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A farmer has two rectangular fields. The larger field has tw

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A farmer has two rectangular fields. The larger field has tw [#permalink] New post 26 Aug 2018, 04:43
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A farmer has two rectangular fields. The larger field has twice the length and 4 times the width of the smaller field. If the smaller field has area K, then the area of the larger field is greater than the area of the smaller field by what amount?

(A) 2K

(B) 6K

(C) 7K

(D) 8K

(E) 12K
[Reveal] Spoiler: OA

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Re: A farmer has two rectangular fields. The larger field has tw [#permalink] New post 26 Aug 2018, 05:52
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Carcass wrote:
A farmer has two rectangular fields. The larger field has twice the length and 4 times the width of the smaller field. If the smaller field has area K, then the area of the larger field is greater than the area of the smaller field by what amount?

(A) 2K

(B) 6K

(C) 7K

(D) 8K

(E) 12K


Let the length of the samller field = L

width of the smaller field = W

So the area of the smaller field = WL = K

Now the length of the bigger field = 2L

Width of the bigger field = 4W

So the Area = 4W * 2L = 8WL = 8K

Therefore the area of the larger field is greater than the area of the smaller field = 8K - K = 7K
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A farmer has two rectangular fields. Field N has 6 times the [#permalink] New post 10 Jul 2019, 05:52
A farmer has two rectangular fields. Field N has 6 times the length and 2/3 times the width of the field M. If field M has area A, then the area of field N is greater than the area of field M by what amount?

2A

2.5A

3A

4A

5A
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Re: A farmer has two rectangular fields. Field N has 6 times the [#permalink] New post 10 Jul 2019, 06:37
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Before posting a question, please perform a quick search first.
You'll find that this question has already been posted here: https://greprepclub.com/forum/a-farmer- ... 10592.html

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Brent
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Re: A farmer has two rectangular fields. The larger field has tw [#permalink] New post 10 Jul 2019, 08:38
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Carcass wrote:
A farmer has two rectangular fields. The larger field has twice the length and 4 times the width of the smaller field. If the smaller field has area K, then the area of the larger field is greater than the area of the smaller field by what amount?

(A) 2K
(B) 6K
(C) 7K
(D) 8K
(E) 12K


The smaller field has area K
Area of a rectangle = (base)(height) = (length)(width)
Let L = length of SMALLER field
Let W = width of SMALLER field
So, we can write: LW = K

The LARGER field has twice the length and 4 times the width of the smaller field.
Let 2L = length of LARGER field
Let 4W = width of LARGER field
So area of LARGER field = (2L)(4W) = 8LW

Since we already know that LW = K, we can replace LW with K to get:
Area of LARGER field = 8(K)

Answer: D

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Re: A farmer has two rectangular fields. The larger field has tw [#permalink] New post 04 Sep 2019, 08:00
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Brent, they say the answer is C. (I thought it was D too at first).

Having said that, if someone said they have a bag of flour that is 1 pound and another bag that is 8 pounds, and they said how much greater is the 2nd bag then the first, in terms of weight, it seems like a correct response would be "8 times greater". I guess saying "7 pounds greater is also correct".

I guess the key is they didn't ask for how many TIMES greater, just how MUCH greater. At least, that's my interpretation.
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Re: A farmer has two rectangular fields. The larger field has tw [#permalink] New post 06 Sep 2019, 02:37
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Let the length of the samller field = L

width of the smaller field = W

So the area of the smaller field = WL = K

Now the length of the bigger field = 2L

Width of the bigger field = 4W

So the Area = 4W * 2L = 8WL = 8K

Therefore the area of the larger field is greater than the area of the smaller field = 8K - K = 7K
Re: A farmer has two rectangular fields. The larger field has tw   [#permalink] 06 Sep 2019, 02:37
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A farmer has two rectangular fields. The larger field has tw

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