Between 1 and 50 excluding both these how many numbers are there which will leave a remainder 1 when divided by 4

Question



Answer 1

So what you are looking for is the range of whole numbers (Y) that satisfies the following equation : (1 < Y < 50) where (Y=4x+1) where x is a whole number... this way when you divide by 4, you have a remainder of 1.

2 ways of solving for this :

1) Count!

Multiples of 4 are : 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48

Thus, the following will have a remainder of 1 : 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49

There are 12 numbers!

2) set 4x+1 = 50 and then round down!

4x + 1 = 50

4x = 50 - 1 = 49

divide by 4

x = 12.25

Round down ... 12

This 2nd method works because you are using all numbers from '1'. If you were to say between 10 and 50, you'd have to use a different method.

Hope this helps you.

Answer 2

To get remainder of 1 when divided by 4 the only numbers that will make that possible is: (4x + 1) / 4

You could simply list out the numbers by adding 4+1 until you reach 49.

The answer is 12 numbers.

All the possible numbers are listed below:

1. 5 / 4
2. 9 / 4
3. 13 / 4
4. 17 / 4
5. 21 / 4
6. 25 / 4
7. 29 / 4
8. 33 / 4
9. 37 / 4
10. 41 / 4
11. 45 / 4
12. 49 / 4