Question

How many positive integers less than 100 leave a remainder of 1 when divided by 15?​

Answer 1

Step-by-step explanation:

The number of positive integers divisible by 7 but not by 11 is 142 - 12 = 130. ==>the number of positive integers less than 1000 that are divisible by either 7 or 11 is 142 + 90 - 12 = 220. ==>the number of positive integers less than 1000 that are divisible by exactly by one of 7 and 11 is 220 - 12 = 208.

Answer 2

Answer: 6

Step-by-step explanation:

The numbers we are looking for have the formula 15n+1 < 100, where n is a positive integer.

Putting n=1,

15×1+1=16

Putting n=2,

15×2+1=31

Putting n=3,

15×3+1=46

Putting n=4,

15×4+1=61

Putting n=5,

15×5+1=76

Putting n=6,

15×6+1=91

Putting n=7,

15×2+1=106

But 106 > 100, so it's not possible.

Therefore, there are 6 possible numbers.