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DS(Overlapping sets)

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DS(Overlapping sets)

by rintoo22 » Sat Mar 30, 2013 12:23 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 percent are also members of Club Y.
(2) Of the members of Club Y, 30 percent are also members of Club X.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Initially I thought it to be a simple Question with Answer E. However in the QA the answer is given as C. Can someone throw some light.
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by mohit_1607 » Sat Mar 30, 2013 1:23 pm
Statement 1: Let the total members of Club X be x
Now, as per the statement 20% of x are members of Club Y.
This statement alone is insufficient to come to a conclusion.

Statement 2: Let the total members of Club Y be y
As per the statement 30% of y are members of Club X.
This statement alone also is insufficient to come to a conclusion.

Statement 1 and 2 combined:
We can deduce that 20/100x=30/100y (common region b/w X and Y if solved using Venn Diagram)
therefore, x/y=3/2 and a conclusion can be reached for the question asked.
Hence, Option C

Please make a Venn Diagram for better understanding!!
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by Anju@Gurome » Sat Mar 30, 2013 10:56 pm
rintoo22 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.
None of the statements are individually sufficient as none of them give us any idea about relative number of members of the clubs.

1 & 2 Together: 20% of X = 30% of Y
Hence, size of X must be greater than size of Y as a smaller percentage of X is equal to a larger percentage of Y.

Sufficient

The correct answer is C.
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by GMATGuruNY » Sun Mar 31, 2013 4:08 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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