If you multiply me by 2, I become a number greater than 20 and less than 40. If you multiply me by 6,I end in 8. If you multiply me by 4 I end in 2.

13 how did you arrive at answer

To find the answer, we can break down the given information and solve it step by step.

Let's call the unknown number "x." We have the following clues:

1. If you multiply "x" by 2, it becomes a number greater than 20 and less than 40.
This can be written as: 2x > 20 and 2x < 40.

2. If you multiply "x" by 6, the product ends in 8.
This information tells us that the last digit of 6x is 8.

3. If you multiply "x" by 4, the product ends in 2.
This information tells us that the last digit of 4x is 2.

Now, let's solve the clues one by one:

1. For 2x > 20 and 2x < 40:
We divide both sides of the inequality by 2 to isolate "x":
20/2 < x < 40/2
10 < x < 20

This means "x" is greater than 10 and less than 20.

2. For the last digit of 6x being 8:
To find the last digit of a number when multiplied by 6, we need to look at the pattern of the last digit of the multiples of 6: 6, 12, 18, 24, 30, 36, 42, ...
From the pattern, we see that when a number is multiplied by 6, the last digit will be 6, 2, 8, 4, 0, 6, 2, ...
So, for 6x to end in 8, "x" must be 4.

3. For the last digit of 4x being 2:
Similarly, we can apply the same concept. The pattern of the last digit of multiples of 4 is: 4, 8, 2, 6, 0, 4, 8, ...
So, for 4x to end in 2, "x" must be 3.

Therefore, based on the given clues, we have two possible values of "x": 4 and 3.