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Math Expert V
Joined: 02 Sep 2009
Posts: 60647
A small table has a length of 12 inches and a breadth of b inches. Cub  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 33% (02:26) correct 68% (03:04) wrong based on 40 sessions

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A small table has a length of 12 inches and a breadth of b inches. Cubes are placed on the surface of the table so as to cover the entire surface. The maximum side of such cubes is found to be 4 inches. Also, a few such tables are arranged to form a square. The minimum length of side possible for such a square is 48 inches. Find b.

A. 8
B. 16
C. 24
D. 32
E. 48

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VP  V
Joined: 19 Oct 2018
Posts: 1295
Location: India
Re: A small table has a length of 12 inches and a breadth of b inches. Cub  [#permalink]

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3
1
Given-
HCF(12,b)=4
LCM(12,b)=48

Hence, 12*b=48*4
b=16

Bunuel wrote:
A small table has a length of 12 inches and a breadth of b inches. Cubes are placed on the surface of the table so as to cover the entire surface. The maximum side of such cubes is found to be 4 inches. Also, a few such tables are arranged to form a square. The minimum length of side possible for such a square is 48 inches. Find b.

A. 8
B. 16
C. 24
D. 32
E. 48

Are You Up For the Challenge: 700 Level Questions
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5731
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: A small table has a length of 12 inches and a breadth of b inches. Cub  [#permalink]

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for the given length of 12 inches the side b inches is found to be 4inches
so now to form a square ie 12x12 ; we need total 3 such tables
and so as to make table with min length 48 inches we need 48/3 ; 16 such tables
IMO B

Bunuel wrote:
A small table has a length of 12 inches and a breadth of b inches. Cubes are placed on the surface of the table so as to cover the entire surface. The maximum side of such cubes is found to be 4 inches. Also, a few such tables are arranged to form a square. The minimum length of side possible for such a square is 48 inches. Find b.

A. 8
B. 16
C. 24
D. 32
E. 48

Are You Up For the Challenge: 700 Level Questions
Intern  Joined: 05 Nov 2019
Posts: 1
Re: A small table has a length of 12 inches and a breadth of b inches. Cub  [#permalink]

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What does it mean "The maximum side of such cubes is found to be 4 inches"? I guessed it means that every cube has a side of 4 inches. Is it right?
While "The minimum length of side possible for such a square is 48 inches" means that the square obtained with the few tables has a side lenght of 48?

Thanks, I am not english and am afraid I might not have understood the text right, because I find 24 as the answer.
VP  V
Joined: 19 Oct 2018
Posts: 1295
Location: India
A small table has a length of 12 inches and a breadth of b inches. Cub  [#permalink]

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You've correctly understood it.

If b=24, then use can use cubes of length 12 cm to cover the table; hence, your solution contradicts the statement given.

axelr wrote:
What does it mean "The maximum side of such cubes is found to be 4 inches"? I guessed it means that every cube has a side of 4 inches. Is it right?
While "The minimum length of side possible for such a square is 48 inches" means that the square obtained with the few tables has a side lenght of 48?

Thanks, I am not english and am afraid I might not have understood the text right, because I find 24 as the answer.
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5731
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: A small table has a length of 12 inches and a breadth of b inches. Cub  [#permalink]

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axelr
See attached image

axelr wrote:
What does it mean "The maximum side of such cubes is found to be 4 inches"? I guessed it means that every cube has a side of 4 inches. Is it right?
While "The minimum length of side possible for such a square is 48 inches" means that the square obtained with the few tables has a side lenght of 48?

Thanks, I am not english and am afraid I might not have understood the text right, because I find 24 as the answer.

Posted from my mobile device
Attachments

File comment: Pic IMG_20191105_230233862_HDR.jpg [ 1.23 MiB | Viewed 476 times ]

VP  V
Joined: 19 Oct 2018
Posts: 1295
Location: India
Re: A small table has a length of 12 inches and a breadth of b inches. Cub  [#permalink]

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1
This is wrong...though you get right answer

Table is not a square first of all.

Cubes are placed on the surface of the table so as to cover the entire surface. The maximum side of such cubes is found to be 4 inches.

This statement implies that b is a multiple of 4. b=4k, where k is not multiple of 3.

a few such tables are arranged to form a square. The minimum length of side possible for such a square is 48 inches

This statement implies that LCM of 12 and b is 48.

12*b/4=48
12*4k/HCF(12,4k)=48

k=4
b=16

Archit3110 wrote:
axelr
See attached image

axelr wrote:
What does it mean "The maximum side of such cubes is found to be 4 inches"? I guessed it means that every cube has a side of 4 inches. Is it right?
While "The minimum length of side possible for such a square is 48 inches" means that the square obtained with the few tables has a side lenght of 48?

Thanks, I am not english and am afraid I might not have understood the text right, because I find 24 as the answer.

Posted from my mobile device

Attachments Untitled.png [ 5.27 KiB | Viewed 452 times ]

GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5731
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: A small table has a length of 12 inches and a breadth of b inches. Cub  [#permalink]

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nick1816 ; okay i got your point what I did was that I actually formed square shaped table considering 3 equal '4inches' sides i.e 12 each .. and so as to get min length side of 48 ; 16 such table arrangements would be required...

nick1816 wrote:
This is wrong...though you get right answer

Table is not a square first of all.

Cubes are placed on the surface of the table so as to cover the entire surface. The maximum side of such cubes is found to be 4 inches.

This statement implies that b is a multiple of 4. b=4k, where k is not multiple of 3.

a few such tables are arranged to form a square. The minimum length of side possible for such a square is 48 inches

This statement implies that LCM of 12 and b is 48.

12*b/4=48
12*4k/HCF(12,4k)=48

k=4
b=16

Archit3110 wrote:
axelr
See attached image

axelr wrote:
What does it mean "The maximum side of such cubes is found to be 4 inches"? I guessed it means that every cube has a side of 4 inches. Is it right?
While "The minimum length of side possible for such a square is 48 inches" means that the square obtained with the few tables has a side lenght of 48?

Thanks, I am not english and am afraid I might not have understood the text right, because I find 24 as the answer.

Posted from my mobile device
Manager  G
Joined: 10 Dec 2017
Posts: 177
Location: India
A small table has a length of 12 inches and a breadth of b inches. Cub  [#permalink]

### Show Tags

2
A small table has a length of 12 inches and a breadth of b inches. Cubes are placed on the surface of the table so as to cover the entire surface. The maximum side of such cubes is found to be 4 inches. Also, a few such tables are arranged to form a square. The minimum length of side possible for such a square is 48 inches. Find b.

A. 8
B. 16
C. 24
D. 32
E. 48

nick1816, Archit3110

Posted from my mobile device
Attachments IMG_20191106_093716__01.jpg [ 1.58 MiB | Viewed 364 times ] A small table has a length of 12 inches and a breadth of b inches. Cub   [#permalink] 05 Nov 2019, 21:30
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