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655-705 (Hard)|   Exponents|   Geometry|   Roots|      
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fskilnik
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A square has an area of (0.027)^(-2/3) square meters. The perimeter of 19 Feb 2019, 13:42
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D
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55% (hard)

Question Stats:

62% (01:53) correct 38% (02:13) wrong based on 209 sessions

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GMATH practice exercise (Quant Class 12)

A square has an area of (0.027)^(-2/3) square meters. The perimeter of this square, in meters, belongs to which of the following intervals?

(A) [0,10.5]
(B) [10.5, 11.5]
(C) [11.5, 12.5]
(D) [12.5, 13.5]
(E) [13.5, 20]
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D
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A square has an area of (0.027)^(-2/3) square meters. The perimeter of 19 Feb 2019, 13:56
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Area of Square is 10/3..upon solving the initial equation..hence perimeter will be 40/3 which is approx less than 13.5...so only D fits in ....
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A square has an area of (0.027)^(-2/3) square meters. The perimeter of 19 Feb 2019, 13:57
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Answer will be D. Using the area of the square, we see that one side will be equal to 10/3 which eventually gives us the perimeter of the square (40/3) and hence D.

Posted from my mobile device
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A square has an area of (0.027)^(-2/3) square meters. The perimeter of 19 Feb 2019, 19:00
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Hello!

Can someone please provide a detailed answer?

Kind regards!
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A square has an area of (0.027)^(-2/3) square meters. The perimeter of 19 Feb 2019, 19:08
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fskilnik
GMATH practice exercise (Quant Class 12)

A square has an area of (0.027)^(-2/3) square meters. The perimeter of this square, in meters, belongs to which of the following intervals?

(A) [0,10.5]
(B) [10.5, 11.5]
(C) [11.5, 12.5]
(D) [12.5, 13.5]
(E) [13.5, 20]
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\(?\,\,\,:\,\,\,4L\)

\({L^2} = {\left( {{3^3} \cdot {{10}^{ - 3}}} \right)^{ - {2 \over 3}}} = {\left[ {{{\left( {{3^3} \cdot {{10}^{ - 3}}} \right)}^{ - {1 \over 3}}}} \right]^2} = {\left( {{3^{ - 1}} \cdot {{10}^1}} \right)^2}\)

\(L > 0\,\,\, \Rightarrow \,\,\,\,\,L = {3^{ - 1}} \cdot {10^1} = {{10} \over 3}\)


\(? = 4L = {{39 + 1} \over 3} = 13{1 \over 3}\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\rm{D}} \right)\)


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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A square has an area of (0.027)^(-2/3) square meters. The perimeter of 20 Feb 2019, 10:48
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fskilnik
GMATH practice exercise (Quant Class 12)

A square has an area of (0.027)^(-2/3) square meters. The perimeter of this square, in meters, belongs to which of the following intervals?

(A) [0,10.5]
(B) [10.5, 11.5]
(C) [11.5, 12.5]
(D) [12.5, 13.5]
(E) [13.5, 20]
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area ; a^2
a^2 ; ((( 0.03)^3 * (10^-3))^-1/3 ) ^2
we will get
a : (10/3)
so 4a ; 40/3 ~ 13.3
IMO D
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A square has an area of (0.027)^(-2/3) square meters. The perimeter of 27 Sep 2022, 23:29
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fskilnik
fskilnik
GMATH practice exercise (Quant Class 12)

A square has an area of (0.027)^(-2/3) square meters. The perimeter of this square, in meters, belongs to which of the following intervals?

(A) [0,10.5]
(B) [10.5, 11.5]
(C) [11.5, 12.5]
(D) [12.5, 13.5]
(E) [13.5, 20]
\(?\,\,\,:\,\,\,4L\)

\({L^2} = {\left( {{3^3} \cdot {{10}^{ - 3}}} \right)^{ - {2 \over 3}}} = {\left[ {{{\left( {{3^3} \cdot {{10}^{ - 3}}} \right)}^{ - {1 \over 3}}}} \right]^2} = {\left( {{3^{ - 1}} \cdot {{10}^1}} \right)^2}\)

\(L > 0\,\,\, \Rightarrow \,\,\,\,\,L = {3^{ - 1}} \cdot {10^1} = {{10} \over 3}\)


\(? = 4L = {{39 + 1} \over 3} = 13{1 \over 3}\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\rm{D}} \right)\)


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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That is a great algebra, but how is this a gmat question? is there any short way of solving this without a calculator?
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A square has an area of (0.027)^(-2/3) square meters. The perimeter of 17 Apr 2025, 03:48
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