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Director  Joined: 30 Jun 2008
Posts: 797

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Which of the following sets must have the same standard deviation as set {a, b, c}?

A. {ab, b^2, cb}
B. {2a, b + a, c + b}
C. {0, b + a, c - a}
D. {ab, bc, ac}
E. {ab + c, a(1 + b), b(1+a)}

(C) 2008 GMAT Club - m11#9

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VP  Joined: 17 Jun 2008
Posts: 1021

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The standard deviation of a set does not change if a constant is added to all the members.

Thus, standard deviation of (a,b,c) will be the same as of (a+ab, b+ab, c+ab).

And, option E is the same as (a+ab, b+ab, c+ab).
SVP  Joined: 29 Aug 2007
Posts: 1775

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scthakur wrote:
The standard deviation of a set does not change if a constant is added to all the members.

Thus, standard deviation of (a,b,c) will be the same as of (a+ab, b+ab, c+ab).

And, option E is the same as (a+ab, b+ab, c+ab).

Beautiful approach by scthakur. Thats the best approach to this question. +1.

SD of a, b and c and (a+x), (b+x) and (c + x) is the same.
Trying to find exactly what is the SD of a, b and c and the same of each of the options in the question doesnot help solve this question. What helps is understanding the question.
Joined: 31 Dec 1969
Location: Russian Federation
WE: Supply Chain Management (Energy and Utilities)

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My approach was actually using real numbers such as a=2, b=3 and c=4. Though abit lengthy it worked since I applied the rule, the less spread out my answers were the closer my answer was making it E. Thanx now I know another rule;The standard deviation of a set does not change if a constant is added to all the members.
Intern  Joined: 28 Jul 2010
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E, addition or subtraction of Same constant term does not change standard deviation of the numbers
Manager  Joined: 21 Nov 2010
Posts: 79

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Standard Deviation is the spread of numbers. question is asking which spread of letters equals a, b, c.

I picked numbers 2, 4, 6 for a, b, c.
Plugged in to find another set that has the same SD of 2. E is the only one that worked.

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Please give me kudos if my post helps you.
Math Expert V
Joined: 02 Sep 2009
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amitdgr wrote:
Which of the following sets has the same standard deviation as set (a, b, c)?

(C) 2008 GMAT Club - m11#9

* $$(ab, b^2, cb)$$
* $$(2a, b + a, c + b)$$
* $$(0, b + a, c - a)$$
* $$(ab, bc, ac)$$
* $$(ab + c, a(1 + b), b(1+a))$$

Spoiler: :: OA
E

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http://gmatclub.com/tests/m11#expl9

Which of the following sets must have the same standard deviation as set {a, b, c}?

A. {ab, b^2, cb}
B. {2a, b + a, c + b}
C. {0, b + a, c - a}
D. {ab, bc, ac}
E. {ab + c, a(1 + b), b(1+a)}

If we add or subtract a constant to each term in a set the standard deviation will not change.

Notice that set {(ab + c, a(1 + b), b(1+a)}={c+ab, a+ab, b+ab}, so this set is obtained by adding some number ab to each term of set {a, b, c}, which means that those sets must have the same standard deviation.

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Manager  B
Joined: 13 Feb 2012
Posts: 128
Location: Italy
Concentration: General Management, Entrepreneurship
GMAT 1: 560 Q36 V34
GPA: 3.1
WE: Sales (Transportation)

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2
Plugging numbers in it's not so time wasting, even though it is prone to errors.

I put a=1, b=2, c=3 with a S.D of +/- 1

A = 2,4,6
B = 2,3,5
C = 0,3,2
D = 2,6,3
E = 5,3,4

E is the only set that has its numbers spread one integer apart.
Intern  Status: At the end all are winners, Some just take a little more time to win.
Joined: 08 Oct 2013
Posts: 14
Location: India
Concentration: Finance, Accounting
GMAT Date: 11-20-2013
GPA: 3.97
WE: Consulting (Computer Software)

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Awesome and crisp approach by scthakur and Bunuel..Great work
Intern  Joined: 05 Dec 2013
Posts: 12

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I took a similar, although longer, approach to solving this problem as the person above me. Immediately understanding that this problem was evaluating the spread, I relied on the use of "plugging" numbers in for a,b,c (1,2,3) and then looked for a similar spread amongst the answer choices.

Having read and followed the Manhattan Advanced Quant books, I first started with E and realized that this is the right answer --> matches to my "target"

Would of been even quicker if I would of realized that "ab" is consistent, a constant, throughout the 3 terms; and adding a constant to the terms does not alter the spread. Thanks for the clarification on this one guys! Re: m11#9   [#permalink] 20 Dec 2013, 18:33
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# m11#9

Moderator: Bunuel  