In the town of Z, the town lion roars on some days and not

[Gmat_mission]

In the 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.

[spoiler]OA=E[/spoiler]

Source: Manhattan GMAT

[Brent@GMATPrepNow]

In the 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.

Target question: What is the probability that on that day, either the town lion roared or it rained?
This is a good candidate for rephrasing the target question.

This is an OR probability. The OR probability rule says, P(A or B) = P(A) + P(B) - P(A and B)
So, P(rained or roared) = P(rained) + P(roared) - P(rained and roared). So . . .

REPHRASED target question: What is the value of P(rained) + P(roared) - P(rained and roared)?

Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Statement 1: Last March, the lion never roared on a rainy day.
In other words, P(rained and roared) = 0
Since we still don't know the values of P(rained) and P(roared), we cannot evaluate P(rained) + P(roared) - P(rained and roared)
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Last March, the lion roared on 10 fewer days than it rained.
Let x = # of days the lion roared
So, x+10 = # of days it rained
This means P(roared) = x/31 and P(rained) = (x+10)/31
Since we still don't know the actual values of P(rained) and P(roared), and we don't know the value of P(roared and rained) we cannot evaluate P(rained) + P(roared) - P(rained and roared)
Since cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
From statement 1 we know that P(rained and roared) = 0
From statement 2 we know that P(roared) = x/31 and P(rained) = (x+10)/31
Put them together and we get: P(rained or roared) = (x+10)/31 + x/31 - 0
Since we still cannot answer the REPHRASED target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent