Is the Number of Members of Club X Greater than the Number of Members GMAT Data Sufficiency

Question: 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

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

Solution and Explanation
Approach Solution (1):

Total members= Member of X only (Say A) + Members of Y only (Say B) + Members of both = A + B + Both
Now from the statements both = either 0.2 A or 0.3 B
Total = A + B + 0.2A
OR
Equating both
A + B + 0.2 A = A + B + 0.3 B
0.2 A = 0.3 B
A = 1.5 B
X > Y

Correct option: C

Approach Solution (2):

(1) Of the members of Club X, 20 percent are also members of Club Y
20% of X are members of both X and Y
0.2 X = {Both}
Not sufficient

(2) Of the members of Club Y, 30 percent are also members of Club X
30% of Y are members of both X and Y
0.3 Y = {Both}
Not sufficient
(1) + (2) 0.2X = {Both} = 0.3Y
X/Y = 3/2
X > Y
Sufficient

Correct option: C

Approach Solution (3):

(1) 20% of the members of Club X are also members of Club Y
If Club X has 100 members, and 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 the Club Y has 1,000 unique members, then the answer to the question is NO.
S1 is insufficient

(2) 30% of the members of Club Y are also members of Club X
This fact offers the same general logic as S1 above. Without knowing the number of unique members in Club X, the answer to the question could be either YES or NO.
S2 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 0.2(X0 = 0.3(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

Correct option: C

“Is the number of members of Club X greater than the number of members of Club Y?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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