Question

5 9 Question #12 How many numbers from 1 to 100 will yield a remainder of 2 when divided by both 3 and 5?​

Answer 1

Answer:

I am interpreting it as a count of numbers giving remainder as 1 when divided by 5 as well as 3.

For this, you come up with the LCM of 3 and 5 and add 1 to it. So, the LCM of 3 and 5 is 15 and after adding 1 to itwe get our 1st Number as 16.

Go on having multiples of 15 and just add one to it to generate more Numbers.

Thus all the Numers are:

1*15 + 1 = 16

2*15 + 1 = 31

3*15 + 1 = 46

4*15 + 1 = 61

5*15 + 1 = 76

6*15 + 1 = 91

We can go on like this but since we arelooking for Numbers less than 100, we just have these Numbers. The next Number would be beyond 100.

Thus, you see that there are 6 such Numbers Viz. 16, 31, 46, 61, 76 and 91.

Explanation: