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

Question

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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chetan2u · Answer

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..

E

ccooley · Answer

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.

MathRevolution · Answer

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.

Crytiocanalyst · Answer

Rather than a theoretical approach we need to get it through a logical approach that being

(1) The number of individuals who moved out of the room was greater than 5
6 let assume , then if one among each sibiling went out of the room 
the remaning sibiling pair would be just 4 so the answer being no 
if those were exactly sibiling pair then yes since there will be 7 sibiling pair

Clearly insufficient

(2) The number of individuals who moved out of the room was less than 12
it can be again 6 
Therefore we can arrive at the same conclusion stated above

Even when 1 and 2 is combined 
still number 6 can be included and the requisite argument can be revived to show it sufficient

Hence IMO E

MarkGMATMentor · Answer

This is a great example of a DS question on which a structured approach can result in a very efficient solving process, saving you time for other questions on the DI section.
 
Before testing the statements, let's  be clear on the prompt . With 10 sibling pairs, the room originally had 20 people. When people move out of the room, they can either move out as sibling pairs or as unrelated individuals (or a mixture of both). If they move out as sibling pairs, this will help preserve the sibling pairs remaining, and if they move out as unrelated individuals, this will quickly diminish the sibling pairs remaining.

Now let's test the statements, using  extremes  to try possibilities.

Statement 1:

If the number who left is greater than 5, there is no upper limit, so there could be no one remaining. So a NO is possible.

But if only 6 individuals left, and they were all sibling pairs, you have 7 sibling pairs remaining. So a YES is possible.  Insufficient.

Statement 2:

If the number who left is less than 12, there is no lower limit, so (nearly) everyone could be remaining. So a YES is possible.

But if 11 individuals left, and they came from 10 different sibling pairs, there are no pairs remaining. So a NO is possible.  Insufficient.

Together:

The number who leave must be between 5 and 12. As we saw in Statement 1, if only 6 individuals left, and they were all sibling pairs, you have 7 sibling pairs remaining. So a YES is possible.

As we saw in Statement 2, if 11 individuals left, and they came from 10 different sibling pairs, there are no pairs remaining. So a NO is possible.  Insufficient.   The answer is E.

By being clear on the prompt and testing extremes with the statements, you can solve this question (rated as hard) quickly and accurately. This is critical for the Data Insights section, which tends to be the most time-pressured section.

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

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GMAT Data Sufficiency (DS) Questions

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

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615 to 715 in 15 Days (Ria's Strategies)

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