Linear arrangement of Unknown number of persons

Linear arrangement questions with an Unknown number of persons is the latest trend in PO/ AAO examinations. The question can be made complicated by adding the floors, or likes, etc. In these types of questions, a person's arrangement is given according to clues but the trick lies in finding the number of persons sitting in the arrangement. We will take 1 question and dissect that question according to the clues given and see what the setter is trying to test. Let's take a question 

 A certain number of persons are sitting in a straight horizontal line, facing to the north direction. A sits fifth from one of the ends of the line. Four persons sit between A and B. Two persons sit between B and C. One person sits between A and C.D sits sixth to the right of B. Persons sitting to the left of D are more than the persons sitting to his right. Seven persons are sitting between D and R.R sits at one of the ends. Two persons are sitting between F and R.More than three persons are sitting between F and A. How many persons are sitting in all?

They are sitting in the north direction meaning normal right and left as we know. If the question would have been south facing, then it is the same as the circular arrangement question where all the persons are facing the center. The 

The information breakup can be used in the following way.

A sits fifth from one of the ends of the line. & R sits one of the ends of the row

Hence A has to be taken from only 1 side. say left side.

 _ _ _ _ A

4 persons sit between A and B

The possible arrangement is

_ _ _ _ A _ _ _ _ B

Or

B _ _ _ A

1 person sits between A and C

The possible arrangement is

 _ _ _ _ _ A _ C _ _ B

or

B _ _ C _ A

D sits sixth to the right of B. The possible arrangement is

B_  _ C _ A D

  Or

_ _ _ _ A _ C _ _ B _  _ _ _ _ D

Persons sitting to the left of D are more than the persons sitting to his right & Seven persons sitting between D and R.  Hence

  B_ _C _A D    .........   The wrong Choice since there are 6 persons to the left of D and the question is saying that there at least 8 persons to the right of D which violates the condition that Persons sitting to the left of D are more than the persons sitting to his right.

Hence the correct arrangement is

_ _ _ _ A _ C _ _ B _  _ _ _ _ D

Seven persons sitting between D and R.R sits one of the ends of the row. This completes the question which is

 _  _  _  _ A_C_  _ B_ _ _ _ _ D_ _ _ _ _ _ _ R   or 24 persons are sitting in total.

Two persons are sitting between F and R. More than three persons are sitting between F and A.

This data is not needed at all in finding the number of persons. Here you can save time

The skill lies in collecting sets of data so as to work around it faster making the question easier as we progress.

More Tricks in my next article.