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You are given the data set {14, 35, 44, 47, 49, 49, 50, 51, 56, N}, wh
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31 Jan 2019, 00:42
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You are given the data set {14, 35, 44, 47, 49, 49, 50, 51, 56, N}, where N is an integer not necessarily greater than 56. What is the value of N?
(1) The mean of the data set is 44.3
(2) The median of the data set is 48.5
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Re: You are given the data set {14, 35, 44, 47, 49, 49, 50, 51, 56, N}, wh
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31 Jan 2019, 02:16
Bunuel wrote:
You are given the data set {14, 35, 44, 47, 49, 49, 50, 51, 56, N}, where N is an integer not necessarily greater than 56. What is the value of N? (1) The mean of the data set is 44.3 (2) The median of the data set is 48.5
#1
sum= 395+x
avg = 44.3
total digits = 10
so x= 48
sufficient
#2
median is 48.5
the median = x+49= 48.5*2
x= 48
sufficient
IMO D
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Re: You are given the data set {14, 35, 44, 47, 49, 49, 50, 51, 56, N}, wh
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31 Jan 2019, 06:44
Solution
Given: • A data set {14, 35, 44, 47, 49, 49, 50, 51, 56, N}, where N is an integer To find: Analysing Statement 1 “The mean of the data set is 44.3”
• Mean of the set = \(\frac{(14 + 35 + 44 + 47 + 49 + 49 + 50 + 51 + 56 + N)}{10} = 44.3\)o Implies, N = 443 – (14 + 35 + 44 + 47 + 49 + 49 + 50 + 51 + 56) • Thus, we can find a unique value of N. Therefore, statement 1 is sufficient
Analysing Statement 2 “The median of the set is 48.5”
• The median of the given set = \(\frac{(5^{th} term + 6^{th} term)}{2}\) • One of the middle terms = 49, for any value of N • Thus, \(48.5 = \frac{(49 + x)}{2}\)o Implies, x = 48 o Since, there is no 48 in the set, the value of N must be 48 Therefore, statement 2 is sufficient
Hence, the correct answer is Option D.
Answer: D
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Re: You are given the data set {14, 35, 44, 47, 49, 49, 50, 51, 56, N}, wh
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31 Jan 2019, 06:44