Question

How many numbers are there between 500 and 600 in which 9 occurs only once?
(A) 19
(B) 18
(C) 10
(D) 9

Answer 1

Hint: Here, write all the numbers between 500 and 600 in which 9 occurs only once. From 500 to 600 we only have three digit numbers and the hundred’s place the same all those numbers, that is 5. We need to filter the numbers, which contain 9 either in the ten's place or in the unit's place.

Complete step by step answer:
Considering the numbers $500$ to $600$, which means the numbers start from $501$ and end at $599$.
Out of these numbers, we need to find the numbers, which contain only one $9$.
Considering the numbers from $501$ to $510$, We only have $509$ which contains only one $9$.
Considering the numbers from $511$ to $520$, We only have $519$ which contains only one $9$.
Considering the numbers from $521$ to $530$, We only have $529$ which contains only one $9$.
Similar pattern repeats till $599$
All numbers between $500$ and $600$ in which 9 occurs only once are:
$509, 519, 529, 539, 549, 559, 569, 579, 589.$
[Here, we will not consider $599$ as contains two $9$’s, not satisfy the given condition]
These are 9 in numbers which are satisfying the given condition.

Therefore, 9 numbers are there between 500 and 600 in which 9 occurs only once. Hence, option (d) is correct.

Note:
In this question, we can easily count the numbers by writing all possible numbers. But you may remember one interesting fact that not only 9, this will be 9 in numbers for all digits between the ranges of $100$. The difference between 500 and 600 is 100, so the number of times each digit i.e.$ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9$ occurs only one time. But the condition is that the range or difference of two given numbers should be 100. This is also possible for 150 to 250, 245 to 345 as range is 100. You can check all by writing the numbers and randomly taking the two numbers between which you want to find. You will get more interesting facts about numbers. Whenever these types of questions are asked, also try to check the same for the other numbers also in some cases not in all cases.