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Why we have considered equal no of members?

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by saurabhdhakad » Sun Jul 21, 2013 11:21 pm
Hi,

I have taken this problem from OG 13:

93. 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.

Why we have considered same no of members as common?
It is possible that from club X and Y can have 100 and 200 members respectively and same can be true other way round also.
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Source: — Data Sufficiency |

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by [email protected] » Mon Jul 22, 2013 12:09 am
Hi saurabhdhakad,

This DS question can be beaten rather quickly by TESTing values.

The prompt asks if the number in Club X is greater than the number in Club Y?

Fact 1 tells us that 20% of X are in Y

If X = 100...
Y would be 20 + however many are unique to Y
If Y = 21 total, then the answer to the question is YES
If Y = 101 total, then the answer to the question is NO
Inconsistent answers means that Fact 1 is INSUFFICIENT

Fact 2 tells us that 30% of Y are in X
If Y = 100...
X would be 30 + however many are unique to X
If X = 31 total, then the answer to the question is NO
If X = 101 total, then the answer to the question is YES
Inconsistent answers means that Fact 2 is INSUFFICIENT

Combining Facts, we'd have this algebra equation (since the "overlapping members" are mentioned in both Facts):

.2X = .3Y

2X = 3Y

X = 3Y/2

X = 1.5Y

By definition, that means that X is greater than Y. The answer to the question is ALWAYS YES.
Consistent = SUFFICIENT.

Final Answer: C

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