Data Sufficiency

Is the number of members of Club X greater than the number of members of Club Y?

1) Of the members of Club X, 20 percent are also members of Club Y.

2) Of the members of Club Y, 30 percent are also members of Club X.

Correct answer is C

Can anyone explain to me in a better way than the book explanations?

Hey cvec,

Basically, each statement gives you information about the intersection between the two groups, but nothing about each group individually.

For example, let's suppose 100 people are in X. According to Statement (1), that would mean 20 people are in the overlap. But how many people are in Y total? There's no way of knowing, and therefore no way to tell if X has more people than Y.

Same logic for Statement (2).

Together, (1) and (2) tell you that 20% of x is equal to 30% of y (where x and y are the number of people in Club X and Club Y, respectively). They are equal, because each represents the intersection between the two groups.

The resulting equation is:

.2x = .3y or 2x=3y

No matter what values of x and y you choose to fit this equation, x will always be bigger than y, and thus the answer is C

Make sense?

Yeah, noticing that both statements are discussing the same group--people who are members of both groups--is the key to this question.

We can reason it out without doing any algebra or using our scratchboard.

Clearly, each of (1) and (2) are insufficient by themselves.

Looking at (1) and (2) together, notice that if you are "a member of X who is also a member of Y", then you are also "a member of Y who is also a member of X". Also, notice that the people who are a member of both groups must be a fixed number--it won't change when we look at the roster of members in either group individually. (As raz points out, it is the intersection of both groups).

Thus, the people who are a member of both groups constitutes a greater percentage of the members of Club Y. Thus, Club X must have more members, total.

raz1024 wrote:Hey cvec,

Basically, each statement gives you information about the intersection between the two groups, but nothing about each group individually.

For example, let's suppose 100 people are in X. According to Statement (1), that would mean 20 people are in the overlap. But how many people are in Y total? There's no way of knowing, and therefore no way to tell if X has more people than Y.

Same logic for Statement (2).

Together, (1) and (2) tell you that 20% of x is equal to 30% of y (where x and y are the number of people in Club X and Club Y, respectively). They are equal, because each represents the intersection between the two groups.

The resulting equation is:

.2x = .3y or 2x=3y

No matter what values of x and y you choose to fit this equation, x will always be bigger than y, and thus the answer is C

Make sense?

Great explanation!!!!