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Math Expert V
Joined: 02 Sep 2009
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A room is 480 centimeters wide and 520 centimeters long. If n identica  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 61% (01:51) correct 39% (01:56) wrong based on 208 sessions

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A room is 480 centimeters wide and 520 centimeters long. If n identical square tiles are arranged in a grid pattern so as to cover the entire floor of the room, what is the value of n?

(1) A whole number of tiles fit exactly along the length and width of the room, and no tiles had to be cut in order to cover the entire floor.
(2) 12 tiles placed adjacent to one another span the width of the room

Kudos for a correct solution.

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Re: A room is 480 centimeters wide and 520 centimeters long. If n identica  [#permalink]

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Bunuel wrote:
A room is 480 centimeters wide and 520 centimeters long. If n identical square tiles are arranged in a grid pattern so as to cover the entire floor of the room, what is the value of n?

(1) A whole number of tiles fit exactly along the length and width of the room, and no tiles had to be cut in order to cover the entire floor.
(2) 12 tiles placed adjacent to one another span the width of the room

Kudos for a correct solution.

Hint: We need the size of one Square tile to find the number of tiles needed to cover the entire floor. Also we need to know whether any tile needs to be broken or not to cover the entire floor

Statement 1: A whole number of tiles fit exactly along the length and width of the room, and no tiles had to be cut in order to cover the entire floor.

But the size of tile can be 1 cm each side or 2 cm each side or any common factor of 480 and 520

Tiles of different sizes are possible hence different number of tiles will be obtained

Hence, NOT SUFFICIENT

Statement 2: 12 tiles placed adjacent to one another span the width of the room

i.e. Width 480 cm is covered by 12 tiles i.e. Each dimension of each tile = 480/12 = 40

i.e. Total No. of tiles = (480 x 520) / (40 x 40) = 12 x 13 = 156

Hence, SUFFICIENT

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Intern  Joined: 04 May 2014
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Re: A room is 480 centimeters wide and 520 centimeters long. If n identica  [#permalink]

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I would say answer B, as statement 1 does not reveal anything about the dimensions of the tiles, the tiles could be 1^2 cm (1 by 1 cm) or 4^2cm (2 by 2 cm) and both would be able to fit in the room, since the width and height are multiples of two and 1 obviously.
Statement 2 says 12 square tiles adjacent to each other cover the width of the room. As it so happens 12 is a factor of 480 and 480 / 12 = 40cm wide tiles. Since there is no restriction on the n number being an integer or something, this would be sufficient!
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Re: A room is 480 centimeters wide and 520 centimeters long. If n identica  [#permalink]

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How many square tiles?

(1) A whole number of tiles fit exactly along the length and width of the room, and no tiles had to be cut in order to cover the entire floor.
480 and 520 are divisible by many numbers
insufficient

(2) 12 tiles placed adjacent to one another span the width of the room
480/12= 40cm^2 tiles
we can use proportions to find the total number
Sufficient

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Re: A room is 480 centimeters wide and 520 centimeters long. If n identica  [#permalink]

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Bunuel wrote:
A room is 480 centimeters wide and 520 centimeters long. If n identical square tiles are arranged in a grid pattern so as to cover the entire floor of the room, what is the value of n?

(1) A whole number of tiles fit exactly along the length and width of the room, and no tiles had to be cut in order to cover the entire floor.
(2) 12 tiles placed adjacent to one another span the width of the room

Kudos for a correct solution.

1: The size of each square tile can be 1 or 2 or anything that is a common divisor of 480 and 520. Not sufficient.
2: This means the size of each square tile is 40 centimeters. Therefore, there will be 13 tiles length wise, which is enough to calculate the number of tiles. Sufficient.
Math Expert V
Joined: 02 Sep 2009
Posts: 55681
Re: A room is 480 centimeters wide and 520 centimeters long. If n identica  [#permalink]

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Bunuel wrote:
A room is 480 centimeters wide and 520 centimeters long. If n identical square tiles are arranged in a grid pattern so as to cover the entire floor of the room, what is the value of n?

