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# In a certain district , the minimum of the monthly rainfall

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Senior Manager
Joined: 19 Oct 2004
Posts: 318
Location: Missouri, USA
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In a certain district , the minimum of the monthly rainfall [#permalink]  14 Nov 2004, 13:18
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In a certain district , the minimum of the monthly rainfall is 0.2, max is 12.2 and the average of 12 months is 3.5. Which of the following is the greatest possible value of the median?

A. 2.4
B 3.5
C 4.2
D 4.8
E 6.2
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GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4312
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D) 4.8
Median is b/w 6-7 month
Total rain: 12*3.5 = 42
Minimize 5 lowest rain months with .2 each month you get 5*.2 = 1
Most rainy month is 12.2
Total is 13.2
To have max median, spread 42-13.2 = 28.8 over remaining 6 months of rain: 28.8/6 = 4.8 --> max median value
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Best Regards,

Paul

Senior Manager
Joined: 19 Oct 2004
Posts: 318
Location: Missouri, USA
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Kudos [?]: 23 [0], given: 0

You are right Paul. Thanks a lot
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Let's get it right!!!!

Senior Manager
Joined: 19 May 2004
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Could you please explain why you minimized it to "5 lowest rain months" ?
Director
Joined: 07 Nov 2004
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Paul, that was very useful. I gues the key is greatest possible value for the median. That can be obtained if the first 5 months had the lowest rainfall!
GMAT Club Legend
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In order to have the highest median value, the average of the 6 and 7 month, you have to make it such that the first 5 months are at a minimum(0.2) so as to keep the most for the median value when you reach 6th and 7th month.
For the values above the 7th month, you have to minimize them so as to keep, save, the highest possible score for the 7th month. However, you know that the highest month is 12.2 so get that one out of the way as I did and you will have the remainder (28.8) which you can now spread over the remaining 6 middle months (6,7,8,9,10,11). This way, you will maximize the median which is b/w 6th and 7th month

From lowest to highest raining month:
1: 0.2
2: 0.2
3: 0.2
4: 0.2
5: 0.2
6: 4.8
7: 4.8

8: 4.8
9: 4.8
10: 4.8
11: 4.8
12: 12.2
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Best Regards,

Paul

Senior Manager
Joined: 19 May 2004
Posts: 291
Followers: 1

Kudos [?]: 8 [0], given: 0

Got it, thanks Paul
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