## Math_Moron 4 years ago How many positive integers less than 100 have a remainder of 3 when divided by 7?

1. abtrehearn

14.

2. satellite73

$3,7+3,2\times 7+3,3\times 7+3,...$

3. satellite73

so abtrehearn is right. since $14\times 7+3=101$ which tells us that there are 13 +1 because of the first one

4. Math_Moron

Are u counting zero? If so why?

5. LA-MrC

I'm thinking 13.

6. satellite73

because 7 goes in to 3 zero times with a remainder of 3

7. Math_Moron

I was thinking what LA-Mrc said but my book says the answer is 14. If 7 doesn't go into 3 wouldn't the remainder be 7 : ?

8. LA-MrC

Here's how I worked it out: 10 is the first positive integer that can be divide by 7 with a remainder of 3. The next is 17, then 24, ... all the way to 94.

9. LA-MrC

10, 17, 24, ..., 94 That should be 13 terms.

10. abtrehearn

The number 3 is also in the list of positive integers less than 100 whose remainder is 3 upon dividing by 7. The list is {3, 10, 17, ... , 94}.

11. LA-MrC

I guess I missed the first one, i.e., 3.

12. LA-MrC

Good job, abtrehearn,

13. Math_Moron

I'm not sure I understand how 3 works also : /

14. abtrehearn

Ten-four, IA-MrC :^)