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# In the data set, {a, 0, 1, 6, 9, 10, 11}, consisting of seven distinct

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Manager
Joined: 18 Jul 2019
Posts: 54
In the data set, {a, 0, 1, 6, 9, 10, 11}, consisting of seven distinct  [#permalink]

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25 Nov 2019, 06:23
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Difficulty:

55% (hard)

Question Stats:

43% (01:51) correct 57% (01:50) wrong based on 21 sessions

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In the data set, {a, 0, 1, 6, 9, 10, 11}, consisting of seven distinct integers, one of the numbers is the mean as well as the median. How many values of ‘a’ are possible?

a) 1
b) 2
c) 3
d) 4
e) 5
Director
Joined: 27 May 2012
Posts: 947
In the data set, {a, 0, 1, 6, 9, 10, 11}, consisting of seven distinct  [#permalink]

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25 Nov 2019, 12:04
CaptainLevi wrote:
In the data set, {a, 0, 1, 6, 9, 10, 11}, consisting of seven distinct integers, one of the numbers is the mean as well as the median. How many values of ‘a’ are possible?

a) 1
b) 2
c) 3
d) 4
e) 5

Total of the data set is $$= 37+a$$

One of the numbers is the mean as well as the median so:

If mean is 0 as then total of Data set would be 7*0= 0 which implies $$37+a=0$$ which implies $$a=$$ -37
So set looks like { -37,0, 1, 6, 9,10,11} is this NOT valid as mean $$\neq$$ median , mean=0 and median =6

If mean is 1 as then total of the data set would be 7*1=7 which implies $$37+a=7$$ which implies $$a=$$ -30
So set looks like { -30,0, 1, 6, 9,10,11} is this NOT valid as mean $$\neq$$ median , mean=7 and median =6

If mean is 6 then total of data set is 7*6= 42 which implies $$37+a=42$$ which implies $$a=$$ 5
So set looks like { 0, 1, 5, 6, 9,10,11} is this valid as mean = median = 6

If mean is 9 then total of data set is 7*9= 63 which implies $$37+a=63$$ which implies $$a=$$ 26
So set looks like { 0, 1, 6, 9,10,11,26} is this also valid as mean = median = 9

If mean is 10 then total of data set is 7*10=70 which implies $$37+a=70$$ which implies $$a=$$33
So set would look like { 0, 1, 6, 9,10,11,33} this is NOT valid as mean $$\neq$$median , mean is 10 and median is 9

Hence among the elements of the data set mean cannot be 0,1, 10,11 and 13 as then mean $$\neq$$median.

Thus we can have only two values of mean 6 and 10 such that mean= median, leading to two values for $$a$$ (5 and 26)

Ans-B
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In the data set, {a, 0, 1, 6, 9, 10, 11}, consisting of seven distinct   [#permalink] 25 Nov 2019, 12:04
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