Number of tiles needed?

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sat Feb 22, 2014 5:01 pm

Hello,

Can you please assist with this:

The figure above shows a large square formed by fitting three L-shaped tiles and one small square tile together. If a rectangular floor l0 feet by 12 feet is to be tiled in large squares of this design, how many L-shaped tiles will be needed?

OA: 810

I was just wondering if these kind of questions are common in the GMAT?

Thanks,
Sri

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Source: Beat The GMAT — Problem Solving | Sat Feb 22, 2014 5:01 pm

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by Brent@GMATPrepNow » Sat Feb 22, 2014 5:16 pm

gmattesttaker2 wrote: The figure above shows a large square formed by fitting three L-shaped tiles and one small square tile together. If a rectangular floor l0 feet by 12 feet is to be tiled in large squares of this design, how many L-shaped tiles will be needed?

OA: 810

I was just wondering if these kind of questions are common in the GMAT?

Hey Sri,

This question seems fine for the GMAT. Of course, the test-makers wouldn't assume that everyone knows there are 12 inches in a foot, so they'd likely include that information somewhere/.

In inches, the floor is 120 inches by 144 inches.
If we treat the 8 inch by 8 inch square (as shown in the diagram) as 1 UNIT, how many units fit in the 120-inch by 144-inch floor?
Well, width-wise, 8 inches divides into 120 inches 15 times.
Length-wise, 8 inches divides into 144 inches 18 times.
So, the TOTAL number of square units that fit on the floor = (15)(18) = 270

So, 270 of the UNITS (as shown in the diagram) fit on the floor.
Since each UNIT consists of 3 L-shaped pieces, the total number of L-shaped pieces = (3)(270) = 810

Cheers,
Brent

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Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members; Thanked: 335 times

by Patrick_GMATFix » Sat Feb 22, 2014 7:59 pm

My approach:

We know that each design uses 3 "L" tiles. If we can figure out how many designs it will take to cover the whole floor, we can multiply that by 3 to find the number of "L" tiles needed.

The only thing to be careful about is that we use consistent units. The design is 8*8 square inches, and the floor area is 10*12 feet, or (10*12) * (12*12) square inches (remember 1 foot = 12 inches).

Let's find the number of full designs needed by dividing the total area by the area of each design:

Notice that when solving a problem that requires many multiplications and divisions, I try to simplify numbers as much as I can before I perform multiplications; this keeps the numbers as small as possible and allows me to work faster.

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by [email protected] » Sun Feb 23, 2014 1:40 am

Hi Sri,

Lately, you've been posting questions that do not include the answer choices. By ignoring the answers, you're forcing yourself into a "math only" mentality, which is something that the GMAT RARELY forces you to do.

While it is certainly worthwhile to know how math "works", the math approach often takes longer than a tactic (TESTing Values, TESTING THE ANSWERS, Number Properties, etc.) would take. Remember that your goal on individual questions is two-fold:

1) Get the question correct.
2) Do so in the fastest way possible.

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

Contact Rich at [email protected]

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by GMATGuruNY » Sun Feb 23, 2014 4:21 am

gmattesttaker2 wrote: The figure above shows a large square formed by fitting three L-shaped tiles and one small square tile together. If a rectangular floor l0 feet by 12 feet is to be tiled in large squares of this design, how many L-shaped tiles will be needed?

The approach below employs the following conversion rates:
3 L-tiles = (8 inches)(8 inches) = 64 square inches.
1 square foot = (1 foot)(1 foot) = (12 inches)(12 inches) = 144 square inches.
1 floor = (10 feet)(12 feet) = 120 square feet.

In the product below, all of the colored units CANCEL OUT, leaving the resulting values in terms of L-TILES PER FLOOR:
(3 L-tiles)/(64 square inches) * (144 square inches)/(1 square foot) * (120 square feet)/(1 floor)

= (3*144*120)/(8*8)

= 3*18*15

= 810 L-tiles per floor.

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