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

[mitzwillrockgmat]

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

[albatross86]

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

[Patrick_GMATFix]

This is DS 89 in OG 12. Attached solution is an extract of the Official Guide Companion

Best of luck
-Patrick

[[email protected]]

y is XY=20% of X = 30% of Y
I interpreted it as XY=20% of x + 30% of y

[GMATGuruNY]

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.

[mcdesty]

See Img

[Ishdeep18]

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