CAT 1999 | Question: 96

Question

Answer the question based on the following information:
There are $50$ integers $a_1, a_2, \dots , a_{50}$, not all of then necessarily different. Let the greatest integer of these 50 integers be referred as G, and the smallest integer be referred to as L. The integers $a_1$ through $a_{24}$ form sequence S1, and the rest form S2. Each member of S1 is less than or equal to each member of S2.

Elements of S1 are in ascending order, and those of S2 are in descending order. $a_{24}$ and $a_{25}$ are interchanged. Then which of the following statements is true?

• A. S1 continues to be in ascending order.
• B. S2 continues to be in descending order.
• C. S1 continues to be in ascending order and S2 in descending order.
• D. None of the above

Answer 1

sequence 1= {a1,a2 ,,, ......................... , a24} where a1<a2<a3<....................... <a24

sequence2 ={a25,a26,.......................... ,a50} where a25>a26>.....................>a50
 and by given condition that each element of seq1 should be less than equal to seq2 element.

so smallest element of sequence 2 (which is a50) should be greater than equal to largest element of sequence 1(which is a24) 

so,possible sequences :

           SEQ 1                                                        SEQ 2

1,2,3,............................ 24                49, 48,47,....................................., 24 

OR 

1,2,3,.............................24               50,49,48,........................................,25

so if we exchange a24 and a25 seq 1 will be in asceding mode . but seq 2 will not be in descending order .

so option A is correct .