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A farmer has a field that measures 1000 ft wide by 2000 ft l [#permalink]
28 May 2011, 02:07
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Difficulty:
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Question Stats:
56% (03:45) correct
44% (03:16) wrong based on 118 sessions
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?
Re: 650 plus level question [#permalink]
28 May 2011, 03:42
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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:
Re: 650 plus level question [#permalink]
28 May 2011, 06:07
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:
Re: 650 plus level question [#permalink]
29 May 2011, 01:42
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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 3732 times ]
Re: 650 plus level question [#permalink]
31 May 2011, 11:00
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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
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Re: 650 plus level question [#permalink]
02 Jun 2011, 12:28
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..
Re: 650 plus level question [#permalink]
13 Jun 2011, 13:52
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
Re: 650 plus level question [#permalink]
21 Jun 2011, 14:41
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?
Re: 650 plus level question [#permalink]
09 Jun 2014, 08:15
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Re: A farmer has a field that measures 1000 ft wide by 2000 ft l [#permalink]
08 Feb 2016, 04:23
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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