Question

All the five digits number in which each successive digit exceeds its predecessor are arranged in the increasing order of their magnitude the ${97}^{th}$number does not contain the digit.

• A. $4$
• B. $5$
• C. $7$
• D. $8$

Answer 1

The correct option is B $5$

B. $5$

There are $(\frac{8}{4})=70$

numbers of the form 1x and $(\frac{7}{4})=35$

numbers of the form 2x. Since $70<97<70+35$ the first digit is 2.

There are $(\frac{6}{3})=20$

numbers of the form 23x and $(\frac{5}{3})=10$

numbers of the form 24x. Since $70+20<97<70+20+10$ the first two digits are 24.

There are $(\frac{4}{2})=6$

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.