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A farmer owns a square parcel of land, on which the longest straight-l

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Bunuel
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A farmer owns a square parcel of land, on which the longest straight-l [#permalink] New post   30 Jan 2015, 07:30
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A farmer owns a square parcel of land, on which the longest straight-line distance he can travel between any two points on his property is 4 kilometers. If he purchases the land immediately to the north of his property, and if that land is the same width east to west but twice as long north to south, how many square kilometers of property would he then own?

A. 16
B. 16√2
C. 24
D. 24√2
E. 48

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C
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Re: A farmer owns a square parcel of land, on which the longest straight-l [#permalink] New post   30 Jan 2015, 09:34
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Hello Bunuel, I gave it a try:

CORRECT ANSWER C. 24

The longest straight-line distance in his square parcel is the diagonals, so the diagonal d of the square = 4.

Using the right triange pitagora formula, we find the side of the square of the actual parcel which I will further note l.

l^2+l^2 = 4^2

2l^2 = 16 => l^2 = 8 =? l = 2√2

If the side of the actual parcel is 2√2 then the long side of the new parcel is 2 x 2√2 = 4√2 which helps us find the side of the total parcel:

2√2 + 4√2 = 6√2

The area of the total parcel is the area of its rectangle which is large side x small side so

2√2 x 6√2 = 24 => CORRECT ANSWER C


Bunuel wrote:
Attachment:
farmland.png
A farmer owns a square parcel of land, on which the longest straight-line distance he can travel between any two points on his property is 4 kilometers. If he purchases the land immediately to the north of his property, and if that land is the same width east to west but twice as long north to south, how many square kilometers of property would he then own?

A. 16
B. 16√2
C. 24
D. 24√2
E. 48

Kudos for a correct solution.

The OA will be revealed on Sunday
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Re: A farmer owns a square parcel of land, on which the longest straight-l [#permalink] New post   31 Jan 2015, 01:03
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Bunuel wrote:
Attachment:
farmland.png
A farmer owns a square parcel of land, on which the longest straight-line distance he can travel between any two points on his property is 4 kilometers. If he purchases the land immediately to the north of his property, and if that land is the same width east to west but twice as long north to south, how many square kilometers of property would he then own?

A. 16
B. 16√2
C. 24
D. 24√2
E. 48

Kudos for a correct solution.

The OA will be revealed on Sunday


C. 24.

Diagonal of original square = 4
Side = 2\(\sqrt{2}\)

New Rectangle Length = 6\(\sqrt{2}\)
Width = 2\(\sqrt{2}\)


Thus Area L*b = 6\(\sqrt{2}\) * 2\(\sqrt{2}\) = 24
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Re: A farmer owns a square parcel of land, on which the longest straight-l [#permalink] New post   30 Jan 2015, 10:06
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ans C 24...
longest straight line in a square=diagonal so sides =2*underrroot2
length of new land =3*2*underrroot2..
a=underrroot2*3*2*underrroot2=24
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Re: A farmer owns a square parcel of land, on which the longest straight-l [#permalink] New post   31 Jan 2015, 02:05
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Bunuel wrote:
Attachment:
farmland.png
A farmer owns a square parcel of land, on which the longest straight-line distance he can travel between any two points on his property is 4 kilometers. If he purchases the land immediately to the north of his property, and if that land is the same width east to west but twice as long north to south, how many square kilometers of property would he then own?

A. 16
B. 16√2
C. 24
D. 24√2
E. 48

Kudos for a correct solution.

The OA will be revealed on Sunday


side of the square 2√2. Area of the square 8. Area of the rectangular land 16

Total area 24.

Answer C
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Re: A farmer owns a square parcel of land, on which the longest straight-l [#permalink] New post   02 Feb 2015, 04:33
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Bunuel wrote:
Attachment:
farmland.png
A farmer owns a square parcel of land, on which the longest straight-line distance he can travel between any two points on his property is 4 kilometers. If he purchases the land immediately to the north of his property, and if that land is the same width east to west but twice as long north to south, how many square kilometers of property would he then own?

A. 16
B. 16√2
C. 24
D. 24√2
E. 48

Kudos for a correct solution.

The OA will be revealed on Sunday


VERITAS PREP OFFICIAL SOLUTION:

While the math looks a little ugly to start, it cleans up nicely (as usual on the GMAT). Since the longest distance between two points on a square is its diagonal, if that distance for the current plot of land is 4, then that means that the length of each side of that smaller square is 4/√2. And since we know that the width of the new property is the same but the length is double, that makes the length of the new property 8/√2. When combined, the width stays the same at 4/√2 and the new length becomes 12/√2, and then to find the area just multiply them together. The roots in the denominator will multiply out to just 2, so the fraction is 48/2 for a total of 24.
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Re: A farmer owns a square parcel of land, on which the longest straight-l [#permalink] New post   31 Jan 2015, 01:06
TudorM wrote:
Hello Bunuel, I gave it a try:

CORRECT ANSWER C. 24

The longest straight-line distance in his square parcel is the diagonals, so the diagonal d of the square = 4.

Using the right triange pitagora formula, we find the side of the square of the actual parcel which I will further note l.

l^2+l^2 = 4^2

2l^2 = 16 => l^2 = 8 =? l = 2√2

If the side of the actual parcel is 2√2 then the long side of the new parcel is 2 x 2√2 = 4√2 which helps us find the side of the total parcel:

2√2 + 4√2 = 6√2

The area of the total parcel is the area of its rectangle which is large side x small side so

2√2 x 6√2 = 24 => CORRECT ANSWER C


Bunuel wrote:
Attachment:
farmland.png
A farmer owns a square parcel of land, on which the longest straight-line distance he can travel between any two points on his property is 4 kilometers. If he purchases the land immediately to the north of his property, and if that land is the same width east to west but twice as long north to south, how many square kilometers of property would he then own?

A. 16
B. 16√2
C. 24
D. 24√2
E. 48

Kudos for a correct solution.

The OA will be revealed on Sunday


Hey TudorM we have the same test date.. All the best..
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Re: A farmer owns a square parcel of land, on which the longest straight-l [#permalink] New post   20 Jul 2019, 03:33
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