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# There are n consecutive positive integers, what is the value of n?

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Intern
Joined: 16 Mar 2017
Posts: 13
There are n consecutive positive integers, what is the value of n?  [#permalink]

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20 Sep 2017, 00:52
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45% (medium)

Question Stats:

67% (01:45) correct 33% (01:40) wrong based on 90 sessions

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There are n consecutive positive integers, what is the value of n?

1) three numbers are divisible by 3
2) four numbers are divisible by 4
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4484
Re: There are n consecutive positive integers, what is the value of n?  [#permalink]

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20 Sep 2017, 09:43
petrified17 wrote:
There are n consecutive positive integers, what is the value of n?

1) three numbers are divisible by 3
2) four numbers are divisible by 4

Dear petrified17,

I'm happy to respond.

My friend, I believe something about the way the question is posted here is flawed. I don't know whether there was a copying mistake or whether the flaw is in the source. The problem is that the two DS statements must be consistent with each other. It may be that there is only one numerical possibility or several, but it can't be the case that no numerical value of n can possibly work with both statements. In other words, regardless of whether we can compute the value of n from the statements, it absolutely must be true that the question writer has at least one value of n in mind that consistently works throughout the whole question. This is the deep flaw in this question: as this stands, this is not a valid question.

You see, consider any case of n consecutive numbers in which four numbers are divisible by n. We would have to have four consecutive multiples of 4, which would have a difference of 12 from each other. Say, we go from 32 to 44, which has exactly four numbers divisible by 4 {32, 36, 40, 44}. In that range, we have at least four divisible by 3: {33, 36, 39, 42} and possibly more if we include 45 and/or 30. There is absolutely no way we could have only three numbers divisible by 3 if we have four numbers divisible by four. The two statements, as they stand now, are inconsistent, and this makes the question invalid.

Is it possible that the question was mistyped?

Mike
_________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
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Joined: 27 May 2012
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Re: There are n consecutive positive integers, what is the value of n?  [#permalink]

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06 Jan 2019, 09:21
mikemcgarry wrote:
petrified17 wrote:
There are n consecutive positive integers, what is the value of n?

1) three numbers are divisible by 3
2) four numbers are divisible by 4

Dear petrified17,

I'm happy to respond.

My friend, I believe something about the way the question is posted here is flawed. I don't know whether there was a copying mistake or whether the flaw is in the source. The problem is that the two DS statements must be consistent with each other. It may be that there is only one numerical possibility or several, but it can't be the case that no numerical value of n can possibly work with both statements. In other words, regardless of whether we can compute the value of n from the statements, it absolutely must be true that the question writer has at least one value of n in mind that consistently works throughout the whole question. This is the deep flaw in this question: as this stands, this is not a valid question.

You see, consider any case of n consecutive numbers in which four numbers are divisible by n. We would have to have four consecutive multiples of 4, which would have a difference of 12 from each other. Say, we go from 32 to 44, which has exactly four numbers divisible by 4 {32, 36, 40, 44}. In that range, we have at least four divisible by 3: {33, 36, 39, 42} and possibly more if we include 45 and/or 30. There is absolutely no way we could have only three numbers divisible by 3 if we have four numbers divisible by four. The two statements, as they stand now, are inconsistent, and this makes the question invalid.

Is it possible that the question was mistyped?

Mike

Dear Moderator,
It seems this question is not correct , as also pointed out by mikemcgarry, hope you will look into this and do the needful.Thank you.
_________________
- Stne
Math Expert
Joined: 02 Sep 2009
Posts: 57155
Re: There are n consecutive positive integers, what is the value of n?  [#permalink]

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06 Jan 2019, 09:31
stne wrote:
mikemcgarry wrote:
petrified17 wrote:
There are n consecutive positive integers, what is the value of n?

1) three numbers are divisible by 3
2) four numbers are divisible by 4

Dear petrified17,

I'm happy to respond.

My friend, I believe something about the way the question is posted here is flawed. I don't know whether there was a copying mistake or whether the flaw is in the source. The problem is that the two DS statements must be consistent with each other. It may be that there is only one numerical possibility or several, but it can't be the case that no numerical value of n can possibly work with both statements. In other words, regardless of whether we can compute the value of n from the statements, it absolutely must be true that the question writer has at least one value of n in mind that consistently works throughout the whole question. This is the deep flaw in this question: as this stands, this is not a valid question.

You see, consider any case of n consecutive numbers in which four numbers are divisible by n. We would have to have four consecutive multiples of 4, which would have a difference of 12 from each other. Say, we go from 32 to 44, which has exactly four numbers divisible by 4 {32, 36, 40, 44}. In that range, we have at least four divisible by 3: {33, 36, 39, 42} and possibly more if we include 45 and/or 30. There is absolutely no way we could have only three numbers divisible by 3 if we have four numbers divisible by four. The two statements, as they stand now, are inconsistent, and this makes the question invalid.

Is it possible that the question was mistyped?

Mike

Dear Moderator,
It seems this question is not correct , as also pointed out by mikemcgarry, hope you will look into this and do the needful.Thank you.

Marked as Poor Quality and locked.
_________________
Re: There are n consecutive positive integers, what is the value of n?   [#permalink] 06 Jan 2019, 09:31
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