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# A small, rectangular park has a perimeter of 560 feet and a

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Senior Manager
Joined: 14 Jul 2006
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A small, rectangular park has a perimeter of 560 feet and a [#permalink]

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22 Aug 2006, 05:55
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet?

A. 19,200
B. 19,600
C. 20,000
D. 20,400
E. 20,800
Senior Manager
Joined: 14 Jul 2006
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22 Aug 2006, 06:36
Hi Sandi,

Answer is A just took a paper base gmat test. Had to guess on this one since I was running out of time. Look simple in the beginning until you needed to factor. Turned out to be a trap.

L+w=280 l=280-w
l^2+w^2=200^2
w^2-280w+19200=)
w(w-280)=-19200
take out the negative num
-w(280-w)=-19200 --> w(280-w)=19200
Senior Manager
Joined: 15 Aug 2004
Posts: 327

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22 Aug 2006, 07:01
Better way...

2(x+y) = 560
=> x+y = 280

Squaring both sides...

x^2 + y^2 + 2xy = 280^2

But we know that x^2 + y^2 = 200^2

So substitute....2xy = 280^2 - 200^2
=> 2xy = 80 * 480
=> xy = 19200

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Joined: 29 Jan 2005
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22 Aug 2006, 07:14
apollo168 wrote:
Hi Sandi,

Answer is A just took a paper base gmat test. Had to guess on this one since I was running out of time. Look simple in the beginning until you needed to factor. Turned out to be a trap.

L+w=280 l=280-w
l^2+w^2=200^2
w^2-280w+19200=)
w(w-280)=-19200
take out the negative num
-w(280-w)=-19200 --> w(280-w)=19200

Yeah, I substituted the first equation into the second and got: w^2-280w+19200=0

Then I broke down 19200 to get the factors (w-160)(w-120)=0

Either way, the area comes to 19,200

What's the shortcut here??

Last edited by GMATT73 on 22 Aug 2006, 08:28, edited 1 time in total.
Intern
Joined: 14 Aug 2006
Posts: 8

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22 Aug 2006, 08:20
hmm. interesting. I ddi the calc in my head but now I will look at it again.

BTW - Can you answer this one?

Data Sufficiency - Section 6 -#20
The symbol @ represents one of the following operations: addition, subtraction, multiplication, or division. What is the value of 3@2?

1) 0@1=1
2) 1@0=1
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sandi10017

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22 Aug 2006, 08:21
GMATT73 wrote:
apollo168 wrote:
Hi Sandi,

w^2-280w+19200=)
w(w-280)=-19200
take out the negative num
-w(280-w)=-19200 --> w(280-w)=19200

Yeah, I substituted the first equation into the second and got: w^2-280w+19200=0

Then I broke down 19200 to get the factors (w-160)(w-180)=0

Either way, the area comes to 19,200

What's the shortcut here??

Hi,

I had a problem factoring the large number. I dont think(w-160)(w-180) is equal to w^2-280w+19200. Couldnt find the factors.

What I did was I form fitted the w^2-280w+19200 to match the equation of the area w(280-w) and equate it to 19200
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Joined: 14 Jul 2005
Posts: 402

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22 Aug 2006, 08:31
sandi10017 wrote:
hmm. interesting. I ddi the calc in my head but now I will look at it again.

BTW - Can you answer this one?

Data Sufficiency - Section 6 -#20
The symbol @ represents one of the following operations: addition, subtraction, multiplication, or division. What is the value of 3@2?

1) 0@1=1
2) 1@0=1

From Statement 1 - @ can only be '+' only hence 3@2 = 3+2 = 5

From Statement 2 - 1@0=1 implies @ could be '+' or '-' which would give you 2 different answers for 3@2 (NOT SUFF)
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22 Aug 2006, 08:42
The text book answer is A, But I'm confused because technically you could switch the numbers - meaning in data point 1) could be 0+1=1 OR it could be 1-0=1, in the latter, this would translate to 2-3=-1, while the former would translate to 3+2=5 and thus A alone is insufficient.

Does anyone have a solution to this?

Now this one. This one is giving me a lot of trouble as well.

21. Are the numbers K/4, Z/3, R/2 in increasing order?

1)3<Z<4
2)R<Z<K
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sandi10017

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Joined: 14 Jul 2006
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22 Aug 2006, 08:45
Hey sumitsarkar82

That is a better way thanks
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22 Aug 2006, 08:45
sandi10017 wrote:
The text book answer is A, But I'm confused because technically you could switch the numbers - meaning in data point 1) could be 0+1=1 OR it could be 1-0=1, in the latter, this would translate to 2-3=-1, while the former would translate to 3+2=5 and thus A alone is insufficient.

Does anyone have a solution to this?

Now this one. This one is giving me a lot of trouble as well.

21. Are the numbers K/4, Z/3, R/2 in increasing order?

1)3<Z<4
2)R<Z<K

Unless the stem specifies that you can switch the numbers, we have to do the calculations in the order given. Somebody here once said it right: Assume nothing. Only (A) stands.
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Joined: 14 Aug 2006
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22 Aug 2006, 08:49
Well thank you very much for clarifying that for me. I would have made teh assumption that the "@" function could be interpreted in any way possible. Its still baffling to me that you have to take the numbers in the order given but I guess for now its one of those things I will have to accept.

Thanks so much!
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sandi10017

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22 Aug 2006, 08:53
Actually now it makes sense. The question states 3@2, where @, represents a function. Hence the reason you take the order as given.

now i get it.
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sandi10017

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22 Aug 2006, 13:33
sandi, could you post your other question as an independent post? it will get better responses that way.

thanks
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afraid of loosing , there is another person who
keeps making mistakes and succeeds..

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22 Aug 2006, 13:39
by the way, i think answer to the R,Z,K question posted by sandi is E

stem 1 => z is a positive number between 3 and 4

stem 2 => R is less than Z and K is greater than Z. So K is a positive number, whereas R can be a positive or negative number of any magnitude. So, you can't tell for sure what relationship K/4, Z/3 and R/2 have.
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for every person who doesn't try because he is
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keeps making mistakes and succeeds..

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22 Aug 2006, 21:03
A. 19,200

2(l+w) = 560 => (l+w)= 280

l^2 + w^2 = 40000

(l+w)^2 -2lw = 40000

78400 - 40000 = 2lw

lw = 19200

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24 Aug 2006, 08:13
What I did was to recognize that 200:280=5:7=5: (3+4) since 3,4,5 is a typical triangle. So I know that the two sides are 3*40 and 4*40 and the area is 12*1600=19200. Just to give an alternative approach.
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Last edited by HongHu on 24 Aug 2006, 08:25, edited 1 time in total.
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24 Aug 2006, 08:21
HongHu wrote:
What I did was to recognize that 200:280=5:7=5:(3+4) since 3,4,5 is a typical triangle. So I know that the two sides are 3*40 and 4*40 and the area is 12*1600=19200. Just to give an alternative approach.

HongHu is awesome as usual
Gr8 approach
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IE IMBA 2010

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24 Aug 2006, 08:26
Yurik79 wrote:
HongHu wrote:
What I did was to recognize that 200:280=5:7=5:(3+4) since 3,4,5 is a typical triangle. So I know that the two sides are 3*40 and 4*40 and the area is 12*1600=19200. Just to give an alternative approach.

HongHu is awesome as usual
Gr8 approach

Where can I go to get a HongHu math chip upgrade?
24 Aug 2006, 08:26
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