"Between" on math questions (inclusive or exclusive?)

[velua]

So for example, I just grabbed this from the Powerprep software: The number of integers between 100 and 500 that are multiples of 11. Are 100 and 500 supposed to be included, or is it strictly between?

 

In this problem, it really doesn't matter since 11 divides neither 100 nor 500. But suppose we wanted to know the number of integers between 14 and 35 divisible by 7. Is the answer 2 ({21, 28}) or 4 ({14, 21, 28, 35})?

 

Edit: This is a question for the General GRE test.

Edited March 9, 2015 by velua

[MathCat]

I had the same annoyance with the general GRE - I think it is inclusive, but I also believe they will give questions where it doesn't make a difference.

[MathCat]

If the problem is as you've worded it then I don't think it matters. Read it over "the number of integers between 100 and 500" , therefore you're neither counting 100 nor 500. Instead you're counting 400 integers in between the two integers 100 and 500. So you're starting at 1,2,3,....400. Since 500-100 = 400. Now from 1 to 400 which integers are multiples of 11? 

Disclaimer, this could be completely wrong, but it's my interpretation of it. 

That's not what the question means. It's asking how many ("the number of") integers in the set {100, 101, 102, 103, ..., 499, 500} (assuming inclusive) are divisible by 11. Remember that this is multiple choice, so it's probably "The number of integers between 100 and 500 that are multiples of 11 is... <5 options>."

Edited March 9, 2015 by MathCat

[TenaciousBushLeaper]

That's not what the question means. It's asking how many integers in the set {100, 101, 102, 103, ..., 499, 500} (assuming inclusive) are divisible by 11.

Is the actual wording then "The number of the integers" as opposed to "The number of inetgers" ?? 

[velua]

If you're not counting 100 or 500, you're counting 399 integers, not 400. Suggesting that translating the problem to an equal-measure domain doesn't change anything is just wrong. For example, the number of integers divisible by 11 between 1 and 100 is different from the number between 11 and 110 (whether you include the endpoints or not).

 

I haven't seen any practice questions yet where inclusive/exclusive changes the answer, but applying for CS programs (especially as a Math major), I don't want to be the victim of a misinterpretation and get a 168 or something instead of a 170.

 

That's not what the question means. It's asking how many ("the number of") integers in the set {100, 101, 102, 103, ..., 499, 500} (assuming inclusive) are divisible by 11. Remember that this is multiple choice, so it's probably "The number of integers between 100 and 500 that are multiples of 11 is... <5 options>."

 

Actually it was one of those comparison questions, comparing to 36. 4 choices: < 36, > 36, = 36, not enough info. Doesn't change it much though.

Edited March 9, 2015 by velua

[MathCat]

I haven't seen any practice questions yet where inclusive/exclusive changes the answer, but applying for CS programs (especially as a Math major), I don't want to be the victim of a misinterpretation and get a 168 or something instead of a 170.

I understand this concern, as I was worried about it too. If it's reassuring for you, I got a 170Q despite getting two questions wrong (you can see how many you got right and what type of question they are with their general GRE diagnostic service).

 

Also, I don't think 168 vs. 170 would be the deciding factor for admission. I don't think I'd want to go to a program where it was.

Edited March 9, 2015 by MathCat

[velua]

Grad school admissions are hard to predict, and I don't think I'd find out if I got in because of some detail on my SOP or because of 2 extra points on the GRE. Either way, getting a 170 is something I can do to maximize my chances.

[velua]

Well I didn't see anything to answer the original question about the general rule in my GRE book, but I found the following online:

 

http://www.newgre.org/preparation/gre-math-tips-tricks/(Problem #2 is a "between" question). In their solution, they are using strict inequalities, so I guess this means the answer should be exclusive if it happens to affect the answer. Assuming this website is a legitimate resource, that is.

[Hani2015]

between  = exclusive. ( unless stated in the question is inclusive )

 

the answer to your example is ({21, 28})

Edited March 10, 2015 by Hani2015

[gr22]

http://www.ets.org/s/gre/pdf/gre_math_conventions.pdf   p.6

http://www.ets.org/s/gre/pdf/gre_math_review.pdf    p.7

 

 

Based on these, it sounds like "from" is considered inclusive and "between" is considered exclusive