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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 9138
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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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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The figure shows a square with a side length of 5m. A side of the squ  [#permalink]

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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 $$= 2√2 = 2.8$$

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Math Revolution GMAT Instructor V
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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=>

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 $$√8 = 2√2.$$

_________________
Math Revolution GMAT Instructor V
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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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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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

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