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Jonathan would like to visit one of the 12 gyms in his area...

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Jonathan would like to visit one of the 12 gyms in his area...

by BTGmoderatorLU » Tue Jan 28, 2020 3:45 pm
Source: Manhattan Prep

Jonathan would like to visit one of the 12 gyms in his area. If he selects a gym at random, what is the probability the gym will have both a swimming pool and squash court?

1) All but 2 gyms in the area have a squash court.
2) Each of the 9 gyms with a pool has a squash court.

The OA is B
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Source: — Data Sufficiency |
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Re: Jonathan would like to visit one of the 12 gyms in his area...

by deloitte247 » Sat Feb 01, 2020 9:23 pm
Total gym available = 12
If we select a gym at random, what is probability that the gym will have both a swimming pool and squash court?

Statement 1
All but 2 gyms in the area have a squash court
Probability of visiting a gym with both swimming pool and squash court.
$$\frac{No\ of\ \ gyms\ with\ both\ pool\ and\ court}{Total\ no\ of\ gyms}$$
Gyms with squash court = 12-2=10
There is no specific information on gym with swimming pools
So number of gyms with both swimming pool and squash court is unknown hence statement 1 is NOT SUFFICIENT.

Statement 2
Each of the 9 gyms with a pool has a squash court
Probability of visiting a gyms with both pool and squash court
$$\frac{No\ of\ gyms\ with\ both\ pool\ and\ squash\ court}{Total\ no\ of\ gyms}$$

No of gym with swimming pool = 9
Given that every gym that has swimming pool also have squash court the number of gyms with swimming pool and squash court = 9
$$\ The\ probability\ =\frac{9}{12}=\frac{3}{4}$$
$$Statement\ 2\ alone\ is\ SUFFICIENT.

$$ $$answer\ is\ Option\ B$$
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