Question

Numbers greater than 7000 and divisible by 5 which can be found using digits 3, 5, 7, 8 and 9. (No digit being repeated) is:
\[\begin{align}
  & A.46 \\
 & B.48 \\
 & C.72 \\
 & D.42 \\
\end{align}\]

Answer 1

Hint: In this question, we need to find the numbers greater than 7000 and divisible by 5 which can be formed using 3, 5, 7, 8, 9. For this, we will find four digit numbers and five digit numbers using given digits and divisible by 5 greater than 7000. We will draw places and find the number of digits possible for any place.

Complete step by step answer:
Here, we are given the digits as 3, 5, 7, 8 and 9. We need to form numbers using these digits which are divisible by 5 and greater than 7000.
As we know, numbers which are divisible by 5 have 0 or 5 in its one’s place , so we will have only 5 for one’s place in the numbers.
We can have four digit numbers and five digit numbers which are required.
For four digit number, \[\dfrac{{}}{\text{Thousands}}\dfrac{{}}{\text{Hundreds}}\dfrac{{}}{\text{Tens}}\dfrac{5}{\text{Ones}}\].
We know that 5 will always be in one's place. So, the number of digits that can be placed in one’s place is 1. As we want a number greater than 7000 so the number at thousand’s place would be 7, 8 or 9.
So the number of digits that can be placed in a thousand places is 3.
So two out of five digits are already used. Hence, the number of digits left for hundred’s place is 3.
And at last number of digits left for tens place is 2
Hence our possibilities become $3\times 3\times 2\times 1=18$.
So possible four digit numbers are 18.
For five digit numbers.
All five digit numbers will be greater than 7000 so let us find five digit numbers using 3, 5, 7, 8 and 9 with 5 at one’s place.
\[\dfrac{{}}{\text{Ten Thousands}}\dfrac{{}}{\text{Thousands}}\dfrac{{}}{\text{Hundreds}}\dfrac{{}}{\text{Tens}}\dfrac{5}{\text{Ones}}\].
Number of digits that can be placed at one’s place is 1. Left digits are 4. So, the number of digits that can be placed at ten thousands places is 4. Number of digits that can be placed at thousands places remains as 3. Number of digits that can be placed at hundreds places remains as 2. Similarly, the number of digits that can be placed at tens place remains as 1. Hence our possibilities becomes $1\times 1\times 2\times 3\times 4=24$.
So possible five digit numbers are 24.
Therefore, total numbers are $18+24=42$.

So, the correct answer is “Option D”.

Note: Students often make mistakes of forgetting one or two possibilities. Make sure that, 5 is always at one’s place for the number to be divisible by 5. Try to draw small diagrams for better understanding.