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Letters in a seven-letter English word ABSCOND is rearranged in such a way that for any of the letters neither of the neighbours is same as in the previous arrangement. Only S and O remain at their previous positions. B and N are not adjacent to each other in the new arrangement. How many letters are between A and D in the new arrangement?

Letters in a seven-letter English word ABSCOND is rearranged in such a way that for any of the letters neither of the neighbours is same as in the previous arrangement. Only S and O remain at their previous positions. B and N are not adjacent to each other in the new arrangement. How many letters are between A and D in the new arrangement? Correct Answer One

Initial arrangement of letters: ABSCOND

1) Only S and O remain at their previous positions.

[ alt="Sangeeta Single Qs 19 June 2018 5q hindi images Q3" src="//storage.googleapis.com/tb-img/production/18/07/Sangeeta_Single%20Qs_19%20June%202018_5q_hindi_images_Q3.PNG" style="height:30px; width:370px">

2) Since, no letter retained the previous positions and neither of the neighbours of any letter remains same, C has to occupy one of the ends.

3) If C occupies extreme left, then B can be at any of the two right positions at the extreme right → B cannot be in its previous position and cannot be adjacent to A and S.

[ alt="Sangeeta Single Qs 19 June 2018 5q hindi images Q3a" src="//storage.googleapis.com/tb-img/production/18/07/Sangeeta_Single%20Qs_19%20June%202018_5q_hindi_images_Q3a.PNG">

4) N cannot be adjacent to B, O and D. Hence, N would occupy the immediate right position to C.

[ alt="Sangeeta Single Qs 19 June 2018 5q hindi images Q3b" src="//storage.googleapis.com/tb-img/production/18/07/Sangeeta_Single%20Qs_19%20June%202018_5q_hindi_images_Q3b.PNG" style="height:90px; width:438px">

5) A cannot be adjacent to B. Hence, in both the cases only one position is left for A to occupy.

[ alt="Sangeeta Single Qs 19 June 2018 5q hindi images Q3c" src="//storage.googleapis.com/tb-img/production/18/07/Sangeeta_Single%20Qs_19%20June%202018_5q_hindi_images_Q3c.PNG" style="height:93px; width:443px">

6) Case 1 is rejected as D cannot be in its previous position in the new arrangement.

7) Now when C is at the extreme right, B would occupy either the leftmost position or immediately left to C. Because B cannot be adjacent to S.

[ alt="Sangeeta Single Qs 19 June 2018 5q hindi images Q3d" src="//storage.googleapis.com/tb-img/production/18/07/Sangeeta_Single%20Qs_19%20June%202018_5q_hindi_images_Q3d.PNG" style="height:93px; width:440px">

8) N cannot be adjacent to O, B and D → Case 4 is rejected.

[ alt="Sangeeta Single Qs 19 June 2018 5q hindi images Q3e" src="//storage.googleapis.com/tb-img/production/18/07/Sangeeta_Single%20Qs_19%20June%202018_5q_hindi_images_Q3e.PNG">

9) D cannot be adjacent to N.

[ alt="Sangeeta Single Qs 19 June 2018 5q hindi images Q3f" src="//storage.googleapis.com/tb-img/production/18/07/Sangeeta_Single%20Qs_19%20June%202018_5q_hindi_images_Q3f.PNG" style="height:94px; width:439px">

10) A cannot occupy first position → Case 3.1 is rejected.

[ alt="Sangeeta Single Qs 19 June 2018 5q hindi images Q3g" src="//storage.googleapis.com/tb-img/production/18/07/Sangeeta_Single%20Qs_19%20June%202018_5q_hindi_images_Q3g.PNG" style="height:50px; width:425px">

11) Hence, two cases are:

[ alt="Sangeeta Single Qs 19 June 2018 5q hindi images Q3h" src="//storage.googleapis.com/tb-img/production/18/07/Sangeeta_Single%20Qs_19%20June%202018_5q_hindi_images_Q3h.PNG">

Clearly, in either case there is only one letter between A and D.

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