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

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.
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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.

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

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