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# If the surface area of a rectangular box with integer edges is 166 squ

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Joined: 02 Sep 2009
Posts: 53066
If the surface area of a rectangular box with integer edges is 166 squ  [#permalink]

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07 Sep 2018, 00:37
00:00

Difficulty:

55% (hard)

Question Stats:

13% (00:44) correct 87% (02:01) wrong based on 34 sessions

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If the surface area of a rectangular box with integer edges is 166 square meters, what is the volume?

(1) The base has an area of 20 square meters.
(2) One of the sides has area 35 square meters.

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Re: If the surface area of a rectangular box with integer edges is 166 squ  [#permalink]

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Updated on: 07 Sep 2018, 21:30
Bunuel wrote:
If the surface area of a box with integer edges is 166 square meters, what is the volume?

(1) The base has an area of 20 square meters.
(2) One of the sides has area 35 square meters.

Surface area of the box = 2*(lb+bh+lh) = 166
i.e. (lb+bh+lh) = 83

Question : Volume = l*b*h = ?

Statement 1: The base has an area of 20 square meters
i.e. l*b = 20 which may be 4*5 or 1*20
i.e. (bh+lh) = 63
i.e. h(l+b)=63
One possibility is h = 7, and l&b are 5&4 in any order
other possibility is h = 3 and l&b are 1 and 20 in any order hence
Volume = 4*5*7 or 1*20*3 = 140 or 60

NOT SUFFICIENT

Statement 2: One of the sides has area 35 square meters

i.e. bh = 35 = 5*7 pr 1*35
i,e. (lb+lh) = 48
i.e. l(b+h)=48
only possibility of integer solutions is b and h are 5 and 7 in any order and l = 4 hence
SUFFICIENT

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Originally posted by GMATinsight on 07 Sep 2018, 01:27.
Last edited by GMATinsight on 07 Sep 2018, 21:30, edited 1 time in total.
Re: If the surface area of a rectangular box with integer edges is 166 squ   [#permalink] 07 Sep 2018, 01:27
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