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Set S consists of n consecutive integers, where n > 1. What is the
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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
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Updated on: 04 Jun 2015, 08:37
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 7i.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 SUFFICIENTStatement 2: The sum of the integers in Set S is 14Please note : The Mean of Consecutive terms = Median of them and Sum of consecutive terms = Median of set x No. of termsi.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 SUFFICIENTAfter combining the two statementsS 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 SUFFICIENTAnswer: Option
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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
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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 7i.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 SUFFICIENTStatement 2: The sum of the integers in Set S is 14Since 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 termsi.e. S could ONLY be {1, 0, 1, 2, 3, 4, 5} i.e. n=7 Hence, SUFFICIENTAnswer: Option 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
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04 Jun 2015, 08:39
VladimirKarpov 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. 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
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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 7i.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 SUFFICIENTStatement 2: The sum of the integers in Set S is 14Please note : The Mean of Consecutive terms = Median of them and Sum of consecutive terms = Median of set x No. of termsi.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 SUFFICIENTAfter combining the two statementsS 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 SUFFICIENTAnswer: Option GMAT Insight. For statement 2, question says, n>1, so we can't take 1 and 0. Answer is B. (2,3,4,5)



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Re: Set S consists of n consecutive integers, where n > 1. What is the
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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 7i.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 SUFFICIENTStatement 2: The sum of the integers in Set S is 14Please note : The Mean of Consecutive terms = Median of them and Sum of consecutive terms = Median of set x No. of termsi.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 SUFFICIENTAfter combining the two statementsS 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 SUFFICIENTAnswer: Option GMAT Insight. For statement 2, question says, n>1, so we can't take 1 and 0. Answer is B. (2,3,4,5) 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
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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 noninteger 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 noninteger 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. The correct answer is E.
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Re: Set S consists of n consecutive integers, where n > 1. What is the
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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
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12 Feb 2019, 08:22
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). So, let's start with statement 2. 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 = 4Case b: set S = {1, 0, 1, 2, 3, 4, 5}. In this case, the answer to the target question is n = 7Since 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 = 4Case b: set S = {1, 0, 1, 2, 3, 4, 5}. In this case, the answer to the target question is n = 7Since 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 counterexamples to show that each statement ALONE is not sufficient. So, the same counterexamples 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 = 4Case b: set S = {1, 0, 1, 2, 3, 4, 5}. In this case, the answer to the target question is n = 7Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT Answer: E Cheers, Brent
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Re: Set S consists of n consecutive integers, where n > 1. What is the
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