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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] New post 29 Sep 2010, 06:05
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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
Please comment, thanks
[Reveal] Spoiler: OA
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Re: Wording [#permalink] New post 29 Sep 2010, 06:18
Expert's post
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
Please comment, thanks


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.

Answer C is correct.
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Re: Wording [#permalink] New post 29 Sep 2010, 08:42
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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Re: Wording [#permalink] New post 29 Sep 2010, 08:56
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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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Re: Wording [#permalink] New post 01 Nov 2010, 00:34
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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Re: How many integers n are there such that r < n < s? [#permalink] New post 30 Dec 2012, 18:50
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] New post 31 Dec 2012, 02:22
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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.



Answer is C, not E.

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] New post 18 Jun 2013, 19:35
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] New post 19 Jun 2013, 01:36
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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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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: How many integers n are there such that r < n < s?   [#permalink] 19 Jun 2013, 01:36
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