(1) A whole number of tiles fit exactly along the length and width of the room, and no tiles had to be cut in order to cover the entire floor.
(2) 12 tiles placed adjacent to one another span the width of the room

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

(1) INSUFFICIENT: There are several square tile sizes that can be placed as described. Consider these example values for S, the length of a side of the square tile:
Attachment: 2015-06-15_1624.png [ 45.28 KiB | Viewed 5476 times ]

(2) SUFFICIENT: The width of the room is 480 centimeters, so the side of the square tile must be 480/12 = 40 centimeters. Therefore, n = xy = (12)(13) = 156.

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Re: A room is 480 centimeters wide and 520 centimeters long. If n identica  [#permalink]

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A room is 480cm by 520cm

480x520 = 249600

n square, identical tiles, what is the value of n?

1) 40x40 would work
4x4 would work

I.

2) 12 tiles in 480cm, is 40cm a tile. Tile is square, 40x40.

S.

B.
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A room is 480 centimeters wide and 520 centimeters long. If n identica  [#permalink]

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SavageBrother wrote:
A room is 480cm by 520cm

480x520 = 249600

n square, identical tiles, what is the value of n?

1) 40x40 would work
4x4 would work

I.

2) 12 tiles in 480cm, is 40cm a tile. Tile is square, 40x40.

S.

B.

One common mistake which many people make is they find the area like calculated here 480x520 = 249600 Here I wish to suggest reader that it is not a good practice because it may lead to wrong answer in a smart question. Here are the examples

If the dimensions of floor are 16 ft. and 23 ft.
then Area = 16x23 = 368

This area 368 sq.ft. is divisible by 4x4 i.e. a Square tile with Area 16 but square tiles of dimensions 4x4 can't cover such a floor without breaking and using the parts of tiles thereafter.

So to judge whether the Dimensions of square tiles are acceptable we must make sure that each dimension of the floor must be divisible by each dimension of the square tile and result in an integer number which will communicate the number of tiles needed on that dimension

i.e. Number of tiles of Dimensions 4x4 needed to cover a floor of area of 360 X 480 should IDEALLY be calculated like this

On the Dimension 360, the Number of Tiled needed = 360/4 = 90
On the Dimension 480, the Number of Tiled needed = 480/4 = 120
i.e. Total Such tiles = 120*90 = 10800

I hope it makes sense to other reader and they don't make any mistake of this type in a smart question _________________
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Manager  Joined: 18 Dec 2014
Posts: 99
Re: A room is 480 centimeters wide and 520 centimeters long. If n identica  [#permalink]

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GMATinsight wrote:
SavageBrother wrote:
A room is 480cm by 520cm

480x520 = 249600

n square, identical tiles, what is the value of n?

1) 40x40 would work
4x4 would work

I.

2) 12 tiles in 480cm, is 40cm a tile. Tile is square, 40x40.

S.

B.

One common mistake which many people make is they find the area like calculated here 480x520 = 249600 Here I wish to suggest reader that it is not a good practice because it may lead to wrong answer in a smart question. Here are the examples

If the dimensions of floor are 16 ft. and 23 ft.
then Area = 16x23 = 368

This area 368 sq.ft. is divisible by 4x4 i.e. a Square tile with Area 16 but square tiles of dimensions 4x4 can't cover such a floor without breaking and using the parts of tiles thereafter.

So to judge whether the Dimensions of square tiles are acceptable we must make sure that each dimension of the floor must be divisible by each dimension of the square tile and result in an integer number which will communicate the number of tiles needed on that dimension

i.e. Number of tiles of Dimensions 4x4 needed to cover a floor of area of 360 X 480 should IDEALLY be calculated like this

On the Dimension 360, the Number of Tiled needed = 360/4 = 90
On the Dimension 480, the Number of Tiled needed = 480/4 = 120
i.e. Total Such tiles = 120*90 = 10800

I hope it makes sense to other reader and they don't make any mistake of this type in a smart question Thanks for the reply. I didn't really use the 480x520=249600 calculation in answering the question, but I always do these kind of calculations in case I need them anyways.

But, thanks again, because it indeed is a very important detail.
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Re: A room is 480 centimeters wide and 520 centimeters long. If n identica  [#permalink]

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_________________ Re: A room is 480 centimeters wide and 520 centimeters long. If n identica   [#permalink] 02 Jan 2018, 19:55
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