How many integers between 100 and 170, inclusive, cannot be evenly divided by 3 nor 5?
How many integers between 100 and 170, inclusive, cannot be evenly divided by 3 nor 5?
Answer/Solution
38
Steps/Work
The total numbers between 100 and 170, inclusive, is 71.
3*34=102 and 3*56=168 so the number of multiples of 3 is 23.
5*20=100 and 5*34=170 so the number of multiples of 5 is 15.
However, the multiples of 15 have been counted twice.
15*7=105 and 15*11=165 so the number of multiples of 15 is 5.
Thus the total number is 71-23-15+5=38.
The answer is B.
3*34=102 and 3*56=168 so the number of multiples of 3 is 23.
5*20=100 and 5*34=170 so the number of multiples of 5 is 15.
However, the multiples of 15 have been counted twice.
15*7=105 and 15*11=165 so the number of multiples of 15 is 5.
Thus the total number is 71-23-15+5=38.
The answer is B.