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OG 18, question-362

by vaibhav101 » Mon Oct 16, 2017 10:22 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.
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Source: — Data Sufficiency |
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by GMATGuruNY » Mon Oct 16, 2017 10:28 am
vaibhav101 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.
This problem is about overlapping sets.
Each statement tells us information about the overlap.
Let B = the number of members who are in both groups.

Statement 1:
B = 0.2X (20% of X is also in Y. In other words, 20% of X is in both groups.)
No information about Y.
INSUFFICIENT.

Statement 2:
B = 0.3Y (30% of Y is also in X. In other words, 30% of Y is in both groups.)
No information about X.
INSUFFICIENT.

Statements combined:
B = 0.2X
B = 0.3Y
Thus:
0.2X = 0.3Y
2X = 3Y
X = (3/2)Y.
Implication:
X>Y.
SUFFICIENT.

The correct answer is C.
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by Brent@GMATPrepNow » Mon Oct 16, 2017 10:59 am
vaibhav101 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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Difficult Problem Solving questions
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Easy Data Sufficiency questions
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
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Difficult Data Sufficiency questions
- https://www.beatthegmat.com/double-set-m ... 71423.html
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Brent Hanneson - Creator of GMATPrepNow.com
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