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# A square has an area of (0.027)^(-2/3) square meters. The perimeter of

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A square has an area of (0.027)^(-2/3) square meters. The perimeter of  [#permalink]

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19 Feb 2019, 13:42
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65% (hard)

Question Stats:

48% (01:51) correct 52% (02:23) wrong based on 44 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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Re: A square has an area of (0.027)^(-2/3) square meters. The perimeter of  [#permalink]

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19 Feb 2019, 13:56
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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Re: A square has an area of (0.027)^(-2/3) square meters. The perimeter of  [#permalink]

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19 Feb 2019, 13:57
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.

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Re: A square has an area of (0.027)^(-2/3) square meters. The perimeter of  [#permalink]

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19 Feb 2019, 19:00
Hello!

Kind regards!
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Re: A square has an area of (0.027)^(-2/3) square meters. The perimeter of  [#permalink]

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19 Feb 2019, 19:08
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fskilnik wrote:
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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Re: A square has an area of (0.027)^(-2/3) square meters. The perimeter of  [#permalink]

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20 Feb 2019, 10:48
fskilnik wrote:
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]

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
Re: A square has an area of (0.027)^(-2/3) square meters. The perimeter of   [#permalink] 20 Feb 2019, 10:48
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