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How many books can fit into a cubic box if the side of the box is 2 fe

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Bunuel
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How many books can fit into a cubic box if the side of the box is 2 fe [#permalink] New post   12 Sep 2018, 00:15
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How many books can fit into a cubic box if the side of the box is 2 feet long?

(1) The thickness of each book is 2 inches.
(2) Each book has a volume of 0.9 cubic feet.
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E
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chetan2u
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Re: How many books can fit into a cubic box if the side of the box is 2 fe [#permalink] New post   27 Sep 2018, 22:55
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Bunuel wrote:
How many books can fit into a cubic box if the side of the box is 2 feet long?

(1) The thickness of each book is 2 inches.
(2) Each book has a volume of 0.9 cubic feet.


We require the size of the box and the size of the book to answer the question...
We have the dimensions of Box, so we require dimensions of book
JUST the volume is not enough..

1) statement I gives us the thickness of book
We do not know the other dimensions of books
Insufficient

2) statement II gives the volume of the book
No dimensions break down
Insufficient

Combined
We have volume and the thickness of book but what about length and breadth..
Volume = 0.9 cu ft = 1555.2 cu in
Since thickness is 2 inches, L*B of book is 1555.2/2=777.6 sq inch
Thickness of 2" means we can
Now L and B can vary accordingly..
Say the length of book is more than 2 ft, no book will fit in as length had to be shorter than 2ft, if it is <2ft, we may fit something ..
So insufficient..

Note..
The area of base of cube =24^2=576 sq inches which is LESS than the area of book 777.6..
So we can fit in some book diagonally as shown

E
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Re: How many books can fit into a cubic box if the side of the box is 2 fe [#permalink] New post   26 Sep 2018, 22:41
Bunuel wrote:
How many books can fit into a cubic box if the side of the box is 2 feet long?

(1) The thickness of each book is 2 inches.
(2) Each book has a volume of 0.9 cubic feet.



Not sure but

1. from this we only know the thickness, but it could be that the length is different. So the number of books will increase.

2. i suppose this could be sufficient right?
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Re: How many books can fit into a cubic box if the side of the box is 2 fe [#permalink] New post   26 Sep 2018, 22:58
Hi,

Question: No. of books fit inside a 2 feet long cubical box ?

Clearly the answer for the question is E. because no information about the shape of the book. Just knowing the thickness and volume doesn’t help to solve this question.

To solve this question, we need to understand length, width or atleast the shape of book like rectangular or cubical shape etc.

Statement I is insufficient:

The thickness of each book is 2 inches.

We don’t know any information of length or width of the book. As the length and width changes the number of books in the box will change. So not sufficient.

Statement II is insufficient:

Each book has a volume of 0.9 feet.

Again no information about the shape of the book. We can’t really find the length and width of the book. We can’t just consider it as a cube shape.

Together still not sufficient.

No extra information.

So the answer is E.

Hope this helps.
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Re: How many books can fit into a cubic box if the side of the box is 2 fe [#permalink] New post   27 Sep 2018, 10:10
Byjus wrote:
Hi,

Question: No. of books fit inside a 2 feet long cubical box ?

Clearly the answer for the question is E. because no information about the shape of the book. Just knowing the thickness and volume doesn’t help to solve this question.

To solve this question, we need to understand length, width or atleast the shape of book like rectangular or cubical shape etc.

Statement I is insufficient:

The thickness of each book is 2 inches.

We don’t know any information of length or width of the book. As the length and width changes the number of books in the box will change. So not sufficient.

Statement II is insufficient:

Each book has a volume of 0.9 feet.

Again no information about the shape of the book. We can’t really find the length and width of the book. We can’t just consider it as a cube shape.

Together still not sufficient.

No extra information.

So the answer is E.

Hope this helps.


For Statement II, isn't it supposed to be sufficient? The fact that the volume is already given, one can calculate how many books can fit in it no matter the length, width, and height of the book since they all have the same volume.

Assume length, width, and height are given, wouldn't this problem be solved by dividing the volume of the cube with the volume of each book?

