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

00:00

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Difficulty:

55% (hard)

Question Stats:

54% (02:47) correct
46% (01:31) wrong based on 58 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

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

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. _________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

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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