shashank.ism wrote:There are exactly three pairs of siblings among ten children namely Sam, Joe, Tim, Ron, Ken, May, Bob, Ian, Den and Emy such that no child is common in these pairs. Mr. Vaughan randomly selects four children and in each selection there is exactly one pair of siblings and the other two children do not have any sibling. Some of the selections done by him are listed in the table given below.

I Sam Tim Den May
II Ken Ron Joe Bob
Selections III Tim Ian Bob Emy
IV May Bob Den Sam

Which of the following can never be a selection done by Mr. Vaughan?


Den, Ken, Sam and May
Ian, Emy, May and Ron
Tim, Ken, Joe and Ron
Ron, Sam, Joe and May
Sam, Den, Ken and Bob

OA is D

If we compare Selection I and Selection III, we can conclude
that Tim is definitely not the child that has a sibling amongst the
given ten children.
Following the same logic if we compare Selection II and
Selection IV, we can conclude that Bob is definitely not the
child that has a sibling amongst the given ten children.
Now, in selection III we can conclude that Ian and Emy are
siblings.
The other two pairs of siblings could be (Sam and Den); (Den
and May); (Sam and May); (Ken and Ron); (Ken and Joe) and
(Joe and Ron).
Option (1): Possible if the other two pairs of siblings are
(Sam and May) and (Joe and Ron)
Option (2): Possible if the other two pairs of siblings are
(Sam and Den) and (Ken and Joe)
Option (3): Possible as along with Tim one out of the remaining
three children does not have any sibling.
Option (5): Possible if the other two pairs of siblings are
(Sam and Den) and (Joe and Ron).
Option (4): Is not possible because if Ron and Joe are siblings,
then both Sam and May do not have any sibling which is not
possible, same way if Sam and May are siblings, then both
Ron and Joe do not have any sibling, which is not possible.
Hence, option (4) is the correct choice.