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M11-09

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Bunuel
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M11-09 [#permalink] New post  16 Sep 2014, 00:44
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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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Bunuel
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Re: M11-09 [#permalink] New post  12 Jun 2020, 00:11
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davidbeckham wrote:
Bunuel - I have a very basic doubt on solving quant questions generally. How do we know when to pick numbers and when to solve the question directly, just by looking at the question? I tried picking up numbers for this question and wasted a lot of time in the process and didn't even get the answer in the first place.


Check the links below:

Backsolving on GMAT Math
How to Plug in Numbers on GMAT Math Questions
Why Approximate?
GMAT Math Strategies — Estimation, Rounding and other Shortcuts
The Power of Estimation for GMAT Quant
The 4 Math Strategies Everyone Must Master, Part 1 (1. Test Cases and 2. Choose Smart Numbers.)
The 4 Math Strategies Everyone Must Master, part 2 (3. Work Backwards and 4. Estimate)
Intelligent Guessing on GMAT
How to Avoid Tedious Calculations on the Quantitative Section of the GMAT
GMAT Tip of the Week: No Calculator? No Problem.
The Importance of Sorting Answer Choices on the GMAT
Identifying the Correct Answer on GMAT Quant Questions
How to Manage Unmanageable Numbers on the GMAT
Should You Double Check Your Answer Choices on the GMAT?
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Re M11-09 [#permalink] New post  16 Sep 2014, 00:44
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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.

Observe that set \(\{ab + c, \ a(1 + b), \ b(1+a)\}=\{c+ab, \ a+ab, \ b+ab\}\). This set is obtained by adding some number \(ab\) to each term of set \(\{a, \ b, \ c\}\). This means that these sets must have the same standard deviation.


Answer: E
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rhio
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Re: M11-09 [#permalink] New post  09 Dec 2015, 15:25
What about choice A? {ab, b2, cb} = b{a,b,c)?
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Re: M11-09 [#permalink] New post  20 Jun 2016, 09:59
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 :)

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Re: M11-09 [#permalink] New post  06 Aug 2016, 11:13
I think this is a high-quality question and I agree with explanation.
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Re: M11-09 [#permalink] New post  07 Jun 2020, 09:21
I think this is a high-quality question and I agree with explanation.
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Re: M11-09 [#permalink] New post  11 Jun 2020, 22:29
Bunuel - I have a very basic doubt on solving quant questions generally. How do we know when to pick numbers and when to solve the question directly, just by looking at the question? I tried picking up numbers for this question and wasted a lot of time in the process and didn't even get the answer in the first place.
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Re: M11-09 [#permalink] New post  03 Jun 2021, 19:04
I think this is a high-quality question and I agree with the explanation.
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Re: M11-09 [#permalink] New post  06 Jun 2021, 07:16
Why is C wrong ? Adding/ subtracting "A" from each should not change the answer?
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Bunuel
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Re: M11-09 [#permalink] New post  06 Jun 2021, 09:44
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RRJ12 wrote:
Why is C wrong ? Adding/ subtracting "A" from each should not change the answer?


The SD will not change if we ONLY add or ONLY subtract a constant from each term in a set. In C we are subtracting from a from a and c but adding a to b.
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Re: M11-09 [#permalink] New post  18 Jun 2023, 14:23
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M11-09 [#permalink]
18 Jun 2023, 14:23
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