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# A farmer has two rectangular fields. The larger field has twice the

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Math Expert
Joined: 02 Sep 2009
Posts: 46291
A farmer has two rectangular fields. The larger field has twice the [#permalink]

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20 Sep 2017, 04:35
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Question Stats:

70% (00:37) correct 30% (00:42) wrong based on 29 sessions

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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

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Re: A farmer has two rectangular fields. The larger field has twice the [#permalink]

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20 Sep 2017, 04:48
Bunuel 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

Length of larger field say L=2L1
Width of larger field say B=4B1
Area of larger field A = LxB = 8xL1B1
Area of smaller field = L1B1 = K
Area of larger field A = 8xK
Hence, area of the larger field is greater than the area of the smaller field by 8K-K = 7K

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A farmer has two rectangular fields. The larger field has twice the [#permalink]

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20 Sep 2017, 07:33
Bunuel 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 width of smaller field = x
Let length of smaller field = y

Width of larger field = 4x
Length of larger field = 2y

Area of smaller field = xy = K

Area of larger field = (4x)(2y) = 8(xy)
xy = K, Area of larger = 8K

Area of larger field is greater by what amount? 8K - K = 7K

OR choose values, where

Area of small = K
Area of small = (L * W)
K = LW

Small W = 1, Small L = 1

Large W = 4, Large L = 2

Small area = (LW) = (1*1) = 1 = K

Large area = (2L*4W) = 8(LW) = 8K

Difference is 8K - K = 7K
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A farmer has two rectangular fields. The larger field has twice the   [#permalink] 20 Sep 2017, 07:33
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