How many are divisible by these numbers? [URGENT]

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nnugochi

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I need a confirmation and explanation on how this question is solved because me and my friends had different answers

Q: In a set of integers between the numbers 100 and 100,000, how many of these numbers are divisible by 2, 5, 9 and 13?

I'm confident with my answer, which is 67112. (Maybe it's a little off but it's the best I can do)
 
Cubist said:
Is the word that I've highlighted below correct?


Your answer seems to imply that the above word might be an "or" (and even so I think your answer is slightly wrong, but before discussing that let's be sure about the actual question :))
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Yes, the word you highlighted is correct ??
 
nnugochi said:
Yes, the word you highlighted is correct ??
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Then the answer should be far smaller. Please show us your reasoning.

You may be misinterpreting the word "and". Let me illustrate:

How many numbers 1 through 10 are divisible by 2 and 3? The answer is 1; the only such number is 6.

How many numbers 1 through 10 are divisible by 2 or 3? The answer is 7; the numbers are 2, 3, 4, 6, 8, 9, and 10.
 
Dr.Peterson said:
Then the answer should be far smaller. Please show us your reasoning.

You may be misinterpreting the word "and". Let me illustrate:

How many numbers 1 through 10 are divisible by 2 and 3? The answer is 1; the only such number is 6.

How many numbers 1 through 10 are divisible by 2 or 3? The answer is 7; the numbers are 2, 3, 4, 6, 8, 9, and 10.
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Ah i see. Since you pointed out the ‘and’ part, i redo my work and got the answer 85.

The number of integers from 100-100,000(included) is 99901

since we’re interested in the integers divisible by 2,5,9 and 13. Thus, 2x5x9x13 = 1170

so the number of integers through 100-100,000 that are divisible by 2,5,9 and 13 is:

99901/1170 = 85

Is this alright? ?
 
nnugochi said:
Ah i see. Since you pointed out the ‘and’ part, i redo my work and got the answer 85.

The number of integers from 100-100,000(included) is 99901

since we’re interested in the integers divisible by 2,5,9 and 13. Thus, 2x5x9x13 = 1170

so the number of integers through 100-100,000 that are divisible by 2,5,9 and 13 is:

99901/1170 = 85

Is this alright? ?
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Yes, though I simply divided 100000 by 1170 = 85.47 and rounded down to get 85, locating the greatest multiple in the range, then observed that there are no multiples less than 100. Your approach, not taking the actual numbers into account, could have been off by 1.

I should also point out that the problem said "between", which I would take as exclusive. That, too, has no effect in this case.
 
Maybe the OP is not American.
This comment is about Americans. Why do so many Americans confuse the words and and or especially since these are words that are used daily?
 
Jomo said:
Maybe the OP is not American.
This comment is about Americans. Why do so many Americans confuse the words and and or especially since these are words that are used daily?
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It's actually not at all surprising that many people (probably in any language and culture) make this sort of confusion, because in everyday language we use each word in various informal ways that we distinguish by context. Math is a different form of language that is more precise, and therefore somewhat foreign.

In particular, this arises in cases where we are talking (explicitly or not) about unions or intersections. The set of all numbers that are A or B is the union, which is informally thought of as A combined with B, that is "A and B together". Here, a number that is divisible by 2 and 5 is in the intersection of the set of numbers divisible by 2 and the set of numbers divisible by 5, but it is easy to confuse that with counting numbers divisible by 2 together with those divisible by 5, which would be the union.
 
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