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# A flat square piece of cardboard is to be made into a cubic open box b

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Math Expert
Joined: 02 Sep 2009
Posts: 58335
A flat square piece of cardboard is to be made into a cubic open box b  [#permalink]

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12 Sep 2018, 00:42
00:00

Difficulty:

65% (hard)

Question Stats:

47% (01:47) correct 53% (01:28) wrong based on 59 sessions

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A flat square piece of cardboard is to be made into a cubic open box by cutting 4 equal squares from its edges. What is the volume of the box created?

(1) The area of the cardboard piece is 144 square inches.
(2) Each of the squares that are cut from the cardboard has an area of 16 square inches.

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A flat square piece of cardboard is to be made into a cubic open box b  [#permalink]

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12 Sep 2018, 05:06
1
Bunuel wrote:
A flat square piece of cardboard is to be made into a cubic open box by cutting 4 equal squares from its edges. What is the volume of the box created?

(1) The area of the cardboard piece is 144 square inches.
(2) Each of the squares that are cut from the cardboard has an area of 16 square inches.

Question : What is the volume of the box created?

The figure looks like as shown in figure
if the side of each face is a
the side of bigger square must be 3a
hence to answer the question we need either side of the cubic box or the side of the square cardboard

Statement 1: The area of the cardboard piece is 144 square inches.
i.e. $$(3a)^2 = 144$$
i.e. $$a = 4$$
SUFFICIENT

Statement 2: Each of the squares that are cut from the cardboard has an area of 16 square inches
i.e. $$(a)^2 = 16$$
i.e. $$a = 4$$
SUFFICIENT

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Re: A flat square piece of cardboard is to be made into a cubic open box b  [#permalink]

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17 Sep 2018, 10:16
1
GMATinsight wrote:
Bunuel wrote:
A flat square piece of cardboard is to be made into a cubic open box by cutting 4 equal squares from its edges. What is the volume of the box created?

(1) The area of the cardboard piece is 144 square inches.
(2) Each of the squares that are cut from the cardboard has an area of 16 square inches.

Question : What is the volume of the box created?

The figure looks like as shown in figure
if the side of each face is a
the side of bigger square must be 3a
hence to answer the question we need either side of the cubic box or the side of the square cardboard

Statement 1: The area of the cardboard piece is 144 square inches.
i.e. $$(3a)^2 = 144$$
i.e. $$a = 4$$
SUFFICIENT

Statement 2: Each of the squares that are cut from the cardboard has an area of 16 square inches
i.e. $$(a)^2 = 16$$
i.e. $$a = 4$$
SUFFICIENT

How did you take the side of a bigger square to be 3a? and also, shouldn't the complete area of the cardboard be divided by (5a)^2 as it consists of 5 squares of the same length?
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Re: A flat square piece of cardboard is to be made into a cubic open box b  [#permalink]

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26 Sep 2018, 21:43
IMO it should be C.

Bunuel Can you please look into this one.

Thanks :D
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A flat square piece of cardboard is to be made into a cubic open box b  [#permalink]

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26 Sep 2018, 23:15
KaulMeAnkit wrote:
GMATinsight wrote:
Bunuel wrote:
A flat square piece of cardboard is to be made into a cubic open box by cutting 4 equal squares from its edges. What is the volume of the box created?

(1) The area of the cardboard piece is 144 square inches.
(2) Each of the squares that are cut from the cardboard has an area of 16 square inches.

Question : What is the volume of the box created?

The figure looks like as shown in figure
if the side of each face is a
the side of bigger square must be 3a
hence to answer the question we need either side of the cubic box or the side of the square cardboard

Statement 1: The area of the cardboard piece is 144 square inches.
i.e. $$(3a)^2 = 144$$
i.e. $$a = 4$$
SUFFICIENT

Statement 2: Each of the squares that are cut from the cardboard has an area of 16 square inches
i.e. $$(a)^2 = 16$$
i.e. $$a = 4$$
SUFFICIENT

How did you take the side of a bigger square to be 3a? and also, shouldn't the complete area of the cardboard be divided by (5a)^2 as it consists of 5 squares of the same length?

Because if you dont take the length of the square base of the cube equal t that of edges you would get a cuboid not a cube.
A flat square piece of cardboard is to be made into a cubic open box b   [#permalink] 26 Sep 2018, 23:15
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