If 0

Question

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.

amanvermagmat · Answer

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.

Hence  D answer

push12345 · Answer

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

Answer D

Posted from my mobile device

kanishaksharma · Answer

1) c-a=2(c-b)
 (c-a)/2 = b , which means b is average mean of a and c, and also is median.
2) first case: a+b+c=3a (Not possible because for that to happen b and c either need to be equal to a or less than a)
 second case: a+b+c=3b
 a+c=2b (again, it means b is average mean of a and c)
 third case: a+b+c=3c (Not possible since for that to happen a and b needs to be at least equal to c, which is not true)
Hence either of the statement is sufficient.

andrenoble · Answer

Hi  Bunuel ! THank you for the question, it's a really interesting one! My only concern is that (2) in 2 cases contradicts the initial statement in the question, because if a < b < c, then a + b + c != 3a or 3c. Is there a way to rephrase the question to eliminate this confusion?

Bunuel · Answer

Yes, because 0 < a < b < c, then from (2) we get that a + b + c = 3b only but where is the contradiction here?

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions