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by arjunshn » Fri Apr 22, 2011 12:53 am
In a rectangular room which is 20 metres long and 24 wide, square tiles of equal size needs to be placed on the floor in such a way that the entire floor area is covered without breaking any of the tiles.What is the minimum number of square tiles required to cover the entire floor area.
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by force5 » Fri Apr 22, 2011 1:21 am
30 tiles with side 4 each..

what are the answer choices??
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by arjunshn » Fri Apr 22, 2011 1:31 am
ya its 30 tiles..but how did you solve it?
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by force5 » Fri Apr 22, 2011 2:05 am
great sorry didnt post solution because there were no answer choices.

great this is how i did it.

the dimension of the room is 20* 24 that is 5x 4 and 6x4 now if you want that the tile should not be broken then we much choose similar dimension smaller tiles first. 4 is common.
hence the smallest tile should be with side 4 hence area 16.
there fore the number of tiles needed will be 20*24/16 = 30

no need to calculate anything

let me know if you have any question
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by Brent@GMATPrepNow » Fri Apr 22, 2011 4:54 am
arjunshn wrote:In a rectangular room which is 20 metres long and 24 wide, square tiles of equal size needs to be placed on the floor in such a way that the entire floor area is covered without breaking any of the tiles.What is the minimum number of square tiles required to cover the entire floor area.
Hi Arjunshin,

These are great questions you are posting. They'd be even better if you posted the answer choices as well.

The answer choices are important because, in some cases, the fastest solution involves using the answer choices.

Alternatively, it's also important for students to get a chance to guess at the correct answer if they don't know how to solve it. Given the adaptive nature of the test, almost all students are confronted with questions they must guess at, so guessing is something all students should practice doing.
Brent Hanneson - Creator of GMATPrepNow.com
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by kapoor.divs » Sat Apr 23, 2011 3:47 am
Hi,

Another way to arrive at the solution:

The qs requires that we find the area of the largest possible square tile which can be placed in the rectangular room to cover it entirely and without breaking any of the square tiles.

The area would be the highest common factor of the dimensions of the rectangle which is HCF(20,24)=4.

from here its similar to the solution offered by force5:

area of the square tile=4*4=16

So,no of tiles=Area of the rectangular room/area of square tile
= 20 * 24 / 16
= 30
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