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OG13 Data Sufficiency Problem 93

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OG13 Data Sufficiency Problem 93

by SteffenSL » Sun Apr 28, 2013 8:15 am
The Question reads as follows:
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.

The OG states that answer choice C shold be correct, however, this seems unreasonable to me. How can we get to any conclusion with the information given. It could be that Club X has 100 members in the first place and Club Y 200. Adding the % fractions wont change anything about the fact that Club Y will have more members than X. Saying Club X has 200 members and Club Y 100 resutls in the opposite solution.
Please .... help! What am I missing?
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by Anju@Gurome » Sun Apr 28, 2013 8:17 am
SteffenSL 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 SteffenSL » Sun Apr 28, 2013 8:27 am
Thank you for your quick reply...though, wouldn't 20% of X = 30% of Y mean that both clubs have the same number of members who are registered in both clubs? Maybe it will help me to grasp your reasonming if you could prove my reasoning in the first post invalid. :-)
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by Anju@Gurome » Sun Apr 28, 2013 8:46 am
SteffenSL wrote:Thank you for your quick reply...though, wouldn't 20% of X = 30% of Y mean that both clubs have the same number of members who are registered in both clubs? Maybe it will help me to grasp your reasonming if you could prove my reasoning in the first post invalid. :-)
Yes, that's exactly what it means.
From statement 1, 20% of the members of Club X are also members of Club Y, and from statement 2, 30% of the members of Club Y are also members of Club X.

Now, if we assume number of members in club X and Y are m and n respectively, 20% of m = 30% of n
--> (20/100)*m = (30/100)*m
--> 2m = 3n
--> m/n = 3/2
--> m > n

So, number of members in club X is greater than the number of members in club Y.

Hope that helps.
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by Blue_Skies » Mon Apr 29, 2013 3:40 pm
The Question reads as follows:
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.

The OG states that answer choice C shold be correct, however, this seems unreasonable to me. How can we get to any conclusion with the information given. It could be that Club X has 100 members in the first place and Club Y 200. Adding the % fractions wont change anything about the fact that Club Y will have more members than X. Saying Club X has 200 members and Club Y 100 resutls in the opposite solution.
Please .... help! What am I missing?

Let me first share my thought process:
Imagine this question as a set problem with clubs having X and Y members.
Now 1 statement says that the common members (lets say Z) are 20%X.
Assuming X= 100, 20% of X = 20. So Z=20.
Doesn't say anything about set Y . Hence Insufficient.

Now 2 says Z = 30%of Y . If Y is 100->Z=30.
Doesn't talk about X hence insufficient.

At this point answers A,B and D are out. Now combine A and B.
Consider A. If X=100 -> Z=20.
Now from 2. This 20 represent 30 % of the members in Y. Hence 30% of Y = 20.
There Y= 67(approx).

This will be the case every time.you can see that if you combine A and B with generic variables.
Z=20%X=30%Y.
X will always be Bigger. Hence C wins.
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by nanz236 » Sat Jun 15, 2013 9:42 am
my process :
Total members = Members of X only (Say A) + Members of Y Only (Say B) + Members of Both
= A + B + both
Now from the statements both= either 0.2A or 0.3B
Total = A + B + 0.2A
or = A + B + 0.3B
Equating both
A + B + 0.2A= A + B +0.3B
0.2A=0.3B
A=1.5B
=> X>Y
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