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# Set S consists of n consecutive integers, where n > 1. What is the

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Set S consists of n consecutive integers, where n > 1. What is the  [#permalink]

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04 Jun 2015, 04:22
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Set S consists of n consecutive integers, where n > 1. What is the value of n?

(1) The sum of the integers in Set S is divisible by 7.
(2) The sum of the integers in Set S is 14.

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Set S consists of n consecutive integers, where n > 1. What is the  [#permalink]

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Updated on: 04 Jun 2015, 08:37
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Bunuel wrote:
Set S consists of n consecutive integers, where n > 1. What is the value of n?

(1) The sum of the integers in Set S is divisible by 7.
(2) The sum of the integers in Set S is 14.

Question : How many terms does the set S have?

Statement 1: The sum of the integers in Set S is divisible by 7

i.e. S could be {1, 2, 3, 4, 5, 6, 7} i.e. n=7

OR

S could be {5, 6, 7, 8, 9} i.e. n=5

Hence, NOT SUFFICIENT

Statement 2: The sum of the integers in Set S is 14

Please note : The Mean of Consecutive terms = Median of them and Sum of consecutive terms = Median of set x No. of terms

i.e. S could be {-1, 0, 1, 2, 3, 4, 5} i.e. n=7
OR S could be {2, 3, 4, 5} i.e. n=4
Hence, NOT SUFFICIENT

After combining the two statements

S could be {-1, 0, 1, 2, 3, 4, 5} i.e. n=7
OR S could be {2, 3, 4, 5} i.e. n=4

Hence, NOT SUFFICIENT

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Originally posted by GMATinsight on 04 Jun 2015, 05:20.
Last edited by GMATinsight on 04 Jun 2015, 08:37, edited 2 times in total.
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Re: Set S consists of n consecutive integers, where n > 1. What is the  [#permalink]

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04 Jun 2015, 08:26
GMATinsight wrote:
Bunuel wrote:
Set S consists of n consecutive integers, where n > 1. What is the value of n?

(1) The sum of the integers in Set S is divisible by 7.
(2) The sum of the integers in Set S is 14.

Question : How many terms does the set S have?

Statement 1: The sum of the integers in Set S is divisible by 7

i.e. S could be {1, 2, 3, 4, 5, 6, 7} i.e. n=7

OR

S could be {5, 6, 7, 8, 9} i.e. n=5

Hence, NOT SUFFICIENT

Statement 2: The sum of the integers in Set S is 14

Since 14 = 2 x 7 therefore either there should be 2 Consecutive terms with median 7 (IMPOSSIBLE) of there should be 7 Consecutive terms with median 2

Please note : The Mean of Consecutive terms = Median of them and Sum of consecutive terms = Median of set x No. of terms

i.e. S could ONLY be {-1, 0, 1, 2, 3, 4, 5}

i.e. n=7

Hence, SUFFICIENT

And what about Set {2, 3, 4, 5} for the second statement?
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Set S consists of n consecutive integers, where n > 1. What is the  [#permalink]

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04 Jun 2015, 08:39
GMATinsight wrote:
Bunuel wrote:
Set S consists of n consecutive integers, where n > 1. What is the value of n?

(1) The sum of the integers in Set S is divisible by 7.
(2) The sum of the integers in Set S is 14.

And what about Set {2, 3, 4, 5} for the second statement?

That was missed by mistake, Correction Done! Thank you!
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Re: Set S consists of n consecutive integers, where n > 1. What is the  [#permalink]

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04 Jun 2015, 08:45
GMATinsight wrote:
Bunuel wrote:
Set S consists of n consecutive integers, where n > 1. What is the value of n?

(1) The sum of the integers in Set S is divisible by 7.
(2) The sum of the integers in Set S is 14.

Question : How many terms does the set S have?

Statement 1: The sum of the integers in Set S is divisible by 7

i.e. S could be {1, 2, 3, 4, 5, 6, 7} i.e. n=7

OR

S could be {5, 6, 7, 8, 9} i.e. n=5

Hence, NOT SUFFICIENT

Statement 2: The sum of the integers in Set S is 14

Please note : The Mean of Consecutive terms = Median of them and Sum of consecutive terms = Median of set x No. of terms

i.e. S could be {-1, 0, 1, 2, 3, 4, 5} i.e. n=7
OR S could be {2, 3, 4, 5} i.e. n=4
Hence, NOT SUFFICIENT

After combining the two statements

S could be {-1, 0, 1, 2, 3, 4, 5} i.e. n=7
OR S could be {2, 3, 4, 5} i.e. n=4

Hence, NOT SUFFICIENT

GMAT Insight.

For statement 2, question says, n>1, so we can't take -1 and 0.

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Re: Set S consists of n consecutive integers, where n > 1. What is the  [#permalink]

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04 Jun 2015, 08:50
viksingh15 wrote:
GMATinsight wrote:
Bunuel wrote:
Set S consists of n consecutive integers, where n > 1. What is the value of n?

(1) The sum of the integers in Set S is divisible by 7.
(2) The sum of the integers in Set S is 14.

Question : How many terms does the set S have?

Statement 1: The sum of the integers in Set S is divisible by 7

i.e. S could be {1, 2, 3, 4, 5, 6, 7} i.e. n=7

OR

S could be {5, 6, 7, 8, 9} i.e. n=5

Hence, NOT SUFFICIENT

Statement 2: The sum of the integers in Set S is 14

Please note : The Mean of Consecutive terms = Median of them and Sum of consecutive terms = Median of set x No. of terms

i.e. S could be {-1, 0, 1, 2, 3, 4, 5} i.e. n=7
OR S could be {2, 3, 4, 5} i.e. n=4
Hence, NOT SUFFICIENT

After combining the two statements

S could be {-1, 0, 1, 2, 3, 4, 5} i.e. n=7
OR S could be {2, 3, 4, 5} i.e. n=4

Hence, NOT SUFFICIENT

GMAT Insight.

