A rectangular lot 120 feet long by 80 feet wide is to be

Hi, there. I'm happy to help with this.

The prompt:
A rectangular lot 120 feet long by 80 feet wide is to be partitioned into 10 rectangular gardens. If each of the gardens will have the same dimensions, how many feet of partitioning will be needed to separate the garden?

That part highlighted is HUGE hint in the prompt. The total area is 120 x 80 = 9600, so the gardens must each have an area of 960. If we know one side of a rectangle with area 960, we can find the other side.

Statement #1: one of the dimensions of each garden is to be 40 feet.

960/40 = 96/4 = 24 (notice, this means 24*40 = 960 ... good to know!)

So we have 40x24 rectangles. The length of 24 doesn't go evenly into 80, so we must use five of the 24 lengths to fill out the 120 dimension. That leaves two 40 lengths in the 80 direction, for a two x five configuration of the gardens. This would allow us to figure out the extra perimeter. Statement #1, by itself, is sufficient.

Statement #2: one of the dimensions of each garden is to be 24 feet.

Because we found that 24*40 = 960, we know 960/24 = 40. This leads to the same situation we had in #1, so statement #2, by itself, is sufficient.



Does that make sense? Please let me know if you have any further questions.

Mike
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Can you pls show in a diagram how u use 80.according to my thought process width 80 ill remain unaffected.and we ill divide length 120 in 10 gardens

MIke, the solution looks simpler after the explanation is read...so is it that whenever somebody says the a plot is divided equally in n divisions, we can calcualte teh area and then divide by it...is it always the method to do this type of problems?

What you are doing is figuring out how to answer the prompt question in your own way, ignoring the two statements. In GMAT DS, that is a trap. Any answers you figure out to the prompt that are not allowed by the statements are not relevant to solving the question.

There are a number of ways to divide a 120 x 80 plot into 10 equal rectangles. As you said, we could have ten plots that were 80 x 12. We could also have ten plots that were 8 x 120. Both of those are possible, but neither is consistent with either statement, so for the purposes of solving this DS, both of those are 100% irrelevant.

Your job on DS is not to read the question and think for yourself how to solve the question. Your job, quite specifically, is to determine whether the statements, individually or together, will help you answer the question.

Remember: answering a DS question is very very different from solving a math problem. See this blog:
https://magoosh.com/gmat/2012/introducti ... fficiency/

Does that make sense? Let me know if you have any questions.

Mike
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Dividing the area is one good strategy to have. Whenever you are dealing with larger numbers, thinking about those numbers in terms of their factors can be a helpful approach. We can't say, though, that this is the approach to use "always." Among other things --- every question about area is going to be different. The GMAC excels at creating new questions that do not resemble anything previously asked. You need to master the math content and have a flexible approach in terms of strategy.

Even if the question is about dividing up a plot, a real curveball can occur if it's possible to lay the rectangles going in two different ways.

In this diagram, which divides the 80 x 120 plot into 16 equal rectangles, not all going the same way. I checked for that in the above DS question, and saw that it wasn't possible, but I didn't go into that level of detail in my explanation. Technically, you should be on the lookout for alternate configurations like that, which means you can't simply divide. Nevertheless, questions in which those alternate geometric configurations of rectangles filling a plot are possible do strike me as a bit harder than what the GMAT would ask.

I realize that this is probably a more complicated answer than that for which you were hoping. Does all this make sense? Please let me know if you have any further questions.

Mike
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stumped by the question. Went over from my head.
Thanks mike for explanation. +1

Hi Experts, Bunuel, KarishmaB,

Can you please share your approach to this question?

Thanks in advance.
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Dividing a rectangle of measurements 120 by 80 into 10 equal rectangles can be done in many different ways. In each, the perimeter will be different.

Each small rectangle will have an area of 120*8. The length and width could be 12 and 80 or 120 and 8 or 16 and 60 or 24 and 40 etc.

(1) one of the demensions of each garden is to be 40 feet.

If one dimension is 40, the other must be 24. So the length of partitions is defined now, no matter what the orientation of the gardens on the plot. Hence the statement is sufficient alone.

If you are not sure, think about dividing a rectangular sheet of paper into 10 equal rectangles. The length of the partitions is every line you draw along which you cut the paper to get the triangles. Each point on each line you draw divides the rectangle into two parts and hence you count it twice in the sum of the perimeters of the small rectangles.

Perimeter of the big rectangle = 2*(120 + 80) = 400
Perimeter of all small rectangles = 10 * 2*(40 +24) = 1280

We subtract 400 out of it because it is not included in the length of "partitions." We get 880.
Now each partition length is counted twice in 880 (because it divides the area into two parts so it forms the perimeter of both the parts).
Hence length of partition will be 440, no matter how the 10 rectangles are placed in the big rectangle.
Sufficient alone.


(2) one of the dimensions of each garden is to be 24 feet.

Exactly same logic as statement 1 above.
Sufficient alone.

Answer (D)
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