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# How many integers n are there such that v<n<w?

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Joined: 12 Oct 2011
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GMAT 1: 700 Q48 V37
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Kudos [?]: 100 [0], given: 23

How many integers n are there such that v<n<w? [#permalink]  14 Mar 2012, 05:13
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Difficulty:

25% (medium)

Question Stats:

57% (01:41) correct 43% (00:33) wrong based on 64 sessions
How many integers n are there such that v<n<w?

(1) v and w are positive integers?
(2) w-v=4

How is it even possible that v<w when v-w=4?

from gmathacks
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Mar 2012, 04:23, edited 2 times in total.
Edited the question
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Math Expert
Joined: 02 Sep 2009
Posts: 29203
Followers: 4743

Kudos [?]: 50187 [0], given: 7537

Re: How many integers are there such that v<n<w? [#permalink]  14 Mar 2012, 05:33
Expert's post
BN1989 wrote:
How many integers n are there such that v<n<w?

1) v and w are positive integers?
2) v-w=4

How is it even possible that v<w when v-w=4?

from gmathacks

(2) should read: w-v=4.

How many integers n are there such that v<n<w?

Notice that if $$w$$ and $$v$$ are integers, for example $$w=5$$ and $$v=1$$ then there will be 3 integers between them: 2, 3, and 4. But if $$w$$ and $$v$$ are NOT integers for example $$w=5.5$$ and $$v=1.5$$ then there will be 4, so one more, integers between them: 2, 3, 4 and 5.

(1) v and w are positive integers. Not sufficient.
(2) w-v=4. Not sufficient.

(1)+(2) According to above reasoning since v and w are positive integers then there are 3 integers between them (case 1). Sufficient.

Similar question to practice: how-many-integers-n-are-there-such-that-r-n-s-101917.html

Hope it helps.
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Kudos [?]: 6 [0], given: 14

Re: How many integers are there such that v<n<w? [#permalink]  17 Mar 2012, 04:21
BN1989 wrote:
How many integers are there such that v<n<w?

(1) v and w are positive integers?
(2) w-v=4

How is it even possible that v<w when v-w=4?

from gmathacks

The question stem seems to ask how many integral triplets exists which are bound by v<n<w?
Whereas the intent is to ask how many integral values of n exist such that v<n<w ?

Only if we are interested in finding the no. of integral values n can take then we can get the answer
by combining 1&2 (as Bunnel stated)
But if we are interested in finding integers then obeying 1&2 we can take any natural no. as v and accordingly our w will get fixed and then we can choose any 3 no.s between w and v to get n.So infinite no. of triplets can be formed.

@Bunnel: I would be thankful if you clarify
Math Expert
Joined: 02 Sep 2009
Posts: 29203
Followers: 4743

Kudos [?]: 50187 [0], given: 7537

Re: How many integers are there such that v<n<w? [#permalink]  17 Mar 2012, 04:25
Expert's post
jach2012 wrote:
BN1989 wrote:
How many integers are there such that v<n<w?

(1) v and w are positive integers?
(2) w-v=4

How is it even possible that v<w when v-w=4?

from gmathacks

The question stem seems to ask how many integral triplets exists which are bound by v<n<w?
Whereas the intent is to ask how many integral values of n exist such that v<n<w ?

Only if we are interested in finding the no. of integral values n can take then we can get the answer
by combining 1&2 (as Bunnel stated)
But if we are interested in finding integers then obeying 1&2 we can take any natural no. as v and accordingly our w will get fixed and then we can choose any 3 no.s between w and v to get n.So infinite no. of triplets can be formed.

@Bunnel: I would be thankful if you clarify

The question should read: "How many integers N are there such that v<n<w?" There was a typo in the original post, which is now edited.
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Re: How many integers are there such that v<n<w?   [#permalink] 17 Mar 2012, 04:25
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# How many integers n are there such that v<n<w?

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