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# If 0 < a < b < c, does the median of a, b, and c equal the mean of a,

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Math Expert
Joined: 02 Sep 2009
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If 0 < a < b < c, does the median of a, b, and c equal the mean of a,  [#permalink]

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13 Apr 2018, 00:21
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Difficulty:

65% (hard)

Question Stats:

50% (01:48) correct 50% (02:14) wrong based on 62 sessions

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If 0 < a < b < c, does the median of a, b, and c equal the mean of a, b, and c?

(1) The range of a, b, and c equals 2(c - b).
(2) The sum of a, b, and c is three times one of the numbers a, b, or c.

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Re: If 0 < a < b < c, does the median of a, b, and c equal the mean of a,  [#permalink]

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13 Apr 2018, 10:01
Bunuel wrote:
If 0 < a < b < c, does the median of a, b, and c equal the mean of a, b, and c?

(1) The range of a, b, and c equals 2(c - b).
(2) The sum of a, b, and c is three times one of the numbers a, b, or c.

Here a, b, c are unequal positive numbers such that a < b < c. So their median is definitely 'b'. We need to know whether their mean is also equal to 'b' or not.

(1) Range of a, b, c = c - a. This is given as 2(c-b). So c - a = 2c - 2b or c = 2b - a or c + a = 2b.
Their mean = (a+b+c)/3 = (2b+b)/3 = b. So the mean is same as median. Sufficient.

(2) Sum = a+b+c. Since the numbers are unequal and sum is three times one of these, it could only be equal to three times b (since b is the middle number).
So a+b+c = 3b or a+c = 2b. Same as in first statement, so mean = b, same as median. Sufficient.

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Re: If 0 < a < b < c, does the median of a, b, and c equal the mean of a,  [#permalink]

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27 Apr 2018, 21:32
Mean would be equal to median if sequence is in AP

I)c-a=2(c-b)
Solving this we get
2b=c+a
Which is basic condition of AP
Sufficient

II)a+b+c=3a or 3b or 3c
Which will yield to a+c=2b or a+b=2c or b+c=2a
In every case basic condition of AP is fulfilled
Sufficient

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Re: If 0 < a < b < c, does the median of a, b, and c equal the mean of a, &nbs [#permalink] 27 Apr 2018, 21:32
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