Regular and jumbo tiles

[j_shreyans]

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?

A)160
B)240
C)360
D)440
E)560

OAD

[[email protected]]

Hi j_shreyans,

This question is loaded with little details. You'll need to take lots of notes, stay organized and do some basic math to get the correct answer.

We're told that there are two types of tiles: REGULAR and JUMBO.

Now come all of the little math facts you have to take note of (and deduce).....
1) 1/3 of the tiles are JUMBO tiles.

Since 1/3 are JUMBO, the other 2/3 are REGULAR.
This means that the ratio of JUMBO:REGULAR = 1:2; in other words, there are twice as many REGULAR tiles as JUMBO tiles.

2) JUMBO tiles have a length that is 3 TIMES that of the REGULAR tiles AND has the same ratio of length:width as the REGULAR tiles.

We'll come back to this information in a moment.

3) REGULAR tiles cover 80 square-feet of the wall.

Since we weren't given any information about the dimensions of the REGULAR tiles, we can TEST VALUES. Let's say....

1 REGULAR tile = 1ft x 1ft.

Since REGULAR tiles cover 80 square feet, that means there are 80 REGULAR tiles.

Now, let's go back to the 2nd piece of information.....

JUMBO TILES have 3 times the length and the same ratio of length:width as REGULAR tiles.

1 REGULAR tile = 1ft x 1ft.
1 JUMBO tile = 3ft x 3ft.

NOW, let's go back to the 1st piece of information.....

The ratio of JUMBO:REGULAR = 1:2

80 REGULAR tiles (each 1ft x 1ft)
40 JUMBO tiles (each 3ft x 3ft).

Total area of the wall = 80(1)(1) + 40(3)(3) = 80 + 360 = 440 square feet

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

[j_shreyans]

Hi Rich ,

Thanks for the explanation , one thing that why REGULAR TILE 1ft X 1ft.

Pls suggest.

[[email protected]]

Hi j_shreyans,

Since we're never given the actual dimensions of the regular tiles, we can TEST VALUES and make the size of a regular tile whatever we choose. I chose to make a regular tile 1ft x 1ft because it made the rest of the calculations (number of regular times, number of jumbo tiles, etc.) really easy to deal with.

GMAT assassins aren't born, they're made,
Rich

[mallika hunsur]

Hi j_shreyans,

You needn't assume the size of the tiles to be 1x1.
Use variables and write the area of regular, jumbo tiles with respect to length, breadth Of regular tiles.
Form equations using the below
1- length x breadth of reg tiles x number of reg tiles=80
2- total number of tiles= t
3- number of jumbo tiles= t÷3
4- number of reg tiles= t-(t÷3)
5- 80+ t÷3(area of 1 jumbo tile)= area of wall
Use these and calc to get 440, in just about a min you can arrive at the answer.

[GMATGuruNY]

Hi Rich ,

Thanks for the explanation , one thing that why REGULAR TILE 1ft X 1ft.

Pls suggest.

As Rich has noted, we can plug in ANY DIMENSIONS for a regular tile.
For proof, check my two posts here:
https://www.beatthegmat.com/mgmat-ps-t270623.html