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!
Thanks.
DS
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- jaspreetsra
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This is a question about OVERLAPPING groups.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.
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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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.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.
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:
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:
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:
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:
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:
In this case X = 10 and Y = 2, which means X is GREATER THAN Y
Case b:
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:
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:
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
----------------------------
This question type is VERY COMMON on the GMAT, so be sure to master the technique.
To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919
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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich