y.

We are given that, of the members of club X, 20% are also members of club Y. We can denote x as the number of members in club X and y as the number of members in club Y.

Lets now fill the information from statement one into our table.

We see that statement one alone is not sufficient to determine whether the number of members in club X is greater than the number of members in club Y. We can eliminate answer choices A and D.

**Statement Two Alone: **

Of the members of club Y, 30% are also members of club X.

We are given that of the members of club Y, 30% are also members of club X. We can denote y as the number of members in club Y.

Let’s fill the information from statement two into our table.

We see that statement two alone is not sufficient to determine whether the number of members in club X is greater than the number of members in club Y. We can eliminate answer choice B.

**Statements One and Two Together: **

We can create one table with the information from both statements one and two.

We see that 0.3y = 0.2x. Multiply both sides of the equation by 10:

3y = 2x

3y/2 = x

1.5y = x

Since 1.5y is equal to x, we see that y must be less than x. Thus, we know that there are fewer members in club Y than there are in club X.

**Answer:** C