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by jaspreetsra » Sat Jan 03, 2015 11:23 pm
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% are also members of club Y.
2) of the members of club Y, 30% are also members of club X.

Help needed!
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by GMATGuruNY » Sun Jan 04, 2015 1:06 am
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.
This is a question about OVERLAPPING groups.
Each statement offers information about the OVERLAP -- the people in BOTH X AND Y.
Let B = the members who are in both groups.

Statement 1:
20% of X is also in Y.
In other words, 20% of X is in BOTH groups:
.2X = B.
No information about Y.
INSUFFICIENT.

Statement 2:
30% of Y is also in X.
In other words, 30% of Y is in BOTH groups:
.3Y = B.
No information about X.
INSUFFICIENT.

Statements 1 and 2 together:
.2X = B.
.3Y = B.
Thus:
.2X = .3Y.
X = (3/2)Y.
Thus, X>Y.
SUFFICIENT.

The correct answer is C.
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by Brent@GMATPrepNow » Sun Jan 04, 2015 8:43 am
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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by [email protected] » Sun Jan 04, 2015 11:07 am
HI jaspreetsra,

This DS question can be solved by TESTing VALUES.

We're asked if the number of members of Club X is greater than the number of members of Club Y? This is a YES/NO question. In these sorts of situations, it's common for some members to belong to BOTH Clubs, so we have to keep careful track of the numbers and possibilities....

Fact 1: 20% of the members of Club X are ALSO members of Club Y

IF...
Club X has 100 members, then 20 of those members ALSO belong to Club Y.
IF Club Y has 0 unique members, then the answer to the question is YES.
IF Club Y as 1,000 unique members, then the answer to the question is NO.
Fact 1 is INSUFFICIENT

Fact 2: 30% of the members of Club Y are ALSO members of Club X

This Fact offers the same general logic as Fact 1 (above). Without knowing the number of unique members in Club X, the answer to the question could be either YES or NO.
Fact 2 is INSUFFICIENT

Combined, we know...
20% of the members of Club X are ALSO members of Club Y
30% of the members of Club Y are ALSO members of Club X
These specific members are the SAME PEOPLE...

This means that .2(X) = .3(Y)

2X = 3Y
X = (3/2)(Y)

This means that X MUST be greater than Y, so the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

Final Answer: C

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