I don't understand why E.
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Re: How many books can fit into a cubic box if the side of the box is 2 fe [#permalink] New post   27 Sep 2018, 22:49
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Bunuel wrote:
How many books can fit into a cubic box if the side of the box is 2 feet long?

(1) The thickness of each book is 2 inches.
(2) Each book has a volume of 0.9 cubic feet.


We require the size of the box and the size of the book to answer the question...
We have the dimensions of Box, so we require dimensions of book
JUST the volume is not enough..

1) statement I gives us the thickness of book
We do not know the other dimensions of books
Insufficient

2) statement II gives the volume of the book
No dimensions break down
Insufficient

Combined
We have volume and the thickness of book but what about length and breadth..
Volume = 0.9 cu ft = 1555.2 cu in
Since thickness is 2 inches, L*B of book is 1555.2/2=777.6 sq inch
Thickness of 2" means we can
Now L and B can vary accordingly..
Say the length of book is more than 2 ft, no book will fit in as length had to be shorter than 2ft, if it is <2ft, we may fit something ..
So insufficient..

Note..
The area of base of cube =24^2=576 sq inches which is LESS than the area of book 777.6..
So we can fit in some book diagonally as shown

E
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Re: How many books can fit into a cubic box if the side of the box is 2 fe [#permalink] New post   28 Sep 2018, 03:36
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If Length and width of the book is given, then of-course we could have tried solving it. But first thing length and width is not given here separately, just knowing the volume wont help,

Like for an example if we have rectangular box with dimensions 4, 5 and 6 and number of 2 units cube placed inside the box is not (Volume of cuboid / volume of cube = 4 * 5 * 6 / 2 * 2 *2 ) = 15.

There are only 12 boxes could fit inside it(Try visualizing it), so what I want to say here is knowing only the volumes may not help, you need to know the dimensions and how it is placed as well.

Hope it helps.

BenchOfilada wrote:
Byjus wrote:
Hi,

Question: No. of books fit inside a 2 feet long cubical box ?

Clearly the answer for the question is E. because no information about the shape of the book. Just knowing the thickness and volume doesn’t help to solve this question.

To solve this question, we need to understand length, width or atleast the shape of book like rectangular or cubical shape etc.

Statement I is insufficient:

The thickness of each book is 2 inches.

We don’t know any information of length or width of the book. As the length and width changes the number of books in the box will change. So not sufficient.

Statement II is insufficient:

Each book has a volume of 0.9 feet.

Again no information about the shape of the book. We can’t really find the length and width of the book. We can’t just consider it as a cube shape.

Together still not sufficient.

No extra information.

So the answer is E.

Hope this helps.


For Statement II, isn't it supposed to be sufficient? The fact that the volume is already given, one can calculate how many books can fit in it no matter the length, width, and height of the book since they all have the same volume.

Assume length, width, and height are given, wouldn't this problem be solved by dividing the volume of the cube with the volume of each book?

I don't understand why E.
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Re: How many books can fit into a cubic box if the side of the box is 2 fe [#permalink] New post   20 Dec 2021, 08:55
chetan2u wrote:
Bunuel wrote:
How many books can fit into a cubic box if the side of the box is 2 feet long?

(1) The thickness of each book is 2 inches.
(2) Each book has a volume of 0.9 cubic feet.


We require the size of the box and the size of the book to answer the question...
We have the dimensions of Box, so we require dimensions of book
JUST the volume is not enough..

1) statement I gives us the thickness of book
We do not know the other dimensions of books
Insufficient

2) statement II gives the volume of the book
No dimensions break down
Insufficient

Combined
We have volume and the thickness of book but what about length and breadth..
Volume = 0.9 cu ft = 1555.2 cu in
Since thickness is 2 inches, L*B of book is 1555.2/2=777.6 sq inch
Thickness of 2" means we can
Now L and B can vary accordingly..
Say the length of book is more than 2 ft, no book will fit in as length had to be shorter than 2ft, if it is <2ft, we may fit something ..
So insufficient..

