Question

If the numbers between 1 to 65 which will be divisible by 4 are taken and then if the number present in the units place and tens place is swapped, post which they are written in ascending order, then which of the following number will be at 10th place from the last?

• A. 40
• B. 24
• C. 44
• D. 25

Hint:

Swap the units and tens digit of each multiple of 4, then sort ascending.

Answer 1

The Correct Option is A

Step 1: List all multiples of 4 from 1 to 65.
These are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, a total of 16 numbers. Single digit multiples like 4 and 8 are treated as 04 and 08 so they also have a tens digit to swap.

Step 2: Swap the units and tens digit of each number.
04 becomes 40, 08 becomes 80, 12 becomes 21, 16 becomes 61, 20 becomes 02, 24 becomes 42, 28 becomes 82, 32 becomes 23, 36 becomes 63, 40 becomes 04, 44 stays 44, 48 becomes 84, 52 becomes 25, 56 becomes 65, 60 becomes 06, 64 becomes 46.

Step 3: Arrange these 16 swapped numbers in ascending order.
2, 4, 6, 21, 23, 25, 40, 42, 44, 46, 61, 63, 65, 80, 82, 84.

Step 4: Count 10 places in from the last number.
With 16 numbers total, the 10th from the last is the same as the \((16-10+1) = 7\)th number from the start. Counting from the front: 2 (1st), 4 (2nd), 6 (3rd), 21 (4th), 23 (5th), 25 (6th), 40 (7th).

Final Answer:
The 7th number from the start, which is also the 10th from the last, is 40.
\[ \boxed{40} \]