how many odd number are there from 25 to 75 which are divisible by 3 AND 5?
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How many odd numbers are there from 25 to 75 which are divisible by 3 and 5?
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Matthew Dray
Answered 2 years ago
To start, a number that is divisible by 3 and 5 means it's divisible by 15.
This becomes important in a second. The first thing we need to do is determine how many numbers there are between 25 and 75 which can be done by doing 75–25 + 1 to include the 25. That leaves us with 51 total numbers.
Now, knowing the fact that a number that has a factor of both 3 and 5 has a factor of 15 means that 1/15 numbers are going to be divisible by 15.
Applying this here, it means that 1/15 of the numbers are going to be divisible by 15 so 51/15 is 3.4 and flooring that gives us 3 numbers.
But there's a problem: we can count these numbers here: 30, 45, 60, 75
That's 4 numbers…which was bigger than what we initially calculated.
How do we correct for that?
Instead, let's try a different approach.
Since we know that 15 is a factor of the different numbers, using the quotient remainder theorem, it means we have number = 15n + 0 where n is a positive integer.
Looking at the range we were given: 25–75 we can actually factor out the 15 and only focus on that quotient. And we can just count the total numbers in that reduced range. There's one last catch and then we can calculate the answer: the quotient is required to be an integer.
We can get that integer with 75 giving us 75 = 15 * 5, but not with 25. We can adjust by shifting the number range to the first one divisible by 15, in this case, 30. The same thing would need to be done on the end of the range if the last number was not divisible by 15 as well. So if the range were 25–76 we would need to move the range to 30–75
Finally we can calculate the total number that are divisible by factoring out the 15 from the numbers at the end of the range, giving us a new range of 2–5 and we can just take how many total numbers are in this range: 5–2 + 1 = 4 numbers, which we know is the correct number
Answer:
anwer is what that is divisible by 3 and 5