If all the numbers which are divisible by 3 and 6 from 5 to 75 are arranged in ascending order, then which number will be at `7^(th)` place from the bottom?

Options

A. 42
B. 36
C. 30
D. 24

Answer

To solve the problem step by step, we need to find all the numbers between 5 and 75 that are divisible by both 3 and 6, arrange them in ascending order, and then identify the number that is in the 7th position from the bottom.

### Step 1: Identify the range and divisibility
We are looking for numbers between 5 and 75 that are divisible by both 3 and 6. Since any number that is divisible by 6 is also divisible by 3, we can focus on finding multiples of 6.

### Step 2: List the multiples of 6
The multiples of 6 can be calculated by multiplying 6 by integers. We will start from the smallest multiple of 6 that is greater than 5 and go up to the largest multiple of 6 that is less than or equal to 75.

- The smallest multiple of 6 greater than 5 is 6 (6 x 1).
- The largest multiple of 6 less than or equal to 75 is 72 (6 x 12).

Now we can list the multiples of 6 from 6 to 72:
- 6 x 1 = 6
- 6 x 2 = 12
- 6 x 3 = 18
- 6 x 4 = 24
- 6 x 5 = 30
- 6 x 6 = 36
- 6 x 7 = 42
- 6 x 8 = 48
- 6 x 9 = 54
- 6 x 10 = 60
- 6 x 11 = 66
- 6 x 12 = 72

### Step 3: Compile the list of numbers
The numbers that are multiples of 6 between 5 and 75 are:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72

### Step 4: Arrange the numbers in ascending order
The numbers are already in ascending order:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72

### Step 5: Identify the 7th number from the bottom
To find the 7th number from the bottom, we can count from the last number in the list:
- 1st from the bottom: 72
- 2nd from the bottom: 66
- 3rd from the bottom: 60
- 4th from the bottom: 54
- 5th from the bottom: 48
- 6th from the bottom: 42
- 7th from the bottom: 36

Thus, the 7th number from the bottom is **36**.

### Final Answer
The number at the 7th place from the bottom is **36**.