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# How many integers n are there such that r < n < s?

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How many integers n are there such that r < n < s? [#permalink]

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29 Sep 2010, 07:05
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Difficulty:

65% (hard)

Question Stats:

51% (00:58) correct 49% (01:01) wrong based on 442 sessions

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Sorry for posting this, it may sound silly to someone, but I have problem understanding the question:

How many integers n are there such that r < n < s?
(1) s - r = 5
(2) r and s are not integers.

My solution: For (1), whether r and s are integer or not, there can be so many "groups" of 4 or 5 n that fit the conditions.
[Reveal] Spoiler:
So (1) not enough
and (2) not enough, apparently
(1) and (2) not enough, according to my "reasoning" above.

So I chose E
[Reveal] Spoiler: OA

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29 Sep 2010, 07:18
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ezinis wrote:
Sorry for posting this, it may sound silly to someone, but I have problem understanding the question:

How many integers n are there such that r < n < s?
(1) s - r = 5
(2) r and s are not integers.

My solution: For (1), whether r and s are integer or not, there can be so many "groups" of 4 or 5 n that fit the conditions.

So (1) not enough
and (2) not enough, apparently
(1) and (2) not enough, according to my "reasoning" above.

So I chose E

The question is: how many integers $$n$$ satisfy $$r < n < s$$, or how many integers are between $$r$$ and $$s$$, not inclusive?

Note that if $$r$$ and $$s$$ are integers, for example $$s=5$$ and $$r=0$$ then there will be 4 integers between them: 1, 2, 3, and 4. But if $$r$$ and $$s$$ are NOT integers for example $$s=5.5$$ and $$r=0.5$$ then there will be 5, so one more, integers between them: 1, 2, 3, 4 and 5.

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29 Sep 2010, 09:42
The "number" of n can be multiple of 4 or 5, says 8 or 10, 12, 15, ... can not be determined...

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29 Sep 2010, 09:56
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ezinis wrote:
The "number" of n can be multiple of 4 or 5, says 8 or 10, 12, 15, ... can not be determined...

It seems that you misinterpreted the question.

Question ask about the number of integers between r and s, not inclusive.

For example: how many integers are between 10 and 15, not inclusive? Answer: 4, namely 11, 12, 13, and 14.
Or: how many integers are between 5.3 and 10.3? Answer: 5, namely 5, 6, 7, 8, 9 and 10.

So taken together statements are sufficient to answer that there are 5 integers between r and s.

Hope it's clear.
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01 Nov 2010, 01:34
this is one of the trickiest questions I have ever seen so far - in test conditions - time and pressure, I am not going to consider C as an option EVER, since there are 5 values for n ... but it is actually that 5 is what the question is looking for ... tough one

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How many integers n are there such that r < n< s ? [#permalink]

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22 Apr 2012, 13:32
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How many integers n are there such that r < n< s ?

(1) s - r = 5
(2) r and s are not integers.
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Re: How many integers n are there such that r < n< 5 ? [#permalink]

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22 Apr 2012, 13:44
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How many integers n are there such that r < n< s ?

The question asks: how many integers $$n$$ satisfy $$r < n < s$$, or how many integers are between $$r$$ and $$s$$, not inclusive?

Notice that if $$r$$ and $$s$$ are integers, for example $$s=5$$ and $$r=0$$ then there will be 4 integers between them: 1, 2, 3, and 4. But if $$r$$ and $$s$$ are NOT integers for example $$s=5.5$$ and $$r=0.5$$ then there will be 5, so one more, integers between them: 1, 2, 3, 4 and 5.

(1) s - r = 5. Not sufficient.
(2) r and s are not integers. Not sufficient.

(1)+(2) According to above reasoning since r and s are not integers then there are 5 integers between them (case 2). Sufficient.

Hope it's clear.
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Re: How many integers n are there such that r < n< s ? [#permalink]

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22 Apr 2012, 14:00
Thanks for putting this together. I received a 29 on my last math section of the GMAT. Any suggestions for improvement since I take it again on May 31st? Why did you choose that picture? I like it and have not seen anything similar to it.

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Re: How many integers n are there such that r < n< 5 ? [#permalink]

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22 Apr 2012, 14:09
Bunuel wrote:
How many integers n are there such that r < n< s ?

The question asks: how many integers $$n$$ satisfy $$r < n < s$$, or how many integers are between $$r$$ and $$s$$, not inclusive?

Notice that if $$r$$ and $$s$$ are integers, for example $$s=5$$ and $$r=0$$ then there will be 4 integers between them: 1, 2, 3, and 4. But if $$r$$ and $$s$$ are NOT integers for example $$s=5.5$$ and $$r=0.5$$ then there will be 5, so one more, integers between them: 1, 2, 3, 4 and 5.

(1) s - r = 5. Not sufficient.
(2) r and s are not integers. Not sufficient.

(1)+(2) According to above reasoning since r and s are not integers then there are 5 integers between them (case 2). Sufficient.

