SOLUTION: Here Are Two Problems I Am Having Trouble With: 1. How many integers greater than 5 but less than 40 are divisible by 2, 3, or both? 2. How many integers from 42 to 92, inc

Question 984660: Here Are Two Problems I Am Having Trouble With:
1. How many integers greater than 5 but less than 40 are divisible by 2, 3, or both?
2. How many integers from 42 to 92, inclusive, have a remainder of 4 when divided by 6?
Thanks, please show me your work!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Greater than 5 but less than 40 is in the inclusive range 6 to 39, a total of 39 minus 6 plus 1 = 34 numbers. Half of these, 17, are divisible by 2. One-third of these, (11 and a fraction so round up) 12, are divisible by 3. And one-sixth of these, (5 and a fraction so round up) 6, are divisible by 6. But if a number is divisible by 6 it is also divisible by both 2 and 3, so subtract 6 of the 17 that are divisible by 2, and 6 of the 12 that are divisible by 3.

Altogether 11 + 6 + 6 = 23

John

My calculator said it, I believe it, that settles it

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