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# M11-09

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Math Expert
Joined: 02 Sep 2009
Posts: 52294

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15 Sep 2014, 23:44
2
11
00:00

Difficulty:

55% (hard)

Question Stats:

57% (00:42) correct 43% (00:56) wrong based on 134 sessions

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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. $$\{ab + c, \ a(1 + b), \ b(1+a)\}$$

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Joined: 02 Sep 2009
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15 Sep 2014, 23:44
2
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Official Solution:

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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Intern
Joined: 25 Apr 2015
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09 Dec 2015, 14:25
What about choice A? {ab, b2, cb} = b{a,b,c)?
Current Student
Joined: 18 Aug 2014
Posts: 324

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03 May 2016, 12:25
rhio wrote:
What about choice A? {ab, b2, cb} = b{a,b,c)?

This is what I did
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Manager
Joined: 15 Apr 2016
Posts: 71

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20 Jun 2016, 08:59
rhio wrote:
What about choice A? {ab, b2, cb} = b{a,b,c)?

Hi Rhio,

Multiplication changes the standard deviation.
Here we are multiplying everything with b which means even the SD is being multiplies with b.

Hope this helps

-------------------------
Shrivathsan
GMAT 700 it is ---
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Cheers,
Shri
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GMAT is not an Exam... it is a war .. Let's Conquer !!!

Senior Manager
Joined: 31 Mar 2016
Posts: 384
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)

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06 Aug 2016, 10:13
I think this is a high-quality question and I agree with explanation.
Intern
Joined: 27 Oct 2015
Posts: 19

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16 Dec 2016, 19:35
Please can someone explain why Choice D {ab,bc, ac} is incorrect?

Many Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 52294

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17 Dec 2016, 02:53
dsheth7 wrote:
Please can someone explain why Choice D {ab,bc, ac} is incorrect?

Many Thanks

Why should {ab, bc, ac} have the same SD as {a, b, c}? You can substitute numbers to check that's it won't always be true.
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Joined: 07 Feb 2016
Posts: 21
GMAT 1: 650 Q47 V34
GMAT 2: 710 Q48 V39

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01 May 2017, 21:25
Bunuel wrote:
dsheth7 wrote:
Please can someone explain why Choice D {ab,bc, ac} is incorrect?

Many Thanks

Why should {ab, bc, ac} have the same SD as {a, b, c}? You can substitute numbers to check that's it won't always be true.

As already mentioned, the standard deviation does not change when a specific value is added/subtracted from ALL values of the set. Multiplication/division is changing the standard deviation.
Intern
Joined: 25 Oct 2017
Posts: 1

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21 May 2018, 07:46
Why is choice B incorrect?
{2a,a+b,c+a} means a is being added to each number of the set
Math Expert
Joined: 02 Sep 2009
Posts: 52294

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21 May 2018, 07:53
aritra210190 wrote:
Why is choice B incorrect?
{2a,a+b,c+a} means a is being added to each number of the set

Option B is $$\{2a, \ b + a, \ c + b\}$$ not {2a, a+b, c+a}
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Manager
Joined: 06 May 2018
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21 May 2018, 08:11
Test numbers. That helps. For example 5,10, 15. For answer choice c you get 65,55,60. As you can easily see, the deviation is the same.
Manager
Joined: 29 Sep 2017
Posts: 114
Location: United States
GMAT 1: 720 Q49 V39
GPA: 3.3
WE: Consulting (Consulting)

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08 Jun 2018, 14:08
2 quick ways to solve:

1. Pick small numbers
2. Follow bunnel's solution (recognize the pattern in E)

I went with 1 and took 2:43 to solve this which is very much above what it should take. The question is... how does one spot patterns quickly (rhetorical)?
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Re: M11-09 &nbs [#permalink] 08 Jun 2018, 14:08
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# M11-09

Moderators: chetan2u, Bunuel

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