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# A farmer has a field that measures 1000 ft wide by 2000 ft l

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Manager
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A farmer has a field that measures 1000 ft wide by 2000 ft l [#permalink]

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28 May 2011, 03:07
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Difficulty:

75% (hard)

Question Stats:

55% (03:49) correct 45% (03:15) wrong based on 127 sessions

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A farmer has a field that measures 1000 ft wide by 2000 ft long. There is an untillable strip 20 ft wide on the inside edge of the field, and a 30 ft wide untillable strip bisects the field into two squares (approximate). Approximately what percentage of the field is tillable?

A. 98%
B. 93%
C. 91%
D. 90%
E. 88%
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Jun 2014, 09:29, edited 1 time in total.
Renamed the topic and edited the question.
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Re: 650 plus level question [#permalink]

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28 May 2011, 04:42
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Expert's post
Actually you can solve the problem pretty fast by using following approach:

1. one shorter inside strip with width of 20 ft takes 20/2000 = 1% of field
2. There is 2 short strips, 2 long strips (twice as long as shorts ones) and one short but wider strip that equals 30/20 = 1.5 short strips.
3. Approximately we have 2 + 2*2 + 1.5 = 7.5 short strips --> ~ 7.5% or 92.5%
4. As we didn't take into account overlaps between strips it will be slightly higher than 92.5%.

Or you can use calculations but I think it will take more time:

$$%=100%*\frac{2*(1000-2*20)*(1000-20-\frac{30}{2})}{1000*2000} = 0.9264$$
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Re: 650 plus level question [#permalink]

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28 May 2011, 07:07
walker wrote:
Actually you can solve the problem pretty fast by using following approach:

1. one shorter inside strip with width of 20 ft takes 20/2000 = 1% of field
2. There is 2 short strips, 2 long strips (twice as long as shorts ones) and one short but wider strip that equals 30/20 = 1.5 short strips.
3. Approximately we have 2 + 2*2 + 1.5 = 7.5 short strips --> ~ 7.5% or 92.5%
4. As we didn't take into account overlaps between strips it will be slightly higher than 92.5%.

Or you can use calculations but I think it will take more time:

$$%=100%*\frac{2*(1000-2*20)*(1000-20-\frac{30}{2})}{1000*2000} = 0.9264$$

Good method ...fast and quick
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Re: 650 plus level question [#permalink]

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28 May 2011, 07:58
can u please explain the same with the help of diagram..
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Re: 650 plus level question [#permalink]

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28 May 2011, 08:51
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[Reveal] Spoiler:
Attachment:

114310.png [ 3.71 KiB | Viewed 4174 times ]

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Re: 650 plus level question [#permalink]

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28 May 2011, 11:42
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960*965*2/(1000*2000) = 93.04%
B.
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Re: 650 plus level question [#permalink]

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28 May 2011, 13:26
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okai .. its C

rectangle of 1000*2000

1000-2*20 = 960
(2000-2*20-30)/2 = 965
2 squares = 2*965*960/(1000*2000) = 93% approx.
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Re: 650 plus level question [#permalink]

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29 May 2011, 02:42
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ruturaj wrote:
A farmer has a field that measures 1000 ft wide by 2000 ft long. There is an untillable strip 20 ft wide on the inside edge of the field, and a 30 ft wide untillable strip bisects the field into two squares (approximate). Approximately what percentage of the field is tillable?

A) 98%

B) 93%

C) 91%

D) 90%

E) 88%

Total Area = 1000*2000
Tillable Square's side horizontally = (2000-20-30-20)/2 = 1930/2 = 965
Tillable Square's side vertically = (1000-20-20) = 960 = 960

Consider it as 960:
$$% = \frac{2*960*960}{1000*2000}*100=\frac{2*0.96*0.96*1}{2}*100=(0.96)^2*100=92.16 \approx 93%$$

Why approximated to 93 and not 91 because we shortened one side from 965 to 960. Thus, in reality the squares are bigger.

Ans: "B"

By the way, I looked up tillable after solving.

tillable: arable, cultivable, cultivatable

Attachment:

tillable_field.PNG [ 5.2 KiB | Viewed 3882 times ]

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Re: 650 plus level question [#permalink]

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31 May 2011, 12:00
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fluke wrote:
ruturaj wrote:
A farmer has a field that measures 1000 ft wide by 2000 ft long. There is an untillable strip 20 ft wide on the inside edge of the field, and a 30 ft wide untillable strip bisects the field into two squares (approximate). Approximately what percentage of the field is tillable?

A) 98%

B) 93%

C) 91%

D) 90%

E) 88%

Total Area = 1000*2000
Tillable Square's side horizontally = (2000-20-30-20)/2 = 1930/2 = 965
Tillable Square's side vertically = (1000-20-20) = 960 = 960

Consider it as 960:
$$% = \frac{2*960*960}{1000*2000}*100=\frac{2*0.96*0.96*1}{2}*100=(0.96)^2*100=92.16 \approx 93%$$

Why approximated to 93 and not 91 because we shortened one side from 965 to 960. Thus, in reality the squares are bigger.

Ans: "B"

By the way, I looked up tillable after solving.

tillable: arable, cultivable, cultivatable

Attachment:
tillable_field.PNG

this was quite smart fluke

kudos from me
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Re: 650 plus level question [#permalink]

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02 Jun 2011, 13:28
Guys, seriously.. If I would get this question on the actual exam I would seriously start crying or something.. Pfff it took me 30minutes to friggin understand what the question is about... Sigh..
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Re: 650 plus level question [#permalink]

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13 Jun 2011, 14:52
i just summed the differences:

20*1000+20*1980+20*980+20*1960 will be the frame. the bisector will be 30* 960 (which can be considered as 20*960 for approximation, remembering that the rounding can cost only 1/2 %)

20*(1980+1960+1000+980+2*960)/2000*1000=the rest is simple and got 7%(+-)which must be substracted from 100

must admit it took me 2 minutes+ to solve
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Re: 650 plus level question [#permalink]

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21 Jun 2011, 13:37
Shalom!
Please tell me that this type of question is not in the 600 to 700 level question range on the GMAT.
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Re: 650 plus level question [#permalink]

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21 Jun 2011, 13:40
Lol, I was REALLY thinking the same thing! I'm afraid it is
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Re: 650 plus level question [#permalink]

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21 Jun 2011, 15:41
Shalom!
I have a question. If I can expect to see this type of question in the 600 to 700 range then how do I prepare to calculate the answer without the use of a calculator?
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Re: 650 plus level question [#permalink]

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09 Jun 2014, 09:15
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Re: A farmer has a field that measures 1000 ft wide by 2000 ft l [#permalink]

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08 Feb 2016, 05:23
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A farmer has a field that measures 1000 ft wide by 2000 ft l   [#permalink] 08 Feb 2016, 05:23
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# A farmer has a field that measures 1000 ft wide by 2000 ft l

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