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Which club has more members?

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Source: — Data Sufficiency |
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by Patrick_GMATFix » Sun Mar 02, 2014 2:03 pm
Alone the statements cannot be sufficient since each gives us info about the people who are members of both groups, not allowing us to compare total group sizes. together the statements get interesting since they give us info about the same subgroup, but expressed in different ways.

The answer is C. I go through the question in detail in the full solution below (taken from the GMATFix App).

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by Bill@VeritasPrep » Mon Mar 03, 2014 12:01 pm
Neither statement is enough on its own because we don't know enough about the "other" club.

Since the number of people in both groups (or the overlap of the Venn diagram) is the same for both groups (if there are 30 people there, they count as 10 members of Club X and 10 members of Group Y), you could solve algebraically with .2X=30 and .3Y=30 to find which club has more members.
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by srfn » Mon Mar 03, 2014 12:31 pm
Bill - not sure I understand your logic above. What do you mean by "if there are 30 people there, they count as 10 members of Club X and 10 members of Group Y"? Also don't understand your algebra.

The way I understand this problem is as follows - the overlap is the SAME people. If that SAME group of people, no matter how big or small, makes up 20% of club X and 30% of club Y, (i.e. a smaller portion of club X than club Y), club X MUST be bigger, and the two statements together are sufficient. No?
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by Bill@VeritasPrep » Mon Mar 03, 2014 12:33 pm
Yeah, I changed my example number halfway through. The two 10's should also be 30's.

Each person in the overlap counts as a member of each group. So if there are 30 people there, those 30 people represent 20% of group X, and those same 30 people also represent 30% of Group Y. From there, you could use those equations (30 = 20% of X and 30 = 30% of Y) to find exact totals for X and Y.
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by Brent@GMATPrepNow » Tue Mar 04, 2014 7:35 am
BlueDragon2010 wrote: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.
Another approach is to use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of people, and the two characteristics are:
- member of Club X or not a member of Club X
- member of Club Y or not a member of Club Y
So, we can set up our diagram as follows:
Image

Since we're not told any populations, let's assign some variables.
Let X = # of Club X members
Let Y = # of Club Y members
So, we now have a diagram that looks like this:
Image

Okay, now let's solve the question...

Target question: Is X greater than Y?

Statement 1: Of the members of Club X, 20 percent are also members of Club Y.
If X people are in Club X, then the number of THESE people whose are ALSO in Club Y = 20% of X (aka 0.2X)
So, let's add this to our diagram:
Image

Does this provide enough information to determine whether or not X is greater than Y?
No. The reason is that we have no information about the bottom-left box:
Image

Since there are no restrictions on the bottom-left box, there are many possible ways to complete the diagram so that we get CONFLICTING answers to the target question. Here are two:
Case a:
Image
In this case X = 10 and Y = 2, which means X is GREATER THAN Y

Case b:
Image
In this case X = 10 and Y = 32, which means X is LESS THAN Y

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Of the members of Club Y, 30 percent are also members of Club X.
If Y people are in Club Y, then the number of THESE people whose are ALSO in Club X = 30% of Y (aka 0.3Y)
So, let's add this to our diagram:
Image

Using logic similar to the logic we used in statement 1, we can conclude that statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
When we combine the information we get TWO POSSIBLE expressions for the top-left corner:
Image
So, these two expressions must be equal.
In other words, 0.2X = 0.3Y
Divide both sides by 0.2 to get: X = (0.3/0.2)Y
Simplify to get: X = 1.5Y
Since X and Y must be positive integers, the expression X = 1.5Y tells us that X is 1.5 TIMES as big as Y
In other words, X is definitely greater than Y
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent


----------------------------
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