For statement 2, question says, n>1, so we can't take -1 and 0.

Hi Viksingh15

You are Mistaken here...

n is the number of terms and not the value in the set hence,

S could be {-1, 0, 1, 2, 3, 4, 5} i.e. n=7
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Re: Set S consists of n consecutive integers, where n > 1. What is the  [#permalink]

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08 Jun 2015, 03:46
Bunuel wrote:
Set S consists of n consecutive integers, where n > 1. What is the value of n?

(1) The sum of the integers in Set S is divisible by 7.
(2) The sum of the integers in Set S is 14.

MANHATTAN GMAT OFFICIAL SOLUTION:

Both statements give us information about the sum of the set, so we will rephrase with this in mind:
Sum of Consecutive Set = (Median)(Number of Terms)
Sum of Consecutive Set = (Median)(n)

For n = odd, the median is the middle term, an integer. For n = even, the median is the average of the two middle terms, a non-integer of the form “integer + 0.5.” We can determine n if we can determine Both the median of Set S and the sum of the integers in Set S.

(1) INSUFFICIENT:
Sum of Consecutive Set = (Median)(n)
multiple of 7 = (Median)(n)

Even if we ignore the possibility of non-integer medians, we can list some possibilities: n is a multiple of 7, the median is a multiple of 7, or both.

Check some possible median and n values:
n = 3 and Median = 7: Set S is {6, 7, 8}, which has a sum of 21. OK.
n = 7 and Median = 2: Set S is { –1, 0, 1, 2, 3, 4, 5}, which has a sum of 14. OK.
n = 7 and Median = 7: Set S is {4, 5, 6, 7, 8, 9, 10}, which has a sum of 49. OK.

We have proven that n could equal 3 or 7, and there are probably many other possible n values.

(2) INSUFFICIENT: Since n must be an integer, we can use divisibility rules to narrow down possible median values.

Sum of Consecutive Set = (Median)(n)
14 = (Median)(n)
(2)(7) = (Median)(n)

Check some possible median and n values:
n = 1 and Median = 14: Set S is {14}, which has a sum of 14, but not enough terms. IGNORE.
n = 2 and Median = 7: Set S can't have an integer median if there are only 2 terms. IGNORE.
n = 7 and Median = 2: Set S is { –1, 0, 1, 2, 3, 4, 5}, which has a sum of 14. OK.
n = 4 and Median = 3.5: Set S is {2, 3, 4, 5}, which has a sum of 14. OK.
n could equal 4 or 7.

(1) AND (2) INSUFFICIENT: Statement (1) does not further restrict the cases allowed by Statement (2), so together the statements are still insufficient.

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Re: Set S consists of n consecutive integers, where n > 1. What is the  [#permalink]

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20 Dec 2016, 19:26
Excellent Question.
Here's my Solution to this one=>

Firstly a set of consecutive integers is an AP(evenly spaced set) with common difference =1
Hence => Mean = Median

In a set of consecutive integers =>Mean can take two forms
First ->N=odd => mean =x
Second -> N=Even => Mean = x.5
For some integer x

Also we shall use $$Mean = \frac{Sum}{#}$$

We need to get N

Statement 1-->
Sum is divisible by 7
Lets use hit and trial =>
3,4=> N=2
0,1,2,3,4,5,6=> N=6
Hence Not sufficient

Statement 2->
Sum=14
N=2 => Mean = 2 => not allowed for N=even => Rejected
N=3 => Mean => 3.666=> Not allowed
N=4 => Mean = 3.5 => Allowed => Set => {2,3,4,5}
N=5 => Mean =2.4=> Not allowed
N=6 => Mean = 2.333 => Not allowed
N=7 => Mean = 2 => Allowed => Set => {-1,0,1,2,3,4,5}

Hence not sufficient

Combing the two statements => N can be 2 or 6 => Not sufficient
NOTE-> There may/may not be other values of N

Hence E

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Re: Set S consists of n consecutive integers, where n > 1. What is the  [#permalink]

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12 Feb 2019, 08:22
Top Contributor
Bunuel wrote:
Set S consists of n consecutive integers, where n > 1. What is the value of n?

(1) The sum of the integers in Set S is divisible by 7.
(2) The sum of the integers in Set S is 14.

Given: Set S consists of n consecutive integers, where n > 1.

Target question: What is the value of n?

IMPORTANT: Notice that the two statements are VERY SIMILAR. That is, if the sum of the values is 14 (statement 2), then it is guaranteed that the sum is divisible by 7 (statement 1).

Statement 2: The sum of the integers in set S is 14.
Let's TEST some values.
Here are two cases that satisfy statement 2:
Case a: set S = {2, 3, 4, 5}. In this case, the answer to the target question is n = 4
Case b: set S = {-1, 0, 1, 2, 3, 4, 5}. In this case, the answer to the target question is n = 7
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statement 1: The sum of the integers in set S is divisible by 7.
Notice that we can reuse the same cases we used for statement 2:
Case a: set S = {2, 3, 4, 5}. In this case, the answer to the target question is n = 4
Case b: set S = {-1, 0, 1, 2, 3, 4, 5}. In this case, the answer to the target question is n = 7
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient.
So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: set S = {2, 3, 4, 5}. In this case, the answer to the target question is n = 4
Case b: set S = {-1, 0, 1, 2, 3, 4, 5}. In this case, the answer to the target question is n = 7
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
Brent
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Re: Set S consists of n consecutive integers, where n > 1. What is the   [#permalink] 12 Feb 2019, 08:22
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