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# A wrapping paper has dimensions 1 yard by 7 yards. What is the volume

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Intern
Joined: 04 Sep 2009
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A wrapping paper has dimensions 1 yard by 7 yards. What is the volume [#permalink]

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17 Oct 2012, 19:21
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Difficulty:

55% (hard)

Question Stats:

56% (01:28) correct 44% (01:42) wrong based on 174 sessions

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A wrapping paper has dimensions 1 yard by 7 yards. What is the volume in Ft3 of the largest cube that could be packed using this paper?

(1 yard = 3 Ft)

A. 8
B. 9
C. 18
D. 27
E. 36
[Reveal] Spoiler: OA

_________________

Aeros
"Why are you trying so hard to fit in when you were born to stand out?"
"Do or do not. There is no 'try'..."

Kudos [?]: 82 [0], given: 9

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Re: A wrapping paper has dimensions 1 yard by 7 yards. What is the volume [#permalink]

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17 Oct 2012, 20:59
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aeros232 wrote:
A wrapping paper has dimensions 1 yard by 7 yards. What is the volume in Ft3 of the largest cube that could be packed using this paper?

(1 yard = 3 Ft)

A. 8
B. 9
C. 18
D. 27
E. 36

[Reveal] Spoiler:
D

Note that it should be mentioned that the side of the largest cube must be an integer (or dimensions should be 1 by 6, not 1 by 7).

The wrapping paper has dimensions $$1*3=3$$ feet by $$7*3=21$$ feet. Thus, its area is $$3*21=63$$ square feet.

Now, the surface area of a cube is $$6a^2$$, where $$a$$ is the length of a side (a cube has 6 faces and the area of each face is $$a^2$$).

So, it must be true that $$6a^2\leq{63}$$.

If $$a=4$$, then $$6a^2=96$$, which means that we won't have enough paper for such cube.
If $$a=3$$, then $$6a^2=54$$. The volume of such cube is $$a^3=27$$ cubic feet.

If we won't limit the value of a side to integers only, then: $$6a^2={63}$$ --> $$a=\sqrt{10.5}$$ --> $$volume=a^3=(\sqrt{10.5})^3$$.

Hope it's clear.
_________________

Kudos [?]: 129093 [1], given: 12194

Intern
Joined: 04 Sep 2009
Posts: 43

Kudos [?]: 82 [0], given: 9

Re: A wrapping paper has dimensions 1 yard by 7 yards. What is the volume [#permalink]

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17 Oct 2012, 21:11
Bunuel wrote:
aeros232 wrote:
A wrapping paper has dimensions 1 yard by 7 yards. What is the volume in Ft3 of the largest cube that could be packed using this paper?

(1 yard = 3 Ft)

A. 8
B. 9
C. 18
D. 27
E. 36

[Reveal] Spoiler:
D

Note that it should be mentioned that the side of the largest cube must be an integer (or dimensions should be 1 by 6, not 1 by 7).

The wrapping paper has dimensions $$1*3=3$$ feet by $$7*3=21$$ feet. Thus, its area is $$3*21=63$$ square feet.

Now, the surface area of a cube is $$6a^2$$, where $$a$$ is the length of a side (a cube has 6 faces and the area of each face is $$a^2$$).

So, it must be true that $$6a^2\leq{63}$$.

If $$a=4$$, then $$6a^2=96$$, which means that we won't have enough paper for such cube.
If $$a=3$$, then $$6a^2=54$$. The volume of such cube is $$a^3=27$$ cubic feet.

If we won't limit the value of a side to integers only, then: $$6a^2={63}$$ --> $$a=\sqrt{10.5}$$ --> $$volume=a^3=(\sqrt{10.5})^3$$.

Hope it's clear.

Great, thanks Bunuel
_________________

Aeros
"Why are you trying so hard to fit in when you were born to stand out?"
"Do or do not. There is no 'try'..."

Kudos [?]: 82 [0], given: 9

Director
Joined: 28 Jul 2011
Posts: 521

Kudos [?]: 297 [0], given: 16

Location: United States
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Re: A wrapping paper has dimensions 1 yard by 7 yards. What is the volume [#permalink]

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19 Oct 2012, 09:42
Bunuel wrote:
aeros232 wrote:
A wrapping paper has dimensions 1 yard by 7 yards. What is the volume in Ft3 of the largest cube that could be packed using this paper?

(1 yard = 3 Ft)

A. 8
B. 9
C. 18
D. 27
E. 36

[Reveal] Spoiler:
D

Note that it should be mentioned that the side of the largest cube must be an integer (or dimensions should be 1 by 6, not 1 by 7).

The wrapping paper has dimensions $$1*3=3$$ feet by $$7*3=21$$ feet. Thus, its area is $$3*21=63$$ square feet.

Now, the surface area of a cube is $$6a^2$$, where $$a$$ is the length of a side (a cube has 6 faces and the area of each face is $$a^2$$).

So, it must be true that $$6a^2\leq{63}$$.

