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16 Jul 2016, 05:39
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
47% (01:47) correct
53%
(01:59)
wrong
based on 32
sessions
History
Date
Time
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Not Attempted Yet
What is the median of the series \(S_1\), \(S_2\), \(S_3\), …, \(S_n\) where \(S_k\) = 2k + 1, for all integer k, k ≥ 1.
(1) n is odd.
(2) There are 3 numbers on this series that are greater than the median.
Please explain in detail your answer, putting examples for each of the cases, and also what is the fastest way to solve the question.
(1) n is odd.
(2) There are 3 numbers on this series that are greater than the median.
Please explain in detail your answer, putting examples for each of the cases, and also what is the fastest way to solve the question.
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16 Jul 2016, 08:57
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I) If n is odd , then n can be any odd number (not sufficient)
II) let the series be a, b, c, d, e, f
here median is (C+D)/2
let the series be a, b, c, d, e, f, g
here median is d
(not sufficient)
Combine I and II
now series can have only 7 numbers starting from 3,......
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16 Jul 2016, 08:59
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This is not a good question: a series in mathematics is a sum of the terms of an infinite sequence, thus a series has no median. No proper GMAT question would use such wording.
I guess the question means sequence instead of series. In this case we have the sequence of positive odd integers starting from 3: 3, 5, 7, 9, 11, 13, 15, ... which is an evenly spaced set, median = middle number, if the number of terms is odd or median = the average of two middle terms, if the number of terms is even.
The first statement says that the number of terms in the sequence is odd. which is clearly insufficient.
The second statement says that there are 3 terms greater than the median. We can have two cases - if n is even: {3, 5, 7, 9, 11, 13}, median 8 or if n is odd: {3, 5, 7, 9, 11, 13, 15}, median 9.
When combined we know that n is odd, thus the sequence is {3, 5, 7, 9, 11, 13, 15} and n = 7.
Overall, I'd ignore the question and the source which provided it.
