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by bryan88 » Sun May 13, 2012 6:27 am
If S is a finite set of consecutive even numbers, is the median of S an odd number?

(1) The mean of set S is an even number.

(2) The range of set S is divisible by 4.


Any useful/quick way for verifying 2?
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Source: — Data Sufficiency |
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by sam2304 » Sun May 13, 2012 6:49 am
If S is a finite set of consecutive even numbers, is the median of S an odd number?

(1) The mean of set S is an even number.
In an equally spaced set mean = median. So if mean is even median is even. NO. SUFF
(2) The range of set S is divisible by 4.
Range is a multiple of 4.
2 4 6
2 4 6 8 10

So the set has odd number of values and median will always be the mid one which is even. SUFF

IMO D.
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by bryan88 » Sun May 13, 2012 7:04 am
By your reasoning A is sufficient as it answers Yes /No
sam2304 wrote:
If S is a finite set of consecutive even numbers, is the median of S an odd number?

(1) The mean of set S is an even number.
In an equally spaced set mean = median. So if mean is even median is even. NO. SUFF
(2) The range of set S is divisible by 4.
Range is a multiple of 4.
2 4 6
2 4 6 8 10

So the set has odd number of values and median will always be the mid one which is even. SUFF

IMO D.
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by sam2304 » Sun May 13, 2012 9:28 am
bryan88 wrote:By your reasoning A is sufficient as it answers Yes /No
I don't get your query. If you are asking whether it is sufficient, then YES it is by itself sufficient.
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by bryan88 » Sun May 13, 2012 9:38 am
I think A is sufficient because the mean/median of consecutive integers cannot be an integer if the number of integers is even.
IMO we dont need to check for "even" / "odd".

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sam2304 wrote:
bryan88 wrote:By your reasoning A is sufficient as it answers Yes /No
I don't get your query. If you are asking whether it is sufficient, then YES it is by itself sufficient.
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by Brent@GMATPrepNow » Mon May 14, 2012 5:15 am
bryan88 wrote:I think A is sufficient because the mean/median of consecutive integers cannot be an integer if the number of integers is even.
IMO we dont need to check for "even" / "odd".

Experts help
sam2304 wrote:
bryan88 wrote:By your reasoning A is sufficient as it answers Yes /No
I don't get your query. If you are asking whether it is sufficient, then YES it is by itself sufficient.
You're right in saying that the mean/median of consecutive integers cannot be an integer if the number of integers is even. However, the question involves a "set of consecutive even numbers."

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by GMATGuruNY » Mon May 14, 2012 7:09 am
bryan88 wrote:If S is a finite set of consecutive even numbers, is the median of S an odd number?

(1) The mean of set S is an even number.

(2) The range of set S is divisible by 4.

Any useful/quick way for verifying 2?
With evenly spaced integers:
Median = mean = (biggest+smallest)/2.

Statement 1: The mean of set S is an even number.
Since median = mean, the median is an even number.
SUFFICIENT.

Statement 2: The range of set S is divisible by 4.
Let b = the biggest integer and s = the smallest.
Since b-s = 4k, b = s+4k.
Thus, the median = (b+s)/2 = ((s+4k) + s)/2 = s + 2k.
Since s and 2k are both even, the median is even.
SUFFICIENT.

The correct answer is D.
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