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# Set S includes elements {8, 2, 11, x, 3, y} and has a mean

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Intern
Joined: 03 Apr 2009
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Set S includes elements {8, 2, 11, x, 3, y} and has a mean [#permalink]

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28 Apr 2009, 19:47
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Difficulty:

45% (medium)

Question Stats:

69% (01:43) correct 31% (01:41) wrong based on 280 sessions

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Set 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
[Reveal] Spoiler: OA

Last edited by Bunuel on 13 Jul 2014, 04:26, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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Manager
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Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean [#permalink]

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29 Apr 2009, 08:59
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First, reach to the point of getting the equation : x + y = 18
It should take about 20 seconds.

Then Substitute the answer choices into the equation.
I don't know what the answer choices in this case are.
But I'm sure, you would be able to eliminate at least 2 or 3 answer choices. (about 10 seconds).

Say you are left with 2 answer choices. (If you are short on time, guess One of the two and you'll have a 50% probability of getting it right.)

The Median (of 6 numbers) = 5.5. See if the AVERAGE of any two numbers among (2,3,8,11) results in the median. In this case, it does for 3 and 8. (15 seconds).
Once you know that the numbers that contribute towards Median are 3 and 8, and not x or y, then given x < y, x 3. (about 10 seconds)

In less than a minute, you have the Correct answer.

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Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean [#permalink]

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01 May 2009, 13:33
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Expert's post
Abdulla wrote:
Set 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?

OA is 3

If any one knows how to solve this problem fast please share it.

Thanks..

Using the fact that the mean is 7, then x+y = 18. Since x and y are different, one must be less than 9, the other greater than 9. Since x is smaller than y, we know that x < 9.

Now we need to use the median, which is the average of the two middle elements. Say x is greater than 3. Then we will have (since y is larger than 9), the elements x and 8 in the middle of our set, and the median will be (8 + x)/2. If x is greater than 3, then this will be larger than 11/2 = 5.5, so x cannot be greater than 3. Can x be exactly equal to 3? Sure. Then y = 15. So the largest possible value for x is 3.
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Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean [#permalink]

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12 Jul 2014, 19:33
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Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean [#permalink]

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11 Sep 2015, 01:55
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2,3,8,11 and x,y

we are asked maximal x, so can start backsolving from E. If x=4 it will be 3th term and median=4+8/2=6, so out.
If x=3, median=3+8/2=5.5, so right

D

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Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean [#permalink]

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10 Dec 2016, 18:13
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All solutions mentioned above are confusion below one seems to be very understandble.

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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Thanks & Regards,
Anaira Mitch

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Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean   [#permalink] 10 Dec 2016, 18:13
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