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26 May 2020, 02:26
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
57% (02:19) correct
43%
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wrong
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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?
5.26ps.png [ 11.37 KiB | Viewed 4136 times ]
A. \(2\)
B. \(√5\)
C. \(√6\)
D. \(√7\)
E. \(2√2\)
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 4136 times ]
A. \(2\)
B. \(√5\)
C. \(√6\)
D. \(√7\)
E. \(2√2\)
26 May 2020, 02:54
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MathRevolution
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
28 May 2020, 03:15
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=>
5.26ps(a).png [ 22.7 KiB | Viewed 3831 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
Attachment:
5.26ps(a).png [ 22.7 KiB | Viewed 3831 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