If $$a=4$$, then $$6a^2=96$$, which means that we won't have enough paper for such cube.
If $$a=3$$, then $$6a^2=54$$. The volume of such cube is $$a^3=27$$ cubic feet.

If we won't limit the value of a side to integers only, then: $$6a^2={63}$$ --> $$a=\sqrt{10.5}$$ --> $$volume=a^3=(\sqrt{10.5})^3$$.

Hope it's clear.

Bunnel

Can you please let me know Why you didn't consider a=2? then the volume would be 8
_________________

Kudos [?]: 297 [0], given: 16

Math Expert
Joined: 02 Sep 2009
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Kudos [?]: 129093 [0], given: 12194

Re: A wrapping paper has dimensions 1 yard by 7 yards. What is the volume [#permalink]

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19 Oct 2012, 09:45
mydreammba wrote:
Bunuel wrote:
aeros232 wrote:
A wrapping paper has dimensions 1 yard by 7 yards. What is the volume in Ft3 of the largest cube that could be packed using this paper?

(1 yard = 3 Ft)

A. 8
B. 9
C. 18
D. 27
E. 36

[Reveal] Spoiler:
D

Note that it should be mentioned that the side of the largest cube must be an integer (or dimensions should be 1 by 6, not 1 by 7).

The wrapping paper has dimensions $$1*3=3$$ feet by $$7*3=21$$ feet. Thus, its area is $$3*21=63$$ square feet.

Now, the surface area of a cube is $$6a^2$$, where $$a$$ is the length of a side (a cube has 6 faces and the area of each face is $$a^2$$).

So, it must be true that $$6a^2\leq{63}$$.

If $$a=4$$, then $$6a^2=96$$, which means that we won't have enough paper for such cube.
If $$a=3$$, then $$6a^2=54$$. The volume of such cube is $$a^3=27$$ cubic feet.

If we won't limit the value of a side to integers only, then: $$6a^2={63}$$ --> $$a=\sqrt{10.5}$$ --> $$volume=a^3=(\sqrt{10.5})^3$$.

Hope it's clear.

Bunnel

Can you please let me know Why you didn't consider a=2? then the volume would be 8

We need the largest cube that could be packed using this paper. Now, the larger the side of a cube larger the volume and since a can be 3, no need to consider smaller lengths.

Hope it's clear.
_________________

Kudos [?]: 129093 [0], given: 12194

Director
Joined: 28 Jul 2011
Posts: 521

Kudos [?]: 297 [0], given: 16

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Re: A wrapping paper has dimensions 1 yard by 7 yards. What is the volume [#permalink]

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19 Oct 2012, 09:53
Thanks Bunnel i din't read the Q properly and can you please respond the private message on statistics which i have sent you yesterday?

and for the post the link is here

clarification-on-statistics-sd-140907.html
_________________

Kudos [?]: 297 [0], given: 16

Director
Joined: 28 Jul 2011
Posts: 521

Kudos [?]: 297 [0], given: 16

Location: United States
GPA: 3.86
WE: Accounting (Commercial Banking)
Re: A wrapping paper has dimensions 1 yard by 7 yards. What is the volume [#permalink]

### Show Tags

19 Oct 2012, 09:54
mydreammba wrote:
Bunuel wrote:
aeros232 wrote:
A wrapping paper has dimensions 1 yard by 7 yards. What is the volume in Ft3 of the largest cube that could be packed using this paper?

(1 yard = 3 Ft)

A. 8
B. 9
C. 18
D. 27
E. 36

[Reveal] Spoiler:
D

Note that it should be mentioned that the side of the largest cube must be an integer (or dimensions should be 1 by 6, not 1 by 7).

The wrapping paper has dimensions $$1*3=3$$ feet by $$7*3=21$$ feet. Thus, its area is $$3*21=63$$ square feet.

Now, the surface area of a cube is $$6a^2$$, where $$a$$ is the length of a side (a cube has 6 faces and the area of each face is $$a^2$$).

So, it must be true that $$6a^2\leq{63}$$.

If $$a=4$$, then $$6a^2=96$$, which means that we won't have enough paper for such cube.
If $$a=3$$, then $$6a^2=54$$. The volume of such cube is $$a^3=27$$ cubic feet.

If we won't limit the value of a side to integers only, then: $$6a^2={63}$$ --> $$a=\sqrt{10.5}$$ --> $$volume=a^3=(\sqrt{10.5})^3$$.

Hope it's clear.

Thanks Bunnel i din't read the Q properly and can you please respond the private message on statistics which i have sent you yesterday?

and for the post the link is here

clarification-on-statistics-sd-140907.html
_________________

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Re: A wrapping paper has dimensions 1 yard by 7 yards. What is the volume [#permalink]

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20 Aug 2014, 23:41
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Re: A wrapping paper has dimensions 1 yard by 7 yards. What is the volume [#permalink]

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29 Apr 2016, 01:05
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Re: A wrapping paper has dimensions 1 yard by 7 yards. What is the volume [#permalink]

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12 Sep 2017, 07:53
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A wrapping paper has dimensions 1 yard by 7 yards. What is the volume   [#permalink] 12 Sep 2017, 07:53
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