Hope it's clear.

can you please eleborate the concept behind this ?? indeed is true but I didn't notice this before.

Thanks
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Re: How many integers n are there such that r < n< 5 ? [#permalink]

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22 Apr 2012, 14:15
carcass wrote:
Bunuel wrote:
How many integers n are there such that r < n< s ?

The question asks: how many integers $$n$$ satisfy $$r < n < s$$, or how many integers are between $$r$$ and $$s$$, not inclusive?

Notice that if $$r$$ and $$s$$ are integers, for example $$s=5$$ and $$r=0$$ then there will be 4 integers between them: 1, 2, 3, and 4. But if $$r$$ and $$s$$ are NOT integers for example $$s=5.5$$ and $$r=0.5$$ then there will be 5, so one more, integers between them: 1, 2, 3, 4 and 5.

(1) s - r = 5. Not sufficient.
(2) r and s are not integers. Not sufficient.

(1)+(2) According to above reasoning since r and s are not integers then there are 5 integers between them (case 2). Sufficient.

Hope it's clear.

can you please eleborate the concept behind this ?? indeed is true but I didn't notice this before.

Thanks

There isn't some special concept behind it. It's just common sense based on observation.
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Re: How many integers n are there such that r < n < s? [#permalink]

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30 Dec 2012, 19:50
hmm... I chose E with the reasoning that the question does not mention that the integers are consecutive. There could be duplicate integers between r and s such that r=0 and s=5 and values of n to be 1, 1, 2, 3, 4, 4.

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Re: How many integers n are there such that r < n < s? [#permalink]

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31 Dec 2012, 03:22
4sguy wrote:
hmm... I chose E with the reasoning that the question does not mention that the integers are consecutive. There could be duplicate integers between r and s such that r=0 and s=5 and values of n to be 1, 1, 2, 3, 4, 4.

Check here: how-many-integers-n-are-there-such-that-r-n-s-101917.html#p790664 and here: how-many-integers-n-are-there-such-that-r-n-s-101917.html#p790767

Similar questions to practice:
how-many-integers-are-there-such-that-v-n-w-129065.html
how-many-integers-n-are-there-such-that-r-n-s-131146.html
how-many-integers-n-are-there-such-that-1-5n-139474.html (OG)

Hope it helps.
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Re: How many integers n are there such that r < n < s? [#permalink]

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18 Jun 2013, 20:35
I had and still continue to have trouble interpreting this question.

how many integers n are there such that r<n<s
r and s are 0 or 5 -> n can be 1,2,3,4
r and s are 110 or 115-> n can be another set of 4 no.s

i thought n can have any number of infinite values for r-s=5 or for r and s are not integers.....can some one pls make it clear...

i understand some of the explanations are towards n=no. of integers between two given values, but question ask how many integers n are there that meet the criteria...

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Re: How many integers n are there such that r < n < s? [#permalink]

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19 Jun 2013, 02:36
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nanz236 wrote:
I had and still continue to have trouble interpreting this question.

how many integers n are there such that r<n<s
r and s are 0 or 5 -> n can be 1,2,3,4
r and s are 110 or 115-> n can be another set of 4 no.s

i thought n can have any number of infinite values for r-s=5 or for r and s are not integers.....can some one pls make it clear...

i understand some of the explanations are towards n=no. of integers between two given values, but question ask how many integers n are there that meet the criteria...

How many integers n are there such that 0 < n < 5? Answer: 4.
How many integers n are there such that 110 < n < 115? Answer: 4.

Does this make sense?
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Re: How many integers n are there such that r < n< s ? [#permalink]

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18 May 2014, 10:46
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if we knew about s and r (integers or not integers) our task would be simplified to st(1) Suff. Since we know nothing about s and r, there could be always four integers (case when s and r are integers) or five integers (when s or r is not integer)

st(2) helps with assigning type for our numbers (s and r), but we know nothing about values

combined st(1&2) supports our previously inquired data, i.e. s and r are not integers, hence the number of integers in the given interval will always be 5.

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Re: How many integers n are there such that r < n < s? [#permalink]

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05 Dec 2014, 21:35
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Re: How many integers n are there such that r < n < s? [#permalink]

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30 Mar 2016, 07:18
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Re: How many integers n are there such that r < n < s? [#permalink]

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01 Jun 2017, 06:38
ezinis wrote:
Sorry for posting this, it may sound silly to someone, but I have problem understanding the question:

How many integers n are there such that r < n < s?
(1) s - r = 5
(2) r and s are not integers.

My solution: For (1), whether r and s are integer or not, there can be so many "groups" of 4 or 5 n that fit the conditions.
[Reveal] Spoiler:
So (1) not enough
and (2) not enough, apparently
(1) and (2) not enough, according to my "reasoning" above.

So I chose E

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/how-many-int ... 66396.html
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Re: How many integers n are there such that r < n < s?   [#permalink] 01 Jun 2017, 06:38
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