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E is a collection of four ODD integers and the greatest

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Re: E is a collection of four ODD integers and the greatest  [#permalink]

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New post 15 Aug 2018, 19:51
Hi zs2,

IF you want to use the numbers +1 and -3 as two of your four odd numbers, then that's absolutely fine; by extension though, since those two values differ by 4, each of the OTHER two ODD numbers in the set would have to be +1, -1 or -3.

Thus, your possible Standard Deviations would be...
-3, 1, 1, 1.... which has the SAME S.D. as -3, -3, -3, 1, so we only count this option ONCE.
-3, -3, 1, 1
-3, -3, -1, 1... which has the SAME S.D as -3, -1, 1, 1, so we only count this option ONCE.
-3, -1, -1, 1

You still end up with 4 DIFFERENT possible S.D.s

This same pattern will occur if you use the numbers 13 and 17 too.

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Re: E is a collection of four ODD integers and the greatest  [#permalink]

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New post 05 Feb 2019, 06:13
Hi Bunuel,

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

-KHow

Bunuel wrote:
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.
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Re: E is a collection of four ODD integers and the greatest  [#permalink]

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New post 17 Feb 2019, 02:21
why are we not using negative integers such as (-3,1,-1,1)
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Re: E is a collection of four ODD integers and the greatest  [#permalink]

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New post 17 Feb 2019, 13:40
1
Hi shivmsp,

IF you want to use the numbers +1 and -3 as two of your four odd numbers, then that's absolutely fine; by extension though, since those two values differ by 4, each of the OTHER two ODD numbers in the set would have to be +1, -1 or -3.

Thus, your possible Standard Deviations would be...
-3, 1, 1, 1.... which has the SAME S.D. as -3, -3, -3, 1, so we only count this option ONCE.
-3, -3, 1, 1
-3, -3, -1, 1... which has the SAME S.D as -3, -1, 1, 1, so we only count this option ONCE.
-3, -1, -1, 1

You still end up with 4 DIFFERENT possible S.D.s

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

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Special Offer: Save $75 + GMAT Club Tests Free
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Re: E is a collection of four ODD integers and the greatest   [#permalink] 17 Feb 2019, 13:40

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E is a collection of four ODD integers and the greatest

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