For which of the following sets does the median of the set equal the

Question

For which of the following sets does the median of the set equal the average (artithmetic mean) of the set?

I. (x, x+2, x+4)
II. (x, 3x, 5x)
III. (x/3, x/2, x)

A. I only
B. III only
C. II and III only
D. I and II only
E. I, II and III

z.helen17 · Answer

For Set I:
median = x+2
avg = (x+x+2+x+4)/3=(3x+6)/3=x+2 - same as median

For Set II:
median = 3x
avg = (x+3x+5x)/3=9x/3=3x - same as median

For set III:
median = x/2
avg = (x/3+x/2+x)/3=(2x/6+3x/6+6x/6)/3=11x/18 which is different from x/2=9x/18

So solution is D

QuantMadeEasy · Answer

Step 1: Understanding the question: For mean = median of three numbers is possible when the numbers are in arithmetic progression (AP). AP is a sequence in which difference between any two consecutive terms is equal. Step 2: Solving the question I. x , x+2, x+4 is in AP as common difference is 2. Correct II. x, 3x, 5x is in AP as common difference is 2x. Correct III. x/3, x/2, x is not in an AP. Incorrect D is correct For complete pocket friendly GMAT Quant video course: https://www.udemy.com/course/best-gmat- ... 37602183BB

For which of the following sets does the median of the set equal the

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For which of the following sets does the median of the set equal the