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# A rectangular crate is packed to capacity with 216 3-inch cubes. What

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A rectangular crate is packed to capacity with 216 3-inch cubes. What  [#permalink]

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29 Mar 2018, 00:45
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Difficulty:

25% (medium)

Question Stats:

78% (01:04) correct 22% (01:27) wrong based on 36 sessions

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A rectangular crate is packed to capacity with 216 3-inch cubes. What is the volume, in cubic inches, of the crate?

(A) 24
(B) 72
(C) 648
(D) 1,944
(E) 5,832

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A rectangular crate is packed to capacity with 216 3-inch cubes. What  [#permalink]

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Updated on: 29 Mar 2018, 01:29
Bunuel wrote:
A rectangular crate is packed to capacity with 216 3-inch cubes. What is the volume, in cubic inches, of the crate?

(A) 24
(B) 72
(C) 648
(D) 1,944
(E) 5,832

Volume of crate = volume of all the things it can hold

$$V = 216*3^3 = (200 + 16)*27 = 5400 + 16*27$$

Hence Option (C) is correct.

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Originally posted by Gladiator59 on 29 Mar 2018, 00:56.
Last edited by Gladiator59 on 29 Mar 2018, 01:29, edited 1 time in total.
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A rectangular crate is packed to capacity with 216 3-inch cubes. What  [#permalink]

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29 Mar 2018, 01:00
Bunuel wrote:
A rectangular crate is packed to capacity with 216 3-inch cubes. What is the volume, in cubic inches, of the crate?

(A) 24
(B) 72
(C) 648
(D) 1,944
(E) 5,832

A 3 inch cube has a volume of $$3^3 = 27$$ inches.

216 such cubes occupy a volume of $$216*27$$ cubic inches(ends with a 2 and a big number)

Therefore, the rectangular crate which contains 216 3-inch cubes will occupy a volume of 5832 cubic units(Option E)
P.S You don't need to make the calculations if you combine rules from units digit(sometimes)
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Re: A rectangular crate is packed to capacity with 216 3-inch cubes. What  [#permalink]

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29 Mar 2018, 06:15
Total Volume = 3^3 * 216
Approximating => (30-3)*216 = 6000 - 600 (30*200 - 3*200)
i.e a figure >5400 and ending in 2 (7*6)

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Re: A rectangular crate is packed to capacity with 216 3-inch cubes. What  [#permalink]

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30 Mar 2018, 10:57
Bunuel wrote:
A rectangular crate is packed to capacity with 216 3-inch cubes. What is the volume, in cubic inches, of the crate?

(A) 24
(B) 72
(C) 648
(D) 1,944
(E) 5,832

The volume of one cube is 3^3 = 27 in^3, so the volume of 216 cubes is 216 x 27 = 5,832 in^3,

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Re: A rectangular crate is packed to capacity with 216 3-inch cubes. What   [#permalink] 30 Mar 2018, 10:57
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