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# In the figure above, the area of the base of the rectangular box is 21

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Math Expert
Joined: 02 Sep 2009
Posts: 50544
In the figure above, the area of the base of the rectangular box is 21  [#permalink]

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08 Dec 2017, 02:48
00:00

Difficulty:

15% (low)

Question Stats:

95% (01:08) correct 5% (00:00) wrong based on 29 sessions

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In the figure above, the area of the base of the rectangular box is 21, and the area of one of the faces is 30. Each of the dimensions m, n and k is an integer greater than 1. What is the volume of the rectangular box?

(A) 60
(B) 120
(C) 180
(D) 210
(E) 330

Attachment:

2017-12-08_1441_001.png [ 4.15 KiB | Viewed 457 times ]

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Joined: 24 Nov 2016
Posts: 152
Re: In the figure above, the area of the base of the rectangular box is 21  [#permalink]

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08 Dec 2017, 05:15
Bunuel wrote:

In the figure above, the area of the base of the rectangular box is 21, and the area of one of the faces is 30. Each of the dimensions m, n and k is an integer greater than 1. What is the volume of the rectangular box?

(A) 60
(B) 120
(C) 180
(D) 210
(E) 330

Attachment:
2017-12-08_1441_001.png

Area of rectangular face: 30 = 2*3*5
Area of base: 21 = 3*7

Since both areas need to have one equal side (that is an integer), then this side has to be 3.

Volume of box = 3*7*(2*5) = 210

(D) is the answer.
Re: In the figure above, the area of the base of the rectangular box is 21 &nbs [#permalink] 08 Dec 2017, 05:15
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# In the figure above, the area of the base of the rectangular box is 21

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