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Mean = median --> evenly spaced question

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Source: — Data Sufficiency |

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by Anurag@Gurome » Fri Sep 23, 2011 7:41 pm
myfish wrote:mean = median means the set is equally spaced? if so, why are the numbers not evenly spaced in the question? Thank you everyone.


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(1) 7 < x < 11
Arranging the numbers in ascending order, we get, 2, 7, x, 11, 16, which clearly implies that x is the median.
Mean = (2 + 7 + x + 11 + 16)/5 = (36 + x)/5
Now, mean = median implies (36 + x)/5 = x
Solving we get, 4x = 36 or x = 9; SUFFICIENT.

(2) x is the median of 5 numbers.
The same calculation as in statement 1 follows; SUFFICIENT.

The correct answer is D.
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by myfish » Fri Sep 23, 2011 8:38 pm
I have read numerous times that when the mean equals the median, the set is equally spaced, right? If this set is equally spaced, the numbers do not add up. There is 5 between 2 and 7, 4 between 7 and 11, and 5 between 11 and 16. So, the set is not equally spaced but the median = average?

[quote="Anurag@Gurome"][quote="myfish"]mean = median means the set is equally spaced? if so, why are the numbers not evenly spaced in the question? Thank you everyone.


[url=https://postimage.org/image/z33d1msk/][img]https://s4.postimage.org/z33d1msk/PS_8_35.jpg[/img][/url][/quote]

(1) 7 < x < 11
Arranging the numbers in ascending order, we get, 2, 7, x, 11, 16, which clearly implies that x is the median.
Mean = (2 + 7 + x + 11 + 16)/5 = (36 + x)/5
Now, mean = median implies (36 + x)/5 = x
Solving we get, 4x = 36 or x = 9; SUFFICIENT.

(2) x is the median of 5 numbers.
The same calculation as in statement 1 follows; SUFFICIENT.

The correct answer is [spoiler]D[/spoiler].[/quote]
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by Ian Stewart » Fri Sep 23, 2011 9:59 pm
myfish wrote:mean = median means the set is equally spaced?
No, that's backwards. When a set is equally spaced, then yes, the mean and median are always equal. But the reverse is not necessarily true. For example, in the set below, the mean and median are equal:

0, 1, 50, 99, 100

but the set is certainly not equally spaced.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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