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In a room, there were 10 sibling pairs. A few individuals moved out of

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In a room, there were 10 sibling pairs. A few individuals moved out of  [#permalink]

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New post 11 Nov 2019, 04:51
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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


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Re: In a room, there were 10 sibling pairs. A few individuals moved out of  [#permalink]

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New post 11 Nov 2019, 09:20
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


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There is NOTHING much in each statement, so we can take both combined..
So the number was anything from 6 to 11...
If all 6 were actually 3 pair of siblings, 7 pair of siblings were left.
But say 7 left and all 7 were from different pair, so only 3 sibling pair left..


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Re: In a room, there were 10 sibling pairs. A few individuals moved out of  [#permalink]

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New post 11 Nov 2019, 13:54
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


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I'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.
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Re: In a room, there were 10 sibling pairs. A few individuals moved out of  [#permalink]

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New post 12 Nov 2019, 09:08
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


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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have 20 people, we can assume we have 12 variables and 0 equations, E is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

Case 1:
5 pairs of siblings moved out.
Then the number of sibling pairs remaining in the room is 5, which is greater than 4.
The answer is 'yes'.

Case 2:
Only one of each sibling pair moved out first and the one in the first sibling pair moved out.
The the number of sibling pairs remaining in the room is 0, which is less than 4.
The answer is 'no'.

Since both conditions together do not yield a unique solution, they are not sufficient.

Therefore, E is the answer.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
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Re: In a room, there were 10 sibling pairs. A few individuals moved out of   [#permalink] 12 Nov 2019, 09:08
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