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Tricky!!...

by Ozlemg » Wed Aug 03, 2011 1:13 pm
On January 1 of this year, d% of the members of a tennis club smoked. Since then, however, exactly one third of the smokers managed to stop smoking, while exactly 10% of those who did not smoke on January 1 now do so. Currently, n% of the members smoke, and nobody has joined or left the tennis club this year. Is d=n?

(1) The club has fewer than 300 members
(2) 20<d<25
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by gmatboost » Wed Aug 03, 2011 10:34 pm
This is not a realistic question. Both statements make it fairly obvious that you cannot find an exact value for d.

If you do go through the setup of the question though:
If 1/3 of smokers quit, then 2/3 still smoke.
In addition, 1/10 of non-smokers now smoke.
We want to know if the new percentage is equal to the original one, d.
We can translate the prompt:

IS IT TRUE THAT (2/3)*d + (1/10)*(100-d) = d ?
IS IT TRUE THAT (2/3)*d + 10 - (1/10)*d = d ?
IS IT TRUE THAT (20/30)*d + 10 - (3/30)*d = (30/30)*d ?
IS IT TRUE THAT (17/30)*d + 10 = (30/30)*d ?
IS IT TRUE THAT 10 = (13/30)*d ?
IS IT TRUE THAT (30/13)*10 = d ?
IS IT TRUE THAT 300/13 = d ?

So that's what you would be trying to answer. But the statements don't make it very hard to say that we don't have sufficient info.
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