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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
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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



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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=280w
l^2+w^2=200^2
w^2280w+19200=)
w(w280)=19200
take out the negative num
w(280w)=19200 > w(280w)=19200
Area = w(280w) answer 19200



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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
Answer : A...



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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=280w l^2+w^2=200^2 w^2280w+19200=) w(w280)=19200 take out the negative num w(280w)=19200 > w(280w)=19200 Area = w(280w) answer 19200
Yeah, I substituted the first equation into the second and got: w^2280w+19200=0
Then I broke down 19200 to get the factors (w160)(w120)=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.



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interesting [#permalink]
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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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GMATT73 wrote: apollo168 wrote: Hi Sandi,
w^2280w+19200=) w(w280)=19200 take out the negative num w(280w)=19200 > w(280w)=19200 Area = w(280w) answer 19200 Yeah, I substituted the first equation into the second and got: w^2280w+19200=0 Then I broke down 19200 to get the factors (w160)(w180)=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(w160)(w180) is equal to w^2280w+19200. Couldnt find the factors.
What I did was I form fitted the w^2280w+19200 to match the equation of the area w(280w) and equate it to 19200



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Re: interesting [#permalink]
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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
Answer should be A
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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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 10=1, in the latter, this would translate to 23=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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Hey sumitsarkar82
That is a better way thanks



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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 10=1, in the latter, this would translate to 23=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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Assume nothing [#permalink]
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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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makes sense [#permalink]
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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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sandi, could you post your other question as an independent post? it will get better responses that way.
thanks
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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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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
DS: Answer A.



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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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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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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?










