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Set S includes elements {8, 2, 11, x, 3, y} and has a mean [#permalink]
28 Apr 2009, 18:47

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Difficulty:

65% (hard)

Question Stats:

61% (02:47) correct
39% (01:50) wrong based on 158 sessions

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?

Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean [#permalink]
29 Apr 2009, 07:59

1

This post received KUDOS

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.

Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean [#permalink]
01 May 2009, 12:33

1

This post received KUDOS

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. _________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Re: Set S includes elements {8, 2, 11, x, 3, y} and has a mean [#permalink]
12 Jul 2014, 18:33

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