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Median 5.5

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Median 5.5

by jain2016 » Wed Feb 24, 2016 9:13 am
List S includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x?

A)0

B)1

C)2

D)3

E)4

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Hi Experts ,

Please explain
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by [email protected] » Wed Feb 24, 2016 9:55 am
Hi jain2016,

I'm going to give you a couple of hints so that you can work through this question on your own:

[spoiler]
1) Since there are 6 terms in List S, the MEDIAN will be the average of the two 'middle terms' (once you put them in order from least to greatest).
2) Since the median = 5.5, the two 'middle terms could both be 5.5, or they could be 5 and 6, or some other pairing that adds up to 11.
3) Since the MEAN = 7, the sum of all 6 terms MUST equal 42... so what would the sum of x+y equal?
4) Remember that the prompt also tells us that X < Y
[/spoiler]

Considering all of the above 'restrictions', AND the fact that the 5 answer choices are numbers, how long would it take you to figure out the MAXIMUM possible value of X?

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Rich
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by jain2016 » Wed Feb 24, 2016 9:12 pm
Hi Rich ,

Thanks for your hint. I got it.

Thanks,

SJ
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by shivsuddala » Thu Feb 25, 2016 1:24 am
jain2016 wrote:List S includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x?

A)0

B)1

C)2

D)3

E)4

OAD

Hi Experts ,

Please explain
Calculate Mean value we get x+y=18; as given in the statement median =5.5;Question is asked about max.possible value of x. so use trail and error method with largest value.
if we choose x=4 ; then y=14 , we get median of 6 which is wrong
if we choose x=3; y=8, we get median of 5.5 which satisfies.
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by Matt@VeritasPrep » Tue Mar 01, 2016 11:43 pm
That is a nice solution!

You could also say that since the mean is 7, x + y = 18. Since we have an even number of terms in the set, the median must be the average of the two middle numbers. Our possibilities are

(x + y)/2 = 5.5
(3 + 8)/2 = 5.5
(x + 8)/2 = 5.5

The first one doesn't work, as it contradicts our equation above (that x + y = 18).

If x = 3, the other two both work, so x = 3 is a possible solution. x > 3 is not, as we won't have a median of 5.5, so we're set!
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