Note..
The area of base of cube =24^2=576 sq inches which is LESS than the area of book 777.6..
So we can fit in some book diagonally as shown

E



Quick question, perhaps I am going wrong somewhere. If statement 2 says cubic feet, shouldn't it the book resemble a cube? as in x^3 = 0.9 cubic feet. Then, clearly it will fit in the volume of box which is also a cube with 2 feet as its dimension (x).
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Re: How many books can fit into a cubic box if the side of the box is 2 fe [#permalink] New post   20 Dec 2021, 09:30
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pssk wrote:
chetan2u wrote:
Bunuel wrote:
How many books can fit into a cubic box if the side of the box is 2 feet long?

(1) The thickness of each book is 2 inches.
(2) Each book has a volume of 0.9 cubic feet.


We require the size of the box and the size of the book to answer the question...
We have the dimensions of Box, so we require dimensions of book
JUST the volume is not enough..

1) statement I gives us the thickness of book
We do not know the other dimensions of books
Insufficient

2) statement II gives the volume of the book
No dimensions break down
Insufficient

Combined
We have volume and the thickness of book but what about length and breadth..
Volume = 0.9 cu ft = 1555.2 cu in
Since thickness is 2 inches, L*B of book is 1555.2/2=777.6 sq inch
Thickness of 2" means we can
Now L and B can vary accordingly..
Say the length of book is more than 2 ft, no book will fit in as length had to be shorter than 2ft, if it is <2ft, we may fit something ..
So insufficient..

Note..
The area of base of cube =24^2=576 sq inches which is LESS than the area of book 777.6..
So we can fit in some book diagonally as shown

E



Quick question, perhaps I am going wrong somewhere. If statement 2 says cubic feet, shouldn't it the book resemble a cube? as in x^3 = 0.9 cubic feet. Then, clearly it will fit in the volume of box which is also a cube with 2 feet as its dimension (x).


No, that will not be correct.

Area will always be in square units. It could be square m or square cm etc.
but this area can be of a circle, rectangle or square or any other 2 dimensional figure. => \(4m^2\) or 4 square meter.
Similarly, the volume is in cubic feet or cubic meter and so on.
Cubic meter just tells you that we are looking at volume, it could be that of a bucket, cylinder, cuboid, cube or any other 3 dimensional figure.
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Re: How many books can fit into a cubic box if the side of the box is 2 fe [#permalink] New post   20 Dec 2021, 12:11
chetan2u wrote:
pssk wrote:
chetan2u wrote:

We require the size of the box and the size of the book to answer the question...
We have the dimensions of Box, so we require dimensions of book
JUST the volume is not enough..

1) statement I gives us the thickness of book
We do not know the other dimensions of books
Insufficient

2) statement II gives the volume of the book
No dimensions break down
Insufficient

Combined
We have volume and the thickness of book but what about length and breadth..
Volume = 0.9 cu ft = 1555.2 cu in
Since thickness is 2 inches, L*B of book is 1555.2/2=777.6 sq inch
Thickness of 2" means we can
Now L and B can vary accordingly..
Say the length of book is more than 2 ft, no book will fit in as length had to be shorter than 2ft, if it is <2ft, we may fit something ..
So insufficient..

Note..
The area of base of cube =24^2=576 sq inches which is LESS than the area of book 777.6..
So we can fit in some book diagonally as shown

E



Quick question, perhaps I am going wrong somewhere. If statement 2 says cubic feet, shouldn't it the book resemble a cube? as in x^3 = 0.9 cubic feet. Then, clearly it will fit in the volume of box which is also a cube with 2 feet as its dimension (x).


No, that will not be correct.

Area will always be in square units. It could be square m or square cm etc.
but this area can be of a circle, rectangle or square or any other 2 dimensional figure. => \(4m^2\) or 4 square meter.
Similarly, the volume is in cubic feet or cubic meter and so on.
Cubic meter just tells you that we are looking at volume, it could be that of a bucket, cylinder, cuboid, cube or any other 3 dimensional figure.



Got it! Thanks a ton Chetan

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Re: How many books can fit into a cubic box if the side of the box is 2 fe [#permalink]
20 Dec 2021, 12:11
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