Find the count of multiples of 2 or 7, for all natural numbers less than equal to 999.

[sabsac]

Find the count of multiples of 2 or 7, for all natural numbers less than equal to 999.

 

[Dr.Peterson]

What have you tried? What techniques have you learned that might be useful?

If nothing else, you might start by directly counting a smaller problem, finding multiples of 2 or 7 (or both) up to 99. That may give you some ideas.

But be sure to follow our guidelines when you respond or ask another question.

 

[sabsac]

I calculated 499 and 142 for 2 and 7 respectively.but the answer provided is 570 which I cannot understand how to arrive at.

 

[pka]

You must apply a basic counting principle.
The number divisible by two plus the number divisible by seven minus the number divisible by fourteen.
Why the minus?

 

[Dr.Peterson]

I calculated 499 and 142 for 2 and 7 respectively.but the answer provided is 570 which I cannot understand how to arrive at.

How many numbers through 999 are divisible by both 2 and 7? They've been counted twice ...

 

[pka]

I calculated 499 and 142 for 2 and 7 respectively.but the answer provided is 570 which I cannot understand how to arrive at.

The provided answer is correct. SEE HERE

 

[Steven G]

I calculated 499 and 142 for 2 and 7 respectively.but the answer provided is 570 which I cannot understand how to arrive at.

What you did is fine, just not complete. The problem is that you do not think that in your list you have some duplicate numbers! As mentioned, just subtract them off.