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# sat math problem from new BB second ed.

1588 replies104 threadsRegistered User Senior Member
edited May 2011
here's a graphic that goes with it: [url]http://i28.****.com/iw82sk.jpg[/url]

The pattern shown above is composed of rectangles. This pattern is used repeatedly to completely cover a rectangular region 12L units long and 10L units wide. How many rectangles of dimension L by W are needed?

A) 30
36
C) 100
D) 150
E) 180 << that's the answer.

i don't get how to arrive at this solution, thanks!
edited May 2011
12 replies
Post edited by desi_chick on

## Replies to: sat math problem from new BB second ed.

• 1970 replies74 threadsRegistered User Senior Member
2L = 3W

therefore, each rectangle is L x 2/3L = 2/3 L^2

Total area is 120L^2

120L^2/ (2/3)L^2 = 180
• 206 replies12 threadsRegistered User Junior Member
well, from the image, we see that 2L=3W.

we can see the dimensions of the pattern are 2L x (L+W)= 2L x (5/3 L). luckily, if you use 6 of these as the length, and 6 as the width (creating a 6x6 array of this pattern), the dimensions would be (2L * 6) x (5/3 L * 6) = 12L x 10L. thus there would be 36 of the pattern shown, and since there are 5 L x W rectangles in each pattern, there are 36 * 5 =180 L x W rectangles needed.
• 1970 replies74 threadsRegistered User Senior Member
^That's unnecessarily complex :P
• 1059 replies20 threadsRegistered User Senior Member
It is even easier if you make up concrete numbers. But you have to make it so 2 L's = 3 W's.

Say you use L=6 and W=4. That makes the areal of the big region 12L x 10L = 72 x 60 = 4320.

Then, since each little rectangle has area 4 x 6 = 24, then the number of them you need is 4320 / 24 = 180
• 1 replies0 threadsRegistered User New Member
Bigb14: Your reply to Urc is incorrect. Urc VERIFIED that there was a solution. You did not. Urc's answer is better (proved) as a result. pckeller has the same problem. 180 means nothing without the Urc's verification.
• 221 replies15 threadsRegistered User Junior Member
I substituted.
2L = 3w
L = 3/2w
Area of Rectangle = L x w = 3/2w x w = 3/2w^2
Area of Rectangular Region = 12L x 10L = 18w x 15w = 270w^2
(270w^2)/(1.5w^2) = 180.
• 24 replies2 threadsRegistered User New Member
My way is different L=1.5W

so

W+x(1.5W)=15W
x(1.5W)=14W
x=28/3

so theres 12 rectangles going down vertically and then 18 going down horizontally in each line. So I just did (28/3)*18=168 and +12 = 180. Different method probably not as efficient as those mentioned above.
• 24 replies2 threadsRegistered User New Member
More easily understood though. Probably the hardest SAT question iv'e ever seen (my opinion)
• 1266 replies24 threadsRegistered User Senior Member
In the expression 2L=3W, the simplest choices for L and W are L=3 and W=2 (because clearly 2*3=3*2).

Now just apply the simple strategy "to see how many 2-dimensional objects fit inside another 2-dimensional object, divide the areas."

So the answer is (12L*10L)/6 = (12*3*10*3)/6 = 180.