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A small table has a length of 12 inches and a breadth of b inches. Cub
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Bunuel
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A small table has a length of 12 inches and a breadth of b inches. Cub [#permalink] New post  05 Nov 2019, 01:00
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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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nick1816
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Re: A small table has a length of 12 inches and a breadth of b inches. Cub [#permalink] New post  05 Nov 2019, 04:20
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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


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Archit3110
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Re: A small table has a length of 12 inches and a breadth of b inches. Cub [#permalink] New post  05 Nov 2019, 07:23
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


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axelr
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Re: A small table has a length of 12 inches and a breadth of b inches. Cub [#permalink] New post  05 Nov 2019, 08:53
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.
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nick1816
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A small table has a length of 12 inches and a breadth of b inches. Cub [#permalink] New post  05 Nov 2019, 09:15
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.
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Archit3110
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Re: A small table has a length of 12 inches and a breadth of b inches. Cub [#permalink] New post  05 Nov 2019, 09:34
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
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IMG_20191105_230233862_HDR.jpg [ 1.23 MiB | Viewed 1538 times ]

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nick1816
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Re: A small table has a length of 12 inches and a breadth of b inches. Cub [#permalink] New post  05 Nov 2019, 09:54
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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
Untitled.png [ 5.27 KiB | Viewed 1510 times ]

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Archit3110
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Re: A small table has a length of 12 inches and a breadth of b inches. Cub [#permalink] New post  05 Nov 2019, 10:03
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.


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satya2029
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A small table has a length of 12 inches and a breadth of b inches. Cub [#permalink] New post  05 Nov 2019, 20:30
3
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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



nick1816, Archit3110

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dc2880
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Re: A small table has a length of 12 inches and a breadth of b inches. Cub [#permalink] New post  27 Jan 2021, 17:26
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



Hi, can you please explain where you obtained the equation: 12*4k/HCF(12,4k)=48 ? Thank you!
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nick1816
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Re: A small table has a length of 12 inches and a breadth of b inches. Cub [#permalink] New post  28 Jan 2021, 02:24
dc2880

Product of a and b= LCM(a,b) * HCF(a,b) ........{ true for any 2 positive integers}

12*b = LCM(12,b) * HCF(12*b)

12*b/[HCF(12*b)] = LCM(12,b)
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