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Consider a sequence of seven consecutive integers
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Updated on: 09 Sep 2017, 10:58
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Consider a sequence of seven consecutive integers. The average of the first five integers is \(n\). The average of all the seven integers is: A. \(n\) B. \(n+1\) C. \(k*n\), where \(k\) is a function of \(n\) D. \(n+\frac{2}{7}\) E. \(n+2\) == Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.
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Originally posted by niks18 on 09 Sep 2017, 01:16.
Last edited by niks18 on 09 Sep 2017, 10:58, edited 1 time in total.



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Re: Consider a sequence of seven consecutive integers
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09 Sep 2017, 01:52
niks18 wrote: Consider a sequence of seven consecutive integers. The average of the first five integers is \(n\). The average of all the seven integers is:
A. \(n\) B. \(n+1\) C. \(k*n\), where \(k\) is a function of \(n\) D. \(n+\frac{2}{7}\) E. \(n+2\) In case of a set of consecutive numbers, Middle number = Average of setSet of 5 numbers  a, a+1, a+2, a+3, a+4 Middle number = Average = a+2 but we are given that average for first 5 numbers is = n hence a+2 = n Set of 7 numbers  a, a+1, a+2, a+3, a+4, a+5, a+6 Middle number = Average = a+3 = (a+2) + 1 = n+1********************************************************************** Consecutive numbers are in A.P. and sum for such a set = number of terms * (first term + last term) / 2
If we divide the sum by number of terms then we get average. hence average = (first term + last term) / 2Set of 5 numbers  a, a+1, a+2, a+3, a+4 Average = (first term + last term) / 2 = (a + a+4) / 2 = a+2 Average = a+2 = n Set of 7 numbers  a, a+1, a+2, a+3, a+4, a+5, a+6 Average = (first term + last term) / 2 = (a + a+6) / 2 = a+3 = (a+2)+1 Average = n + 1
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Re: Consider a sequence of seven consecutive integers
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10 Sep 2017, 08:52
niks18 wrote: Consider a sequence of seven consecutive integers. The average of the first five integers is \(n\). The average of all the seven integers is:
A. \(n\) B. \(n+1\) C. \(k*n\), where \(k\) is a function of \(n\) D. \(n+\frac{2}{7}\) E. \(n+2\) OEAverage of consecutive numbers in an ODD sequence = Middle number of the sequenceLet the seven consecutive integers be \(1,2,3,4,5,6,7\). Hence average of this sequence \(= 4\) First five integers of the above sequence are \(1,2,3,4,5\). Average of this sequence \(= 3 = n\) Clearly, \(4 = 3 +1 = n+1\) Hence Option B



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Consider a sequence of seven consecutive integers
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10 Sep 2017, 10:35
niks18 wrote: Consider a sequence of seven consecutive integers. The average of the first five integers is \(n\). The average of all the seven integers is:
A. \(n\) B. \(n+1\) C. \(k*n\), where \(k\) is a function of \(n\) D. \(n+\frac{2}{7}\) E. \(n+2\) average of first five integers=middle (third) term=n average of seven integers=middle (fourth) term=n+1 B



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Re: Consider a sequence of seven consecutive integers
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10 Sep 2017, 10:41
This is perhaps another interpretation that I thought I would suggest: Consider a sequence of seven consecutive integers. The average of the first five integers is n.The above can be restated as the first five integers are n2, n1, n, n+1, n+2. Knowing the final two numbers in the sequence are n+3 and n+4, eliminate option A. Substitution to find the correct answer out of B to E 5 (n2) + 6 (n1) + 7 (n) + 8 (n+1) + 9 (n+2) + 10 (n+3) + 11 (n+4) = 56. 56/7 (total number of terms in sequence)=8. 8 is n+1, so option B == Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.




Re: Consider a sequence of seven consecutive integers
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10 Sep 2017, 10:41






