Bunuel wrote:
In a room, there were 10 sibling pairs. A few individuals moved out of the room. Is the number of sibling pairs remaining in the room greater than 4?
(1) The number of individuals who moved out of the room was greater than 5
(2) The number of individuals who moved out of the room was less than 12
Are You Up For the Challenge: 700 Level QuestionsI'd test cases here - I wouldn't necessarily write down the cases I'm testing, but I'd make sure to think through the different scenarios to avoid missing something. Otherwise, it almost seems too simple.
The goal, when testing cases: can I come up with a case where there are more than 4 sibling pairs, and can I also come up with a case where there are 4 or fewer sibling pairs?
Let's write out the sibling pairs like this:
aa bb cc dd ee ff gg hh ii jj
Each letter represents one person.
Statement 1: More than 5 people leave the room. We could end up with more than 4 sibling pairs, if exactly 6 people leave: aa, bb, and cc. In that case, there are 7 sibling pairs remaining, and the answer is "yes."
But if 10 people leave the room - one from each pair - there are 0 sibling pairs remaining, and the answer is "no".
So, statement 1 is insufficient. Eliminate A and D.
Statement 2: Fewer than 12 people leave the room. Both of the cases tested above also fit this statement, and they give us two different answers. So, this one is also insufficient. Eliminate B.
Statements 1 and 2: Again, both cases we already tested will match both statements. So, the statements are also insufficient together. Select (E)!
The lesson here: take advantage of cases you can reuse across statements. It's probably not worth the time and mental energy to specifically think of cases like that from the beginning - after all, for a lot of problems, those cases might not even exist - but if you happen to find them, try to notice them! Don't waste time testing new cases when you already found ones that work just as well.
_________________