Roar and Rain

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newton9: Senior | Next Rank: 100 Posts; Posts: 71; Joined: Wed Mar 17, 2010 1:31 pmFollowed by: 1 member; Thanked: 5 times

by newton9 » Fri Mar 26, 2010 9:05 am

In a town of Z, the town lion roars on some days and not on others. If a day is chosen at random from last March, what is the probability that on that day, either the town lion roared or it rained?

1) Last March, the lion never roared on a rainy day.

2) Last March, the lion roared on 10 fewer days than it rained.

Source : MGMAT Word Translation SG.

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Source: Beat The GMAT — Data Sufficiency | Fri Mar 26, 2010 9:05 am

neoreaves: Master | Next Rank: 500 Posts; Posts: 208; Joined: Sun Sep 28, 2008 12:30 pm; Thanked: 22 times

by neoreaves » Fri Mar 26, 2010 11:52 am

P(R) = prob of Roar
P(r) = prob of rain

What we need to know is P(r) U P(R)

1) we know that P(r) intersection P(R) = 0 --> They are mutually exclusive. However, what we want to know is prob of either it rained or the lion roared. So Insufficient.

2) R = r -10 ...doesnt give us enough information to calculate probabilities so Insufficient

C) together still insuff

IMO E

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el_torero: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Mon Nov 17, 2008 9:07 pm; Thanked: 3 times

by el_torero » Fri Mar 26, 2010 1:46 pm

i agree with neoreaves.

just to clear up, we want to find:

P(roar or rain) = P(roar) + P(rain) - P(roar AND rain)

(1) makes P(roar AND rain) = 0, but we still need to find P(roar) + P(rain)

(2) gives us a relationship between roars and rain, but we still need to find at least one of those unknowns to find the other.

==> E

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mboeker11: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Mon Oct 10, 2011 11:37 am

by mboeker11 » Wed Oct 12, 2011 2:51 pm

I am confused why the correct answer is not C. If we know there are 30 days in March, from A the lion never roared on a rainy day, and B the lion roared on 10 fewer days than it rained, then wouldnt the only possibility be roared 10/30 and rained 20/30?

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cbaum: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Wed Jul 06, 2011 8:24 am

by cbaum » Thu Oct 13, 2011 8:39 am

I am confused why the correct answer is not C. If we know there are 30 days in March, from A the lion never roared on a rainy day, and B the lion roared on 10 fewer days than it rained, then wouldnt the only possibility be roared 10/30 and rained 20/30?

There are 31 days in March, but the split could be 10-20, 9-19, 8-18, etc. The '10 fewer' in statement (2) is the tricky part... it's not saying that then lion roared on 10 days, it's saying that the difference between the number of days the lion roared and the number of days it rained is 10. Since the statements don't give us any information about how many days neither of the two happened, we can't determine the probability.

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