Question

All the five digit numbers in which each successive digit exceeds its predecessor are arranged

Answer 1

Question : All the five digit numbers in which each successive digit exceeds its predecessor are arranged in the increasing order of their magnitude.The 97th number in the list does not contain the digit

(A)4(B)5(C)7(D)8

Answer:

Selecting an admissible number means selecting a five element subset of {1,2,3,4,5,6,7,8,9}.

There are (8 /4)=70 numbers of the form 1x and (7 /4)=35 numbers of the form 2x. Since 70<97<70+35 the first digit is 2.

There are (6 /3)=20 numbers of the form 23x and (5/3)=10 numbers of the form 24x. Since 70+20<97<70+20+10 the first two digits are 24.

There are (42)=6 numbers of the form 245x. Since 70+20+6=96 the number we are after is the first number of the form 246x, which is 24678. It follows that (B) is true.