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# The figure shows a square with a side length of 5m. A side of the squ

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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The figure shows a square with a side length of 5m. A side of the squ  [#permalink]

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26 May 2020, 01:26
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Difficulty:

65% (hard)

Question Stats:

53% (02:29) correct 47% (02:00) wrong based on 49 sessions

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[GMAT math practice question]

The figure shows a square with a side length of $$5m$$. A side of the square is divided equally into $$5$$ segments. The square is cut into $$5$$ pieces, as the figure shows. What is the standard deviation of the areas of those $$5$$ pieces?

Attachment:

5.26ps.png [ 11.37 KiB | Viewed 609 times ]

A. $$2$$

B. $$√5$$

C. $$√6$$

D. $$√7$$

E. $$2√2$$

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" GMAT Club Legend Status: GMATINSIGHT Tutor Joined: 08 Jul 2010 Posts: 4312 Location: India GMAT: QUANT EXPERT Schools: IIM (A) GMAT 1: 750 Q51 V41 WE: Education (Education) The figure shows a square with a side length of 5m. A side of the squ [#permalink] ### Show Tags 26 May 2020, 01:54 MathRevolution wrote: [GMAT math practice question] The figure shows a square with a side length of $$5m$$. A side of the square is divided equally into $$5$$ segments. The square is cut into $$5$$ pieces, as the figure shows. What is the standard deviation of the areas of those $$5$$ pieces? Attachment: 5.26ps.png A. $$2$$ B. $$√5$$ C. $$√6$$ D. $$√7$$ E. $$2√2$$ Ratio of sides of squares = 1:2:3:4:5 Ratio of Ateas of squares = 1:4:9:16:25 Ratio fo areas of 5 pieces = 1:(4-1):(9-4):(16-9):(25-16) = 1:3:5:7:9 i.e. Standard deviation will be slightly greater than 2 (because gaps between terms is 2) We do NOT need to know the real calculation of standard deviation so I don't consider it a good question for GMAT question pool Symbolic equation of DS $$= \frac{(5-1)+(5-3)+(5-5)+(7-5)+(9-5)}{5} = \frac{4+2+0+2+4}{5} = \frac{12}{5} = 2.4$$ √5 ≈ 2.2 √6 ≈ 2.5 √7 ≈ 2.7 therefore √6 seems the closest option so I would have gone for Option C as per GMAT standard calculation But exact calculation of SD is $$\frac{√∑(x_i - M)^2}{n}$$ which gives actual standard deviation $$= 2√2 = 2.8$$ Answer: Option E _________________ Prepare with PERFECTION to claim Q≥50 and V≥40 !!! GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha) e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772 One-on-One Skype classes l Classroom Coaching l On-demand Quant course l Admissions Consulting Most affordable l Comprehensive l 2000+ Qn ALL with Video explanations l LINK: Courses and Pricing Click for FREE Demo on VERBAL & QUANT Our SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l FREE GMAT Resource: 22 FREE (FULL LENGTH) GMAT CATs LINKS l NEW OG QUANT 50 Qn+VIDEO Sol. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 9138 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The figure shows a square with a side length of 5m. A side of the squ [#permalink] ### Show Tags 28 May 2020, 02:15 => Attachment: 5.26ps(a).png [ 22.7 KiB | Viewed 475 times ] The areas of those $$5$$ pieces are $$1, 3, 5, 7$$, and $$9$$, and their average is $$3.$$ The variance is $$\frac{[(1-5)^2 + (3-5)^2 + (5-5)^2 + (7-5)^2 + (9-5)^2 ] }{ 5} = \frac{( 16 + 4 + 0 + 4 + 16 ) }{ 5} = \frac{40}{5} = 8.$$ Then, the standard deviation is $$√8 = 2√2.$$ Therefore, the answer is E. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 9138
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The figure shows a square with a side length of 5m. A side of the squ  [#permalink]

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01 Jun 2020, 13:58
GMATinsight wrote:
MathRevolution wrote:
[GMAT math practice question]

The figure shows a square with a side length of $$5m$$. A side of the square is divided equally into $$5$$ segments. The square is cut into $$5$$ pieces, as the figure shows. What is the standard deviation of the areas of those $$5$$ pieces?

Attachment:
5.26ps.png

A. $$2$$

B. $$√5$$

C. $$√6$$

D. $$√7$$

E. $$2√2$$

Ratio of sides of squares = 1:2:3:4:5
Ratio of Ateas of squares = 1:4:9:16:25

Ratio fo areas of 5 pieces = 1:(4-1):(9-4):(16-9):(25-16) = 1:3:5:7:9

i.e. Standard deviation will be slightly greater than 2 (because gaps between terms is 2)

We do NOT need to know the real calculation of standard deviation so I don't consider it a good question for GMAT question pool

Symbolic equation of DS $$= \frac{(5-1)+(5-3)+(5-5)+(7-5)+(9-5)}{5} = \frac{4+2+0+2+4}{5} = \frac{12}{5} = 2.4$$

√5 ≈ 2.2
√6 ≈ 2.5
√7 ≈ 2.7

therefore √6 seems the closest option so I would have gone for Option C

as per GMAT standard calculation

But exact calculation of SD is $$\frac{√∑(x_i - M)^2}{n}$$ which gives actual standard deviation $$= 2√2 = 2.8$$

Agreed.
But, the formula for the standard deviation would be helpful for some of GMAT problems.
_________________
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Re: The figure shows a square with a side length of 5m. A side of the squ  [#permalink]

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13 Jun 2020, 11:00
1
MathRevolution wrote:
=>

Attachment:
5.26ps(a).png

The areas of those $$5$$ pieces are $$1, 3, 5, 7$$, and $$9$$, and their average is $$3.$$

The variance is $$\frac{[(1-5)^2 + (3-5)^2 + (5-5)^2 + (7-5)^2 + (9-5)^2 ] }{ 5} = \frac{( 16 + 4 + 0 + 4 + 16 ) }{ 5} = \frac{40}{5} = 8.$$

Then, the standard deviation is $$√8 = 2√2.$$

MathRevolution I guess you mean average is 5?
Re: The figure shows a square with a side length of 5m. A side of the squ   [#permalink] 13 Jun 2020, 11:00