Jeff Miller

GMAT OFFICIAL GUIDE DS – Is the number of members of…

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)

table1_club_x

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.

table2_club_x

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.

table3_club_x

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.

table4_club_x

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

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