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

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BN1989
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How many integers n are there such than v < n < w ? [#permalink] New post   Updated on: 14 Jun 2019, 03:47
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How many integers n are there such than v < n < w ?

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


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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
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Originally posted by BN1989 on 14 Mar 2012, 06:13.
Last edited by Bunuel on 14 Jun 2019, 03:47, edited 4 times in total.
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Re: How many integers n are there such than v < n < w ? [#permalink] New post   14 Mar 2012, 06:33
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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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Re: How many integers n are there such than v < n < w ? [#permalink] New post   17 Mar 2012, 05:21
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
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Re: How many integers n are there such than v < n < w ? [#permalink] New post   17 Mar 2012, 05:25
Expert Reply
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 n are there such than v < n < w ? [#permalink] New post   18 Jun 2016, 05:30
Hi Bunuel,

Thanks for your explanation.

But why cant the answer be A.?
If we conclude condition 1 :v and w are the positive integer
We can say that Count of possible Integer Values of n will always be = w-v-1

For Example : assume w=15 , v=11
we will have count as 15-11-1 = 3
@
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Re: How many integers n are there such than v < n < w ? [#permalink] New post   19 Jun 2016, 09:33
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AbhijitGoswami wrote:
Hi Bunuel,

Thanks for your explanation.

But why cant the answer be A.?
If we conclude condition 1 :v and w are the positive integer
We can say that Count of possible Integer Values of n will always be = w-v-1

For Example : assume w=15 , v=11
we will have count as 15-11-1 = 3
@


When a DS question asks about the value of some variable, then the statement(s) is sufficient ONLY if you can get the single numerical value of this variable.
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Re: How many integers n are there such than v < n < w ? [#permalink] New post   22 Nov 2022, 07:00
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Re: How many integers n are there such than v < n < w ? [#permalink]
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