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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]  26 Aug 2018, 04:43
Expert's post
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Question Stats:

72% (00:27) correct 27% (00:59) wrong based on 11 sessions
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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Posts: 994
WE: Engineering (Energy and Utilities)
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Re: A farmer has two rectangular fields. The larger field has tw [#permalink]  26 Aug 2018, 05:52
1
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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]  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
GRE Instructor
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Re: A farmer has two rectangular fields. Field N has 6 times the [#permalink]  10 Jul 2019, 06:37
Expert's post
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

Cheers,
Brent
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GRE Instructor
Joined: 10 Apr 2015
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Kudos [?]: 2352 [1] , given: 33

Re: A farmer has two rectangular fields. The larger field has tw [#permalink]  10 Jul 2019, 08:38
1
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Expert's post
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)

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Re: A farmer has two rectangular fields. The larger field has tw [#permalink]  04 Sep 2019, 08:00
1
KUDOS
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]  06 Sep 2019, 02:37
1
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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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