Data Sufficiency

Q.1)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.

First of all where were you man or Manpreet Ji. I always find your questions of high quality.

We need to find P(rain or roar). And March has 31 days.

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

I can safely assume that this statement is not sufficient as it does not give me any data and secondly it only provides me that P(rain and roar) = 0.

Not Sufficient!!!

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

Lets say it rained on x days, so the lion roared on (x - 10) days.

P(rain or roar) = x/31 + (x- 10)/31 - P(rain and roar), since we don't know x. Not Sufficient!!!

Together we have, P(rain and roar) = 0 , but still no value of x. Hence Not Sufficient!!!

Answer E.

In addition to the solutions posted above, I'd just like to mention an oversight on my part when I tried solving this.

My answer was (C), which is obviously wrong but here's how I wrongly deduced it was (C).

Statement 1: Last March, the lion never roared on a rainy day.
It only tells us P(roar and rain)=0. INSUFFICIENT.

Statement 2: Last March, the lion roared on 10 fewer days than it rained.
But you still don't know if the lion roared on any rainy day.
INSUFFICIENT.

Now, when you combine the two:
(Here's where I goofed up)
From 1, you know that P(roar and rain)=0. So the lion didn't roar on a rainy day.

Now, there are 31 days in March
Using 2,
Let "x" be the # days it rained
Then x-10 is the # days the lion roared

Thus, x+(x-10)=31 --(I knew something was wrong at this point coz I wasn't getting a whole number, so i rounded off 31 to 30!!!!)

Thus, no. of rainy days=20 and no. of days lion roared=10.
So, since we got the value of "x" answer = (C).

The OVERSIGHT: There could have been days when it neither rained nor the lion roared !!!

In that case the x+(x-10)=31(or 30) fails.
And you could have cases like: 13 rainy days 3 roar days OR 29 rainy days and 19 roar days, etc., etc.

Moreover, had I actually calculated the probability, I would've got the following answer:

P(roar or rain)= P(roar)+P(rain)-P(roar and rain)
= 10/30 + 20/30 - 0
= 1 !!!!!!
Which makes sense coz according to my assumption, on any given day, the lion is either roaring or it's raining.

It's amazing just how much making mistakes can teach you so much

Is there anyone else who went down this path???

Anyway, thanks to Puneet and Brent for their wonderful explanations

Cheers,
Taz

P.S.: Please take a moment to hit the "Thank" button if this post helped.

Here are other explanations for further understanding:

https://www.beatthegmat.com/roar-and-rain-t55146.html

https://www.beatthegmat.com/probability-t56096.html

Cheers,
Taz

Thanks Punneet for missing me and liking my question feels great to know people appreciate the question i put here.I was little busy with personel mess, now i am looking to concentrate back on the exam and wrap it up in jan or feb 2013.Been delaying it for long now.

I yes you are right with answers .

Thanks brent too for his explanation ,simple and easy as always and Hope Taz you got your doubt cleared thanks for giving an insight into your error.

Manpreet
-----------------------------------------------------------
There is only one success--to be able to spend your life in your own way.