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A farmer has two rectangular fields. The larger field has tw [#permalink]
26 Aug 2018, 04:43

Expert's post

00:00

Question Stats:

45% (00:34) correct
54% (00:48) wrong based on 120 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?

Re: A farmer has two rectangular fields. The larger field has tw [#permalink]
26 Aug 2018, 05:52

2

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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

1

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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?

Re: A farmer has two rectangular fields. The larger field has tw [#permalink]
10 Jul 2019, 08:38

2

This post received KUDOS

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)

Answer: D

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

1

This post received 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.

Re: A farmer has two rectangular fields. The larger field has tw [#permalink]
14 Jul 2020, 04:54

Testing numbers here may get you confuse. If we say that, small rectangle has Length and width = 1 and then area of 1, and the larger will have 2*4=8 yeah here difference is 7. However, let pick different numbers lets say small has length of 2 and width of 1 = area= 2 and larger will have 4*2=8 and here the difference will be 6! Can anyone please elaborate on this?

Re: A farmer has two rectangular fields. The larger field has tw [#permalink]
14 Jul 2020, 06:55

GR3A wrote:

Testing numbers here may get you confuse. If we say that, small rectangle has Length and width = 1 and then area of 1, and the larger will have 2*4=8 yeah here difference is 7. However, let pick different numbers lets say small has length of 2 and width of 1 = area= 2 and larger will have 4*2=8 and here the difference will be 6! Can anyone please elaborate on this?

I agree I also chose values like L= 2 and W=3 for smaller rectangle and 2L = 2*2=4, W=3*4=12 Area of small rectangle = 2*3 = 6 Area of Large rectangle = 4*12=48

48/6=8 option D is answer..why its incorrect?
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A farmer has two rectangular fields. Field N has 6 times the [#permalink]
08 Sep 2020, 03:35

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?