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rakeshd347: Master | Next Rank: 500 Posts; Posts: 391; Joined: Sat Mar 02, 2013 5:13 amFollowed by: 4 members; Thanked: 50 times

by rakeshd347 » Sun Oct 13, 2013 2:20 am

A rectangular wall is covered entirely with two kinds of decorative tiles: regular and jumbo. 1/3 of the tiles are jumbo tiles, which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles. If regular tiles cover 80 square feet of the wall, and no tiles overlap, what is the area of the entire wall?

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560

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Source: Beat The GMAT — Problem Solving | Sun Oct 13, 2013 2:20 am

theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Sun Oct 13, 2013 2:42 am

Tiles = x

Regular = 2x/3 (length = A, width = B)

Jumbo = x/3 ( Length = L =3A, width = W)

TO find : 80 + x/3 * (L * W)

A/B = 3A/W
W = 3B

Area of Regular tiles = 80

2x/3 * ( A * B ) = 80

x/3 * (L/3 * W/3) = 40
x/3 *( L * W ) = 360

So, Total Area = 80 + 360 = 440

Answer [spoiler]{D}[/spoiler]

R A H U L

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Oct 13, 2013 3:41 am

rakeshd347 wrote:A rectangular wall is covered entirely with two kinds of decorative tiles: regular and jumbo. 1/3 of the tiles are jumbo tiles, which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles. If regular tiles cover 80 square feet of the wall, and no tiles overlap, what is the area of the entire wall?

160
240
360
440
560

Regular tiles:
Let L=1 and W=1, so that L:W = 1:1.
Area of each regular tile = 1:1 = 1 square foot.
Since regular tiles cover 80 square feet, the total number of regular tiles = 80/1 = 80.

Jumbo tiles:
Since the length of a jumbo tile is 3 times the length of a regular tile, L = 3*1 = 3.
Since the ratio of L to W is the same in each tile, W=3, so that L:W = 3:3 = 1:1.
Area of each jumbo tile = 3*3 = 9 square feet.

Since 1/3 of the tiles are jumbo, of every 3 tiles, 1 is a jumbo, while 2 are regular.
Thus, the number of jumbo tiles is 1/2 the number of regular tiles:
(1/2) * 80 = 40.

Since there are 40 jumbo tiles, each with area of 9 square feet, the total area covered by the jumbo tiles = 40*9 = 360 square feet.

Thus:
Area of the entire wall = (regular tile area) + (jumbo tile area) = 80+360 = 440.

The correct answer is D.

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manhhiep2509: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Mon Mar 04, 2013 1:18 am; Thanked: 1 times; GMAT Score:700

by manhhiep2509 » Thu Jan 16, 2014 7:07 pm

Hi GMATGrunuNY

Why do you say that "Let L=1 and W=1, so that L:W = 1:1. Area of each regular tile = 1:1 = 1 square foot."
To me, regular tiles or jumbo tiles are just two kind of tiles and I cannot tell any feature of them.
-----

The explanation of manhattan says "Alternatively, use a neat shortcut. If 1/3 of the tiles are jumbo, then 2/3 are regular. In that case, for every two regular tiles, there is one jumbo tile. One jumbo tile has an area 9Lw and two regular tiles have an area 2Lw, so the tiles will be placed in "sets" of 9Lw + 2Lw = 11Lw. The correct answer, then, must be a multiple of 11, and only answer (D) is a multiple of 11."

Is the author assumes that LW is an integer? If not, I cannot understand why he think the area of the wall must be a multiple of 11. The area is still an integer even if "L" = 20/11 and "W" = 5, for example.

Thank you.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Jan 16, 2014 7:44 pm

manhhiep2509 wrote:Hi GMATGrunuNY

Why do you say that "Let L=1 and W=1, so that L:W = 1:1. Area of each regular tile = 1:1 = 1 square foot."
To me, regular tiles or jumbo tiles are just two kind of tiles and I cannot tell any feature of them.

For the regular tiles, only ONE constraint is given:
They cover a TOTAL area of 80 square feet.
Thus, we can plug in ANY length and width such that LWâ‰¤80.
To illustrate:

Regular tiles:
Let L=4 and W=10.
Then the area of each regular tile = 4*10 = 40.
Number of regular tiles required to cover 80 square feet = 80/40 = 2.

Jumbo tiles:
Since there are 1/2 as many jumbo tiles (as shown in my post above), the number of jumbo tiles = 1.
Since each jumbo tiles is 3 times as long as each regular tile, L = 3*4 = 12.
Since L:W must be the same for each kind of tile -- and 4:10 = 12:30 -- W=30.
Area of the 1 jumbo tile = 12*30 = 360.

Thus:
Area of the entire wall = 80+360 = 440.

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vipulgoyal: Master | Next Rank: 500 Posts; Posts: 468; Joined: Mon Jul 25, 2011 10:20 pmFollowed by: 4 members; Thanked: 29 times

by vipulgoyal » Fri Jan 24, 2014 12:35 am

alt approach

since it is clear that the area of jumbo tiles will be 9 times as the area of mormal tile
and it given that area of normal tile wall is 80 Sq ft
normal tile no : jumbo tile no:: 2/3*x : 1/3*x
if number of tile were equal then are should be like 80 and 720, now putting above constrain which says area should be half(of wall of jumbo tile 720/2)
360+80 = 440

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