Is the number of members of Club X greater ....

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factor26: Senior | Next Rank: 100 Posts; Posts: 99; Joined: Sun Mar 13, 2011 12:42 pm

by factor26 » Wed Dec 07, 2011 6:21 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.

OG answer is C ... Can someone explain how to solve by plugging in values for x and y ... thanks!

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Source: Beat The GMAT — Data Sufficiency | Wed Dec 07, 2011 6:21 pm

chufus: Master | Next Rank: 500 Posts; Posts: 102; Joined: Thu Jul 21, 2011 2:22 amFollowed by: 1 member; Location: Lahore, Pakistan; Thanked: 4 times

by chufus » Wed Dec 07, 2011 6:31 pm

The thing is you don't know the relationship between x and y. So you can only choose one of them for values since we don't know their ratio.

1. Lets assumes x is 100. Than people both in X and Y are 20 as per the statement.. Still doesn't tell us anything about Y

INSUFFICIENT

2. Lets assume Y is 100. Than people both in X and Y are 30 as per the statement. Still doesn't tell us anything about X

INSUFFICIENT

The key thing here is to understand that the question is asking us about the relationship between X and Y and both statements fail on that count.

Now if statement 1 were true.

there are 20 people in both X and Y.

Now if both statements are true, these 20 people represent 30% of Y

So we can calculate Y:

(30/100)Y = 20

Solve for Y = 200/3 which is less than 100 . Hence SUFFICIENT !

Pick C

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Dec 07, 2011 6:54 pm

factor26 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.

OG answer is C ... Can someone explain how to solve by plugging in values for x and y ... thanks!

Let the total number of members of Club X = X
and the total number of members of Club Y = Y
People who are members of both clubs X and Y = XY

(1) XY = 20% of X or XY = 0.2X
If X = 100, then XY = 20 but we do not anything about the members of club Y; NOT sufficient.

(2) XY = 30% of Y or XY = 0.3Y
If Y = 100, then XY = 30 but here but we do not anything about the members of club X; NOT sufficient.

Combining (1) and (2), XY = 0.2X = 0.3Y, which implies X = 3Y/2, so X is greater than Y; SUFFICIENT.

The correct answer is C.

Anurag Mairal, Ph.D., MBA
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Gurome, Inc.
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factor26: Senior | Next Rank: 100 Posts; Posts: 99; Joined: Sun Mar 13, 2011 12:42 pm

by factor26 » Sat Dec 17, 2011 1:04 pm

@ chufus .... should i also be concerned with the # of individuals that are in both x and y .... meaning should i eliminate individuals that aree in both x and y because they are in both groups and not just one?

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GmatMathPro: GMAT Instructor; Posts: 349; Joined: Wed Sep 28, 2011 3:38 pmFollowed by: 54 members; Location: Austin, TX; Thanked: 236 times; GMAT Score:770

by GmatMathPro » Sat Dec 17, 2011 5:16 pm

factor26 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.

OG answer is C ... Can someone explain how to solve by plugging in values for x and y ... thanks!

Also, make sure you see that statements 1 and 2 are both referring to the same group of people. The members of X that are in Y refers to the same group of people as the members of Y that are in X. If you draw the Venn diagram, it would be the group of people in the middle where the two circles overlap.

Now, it may be easier to plug in a number for this middle group rather than numbers for the groups as a whole. Let's say 9 people are in both groups:

Statement 1: This would tell us that there are 45 people in club X

Statement 2: this would tell us that there are 30 people in club Y

More generally, if the people in the middle constitute a bigger percentage of club Y than club X, then club Y must be smaller.

Pete Ackley
GMAT Math Pro
Free Online Tutoring Trial

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