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# gmatprep statistics ds

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Joined: 22 Nov 2007
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09 Mar 2008, 03:07
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x, 3, 1, 12, 8

If x is an integer, is the median of the 5 numbers shown greater than the
average (arithmetic mean) of the 5 numbers?

(1) x > 6
(2) x is greater than the median of the 5 numbers.

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Senior Manager
Joined: 20 Dec 2004
Posts: 252

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09 Mar 2008, 07:27
Rearrange the letters as 1,3,8,12 and a x.

From statement 1: x can take values: 7, 9, 10,11, 13,....100
Corresponding Median/Avg for these values of x would be : [7,5.2], [8,5.5], [8,5.66],[8,5.8],[8,6.1],[8,24.8]
So statement 1 is insufficient.

From statement2: x can take values: 9,10,11,13,...100
Corresponding Median/Avg for these values of x would be : [8,5.5], [8,5.66],[8,5.8],[8,6.1],[8,24.8]
So statement 2 is insufficient.

Taking both of them together would still not help.

So should be E. OA pls.
_________________

Stay Hungry, Stay Foolish

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Senior Manager
Joined: 30 Nov 2008
Posts: 485

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Schools: Fuqua

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04 Dec 2008, 10:15
Answer is B. Here is the explanation.

For a median, the numbers should be in the ascending order and the median is the middle number in the series.

From clue 1, x>6, it can be 7,8,9,10.....etc (In the series, numbers can be repeated)

So possible series can be 1 3 7 8 12, 1 3 8 8 12, 1 3 8 9 12, 1 3 8 10 12, 1 3 8 12 12 etc....
So possible Median to Avg figures are (7,6.2 or 8,6.4 or 8, 6.6 etc) as X increases, AVG increases but median can be fixed at 8. So we cannot conclude from Clue 1.

From clue 2, we can arrange the series as 1 3 8 x 12 or 1 3 8 12 x. So possible values are x >= 8. So if you take x as 8, then Median is 8 and Avg is (1+3+8+8+12) / 5 = 8.8 which is greater than Median.

From clue 2, we can definitely say No for the question "Is Median greater than average of the 5 numbers). In other words, with Clue 2 you can answer the question. So answer is B.

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Senior Manager
Joined: 30 Nov 2008
Posts: 485

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05 Dec 2008, 10:51
That's true. Answer should be E.

I did a minor mistake in my speed caluculation.

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Re: gmatprep statistics ds   [#permalink] 05 Dec 2008, 10:51
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