Is there a simple algebraic approach to solve this within 2 minutes? I am really getting stuck on this one. Thank you!!

I know this question, I've posted it in my topic:

http://gmatclub.com/forum/ps-questions- ... 85897.html But there is a typo, it should be:

E is a collection of four ODD integers and the greatest difference between any two integers in E is 4. The standard deviation of E must be one of how many numbers?(A) 3

(B) 4

(C) 5

(D) 6

(E) 7

Let the smallest odd integer be 1, thus the largest one will be 5. We can have following 6 types of sets:

1. {1, 1, 1, 5} --> mean=2 --> |mean-x|=(1, 1, 1, 3);

2. {1, 1, 3, 5} --> mean=2.5 --> |mean-x|=(1.5, 1.5, 0.5, 2.5);

3. {1, 1, 5, 5} --> mean=3 --> |mean-x|=(2, 2, 2, 2);

4. {1, 3, 3, 5} --> mean=3 --> |mean-x|=(2, 0, 0, 2);

5. {1, 3, 5, 5} --> mean=3.5 --> |mean-x|=(2.5, 0.5, 1.5, 1.5);

6. {1, 5, 5, 5} --> mean=4 --> |mean-x|=(3, 1, 1, 1).

CALCULATING STANDARD DEVIATION OF A SET {x1, x2, ... xn}:1. Find the mean, \(m\), of the values.

2. For each value \(x_i\) calculate its deviation (\(m-x_i\)) from the mean.

3. Calculate the squares of these deviations.

4. Find the mean of the squared deviations. This quantity is the variance.

5. Take the square root of the variance. The quantity is th SD.

Expressed by formula: \(standard \ deviation= \sqrt{variance} = \sqrt{\frac{\sum(m-x_i)^2}{N}}\).

You can see that deviation from the mean for 2 pairs of the set is the same, which means that SD of 1 and 6 will be the same and SD of 2 and 5 also will be the same. So SD of such set can take only 4 values.

Answer: B.

Hope it's clear.