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Is the number of members of Club X greater than the number o

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by mitzwillrockgmat » Mon May 24, 2010 10:33 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.

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.

Can someone explain why answer is C? THANKS :)
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Source: — Data Sufficiency |
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by albatross86 » Mon May 24, 2010 11:09 am
Question stem is straightforward. Let total number of members of Club X be X, and similarly Y for Club Y.
Those who are members of both X and Y = XY (Just XY, not X*Y!)

Statement 1:
XY = 20% of X
Say X = 100
XY = 20
Nothing to be said of the members in Y. Insufficient.

Statement 2:
XY = 30% of Y
Say Y = 100
XY = 30
Nothing to be said of the members in X. Insufficient.

Both statements together:

XY = 20% of X = 30% of Y
This essentially means X > Y
Sufficient.

Pick C
Last edited by albatross86 on Mon May 24, 2010 11:11 am, edited 1 time in total.
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by Patrick_GMATFix » Mon May 24, 2010 11:11 am
This is DS 89 in OG 12. Attached solution is an extract of the Official Guide Companion

Best of luck
-Patrick
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by [email protected] » Fri Nov 12, 2010 10:11 am
y is XY=20% of X = 30% of Y
I interpreted it as XY=20% of x + 30% of y
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by GMATGuruNY » Fri Nov 12, 2010 11:52 am
mitzwillrockgmat 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.

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.

Can someone explain why answer is C? THANKS :)
This is a question about overlapping groups. Each statement tells us information about the overlap.
Let B = the number of members who are in both groups.

Statement 1:
B = .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 = .3Y (30% of Y is also in X. In other words, 30% of Y is in both groups.)
No information about X.
Insufficient.

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

The correct answer is C.
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by mcdesty » Wed Dec 19, 2012 12:25 pm
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by Ishdeep18 » Wed Sep 04, 2013 5:51 am
GMATGuruNY wrote:
mitzwillrockgmat 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.

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.

Can someone explain why answer is C? THANKS :)
This is a question about overlapping groups. Each statement tells us information about the overlap.
Let B = the number of members who are in both groups.

Statement 1:
B = .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 = .3Y (30% of Y is also in X. In other words, 30% of Y is in both groups.)
No information about X.
Insufficient.

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

The correct answer is C.
Thankew .. great understtanding
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