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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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Math Expert
Joined: 02 Sep 2009
Posts: 53063
You are given the data set {14, 35, 44, 47, 49, 49, 50, 51, 56, N}, wh  [#permalink]

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31 Jan 2019, 00:42
00:00

Difficulty:

35% (medium)

Question Stats:

64% (01:08) correct 36% (00:46) wrong based on 33 sessions

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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  [#permalink]

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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  [#permalink]

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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:
• The value of N

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.

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Re: You are given the data set {14, 35, 44, 47, 49, 49, 50, 51, 56, N}, wh   [#permalink] 31 Jan 2019, 06:44
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