Question

If each digit in an integer is greater than the digit to the left, the integer is said to be monotonic. For example, $12$ is a monotonic integer since $2>1$. Calculate the number of positive two-digit monotonic integers.

• A. $28$
• B. $32$
• C. $36$
• D. $400$
• E. $44$

Answer 1

Answer: (C)

$36$

As given, if each digit in an integer is greater than the digit to the left, the integer is said to be monotonic.From $10-20$ eight monotonic integers are there i.e$:12,13,14,15,16,17,18,19.$
Similarly From $20-30$ seven monotonic integers are there i.e:$23,24,25,26,27,28,29.$
As you see the pattern the $30-40$ will have $6$ monotonic integers$,40-50$ will have $5$ monotonic integers $,50-60$ will have $4$ monotonic integers,$60-70$ will have $3$ monotonic integers$,70-80$ will have $2$ monotonic integers, $80-90$ will have$1$ monotonic integers and $90-99$ will have $0$ monotonic integers.
so,The total two digits monotonic integers are $8+7+6+5+4+3+2+1+0=36$.
Hence, option C is correct.