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Source: — Problem Solving |
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by vijaynarayanan » Thu Jul 01, 2010 6:11 am
answer is 24.

If you substitute the choices in for the Pythagoras Theorem... you will see that only,

24^2 + 7^2 = 25^2

and also 24x7=168
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by jeremy8 » Sat Jul 03, 2010 11:32 pm
Is there any way to do algebra on this, using lenght + width as L and W, so that:

LxW=168

L^2+W^2=25^2

?

I tried, but came up with a ridiculous quadratic. I'm not very comfortable with exponents in equations.
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by selango » Sun Jul 04, 2010 12:45 am
L*W=168

L^2+W^2=D^2

(L+W)^2-2LW=25^2

(L+W)^2-2*168=25^2

(L+W)^2=961

L+W=31 and L*W=168

With this you can get l=24 and B =7
--Anand--
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by jeremy8 » Sun Jul 04, 2010 2:20 am
selango wrote:L*W=168

L^2+W^2=D^2

(L+W)^2-2LW=25^2

(L+W)^2-2*168=25^2

(L+W)^2=961

L+W=31 and L*W=168

With this you can get l=24 and B =7

Thanks for your help.

It took me a while to understand how you got from L^2+W^2 to (L+W)^2-2LW.
Is this a mandatory step to finding L+W? Is factoring like this the only way to isolate and solve for L+W?

Is there any way of using the first equation in the form W=168/L and replacing W by this result in the other equation?

Something like: L^2+(168/L)^2=25^2
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by selango » Sun Jul 04, 2010 3:19 am
Jeremy,

It can be solved by substituting L or W value.But it takes a bit longer time.

LW=168

L^2+W^2=625

Sub W=168/L

L^2+(168/L)^2=625

L^2+28224/L^2=625

L^4+28224=625L^2

L^4-625L^2+28224=0

As u can see this equation takes longer time to solve.

(L^2-576)*(L^2-49)=0

L^2=576,L=24 or L^2=49,L=7

L=24 or L=7

From the options only 24 is available.So L=24.

Pl let me know if this clarify ur doubt.

In algebra,u can solve the equation in many ways.The trick is you should know which one take less time to solve.
--Anand--
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by jeremy8 » Sun Jul 04, 2010 4:08 am
selango wrote:
Pl let me know if this clarify ur doubt.

In algebra,u can solve the equation in many ways.The trick is you should know which one take less time to solve.
Anand,

Thanks again for your help. This shows me I'm not anywhere near ready to take the exam yet.
I really need to get a lot more comfortable with manipulating algebraic expressions.
I wasn't even sure it was possible to solve by substitution, although like you said, it's clearly not the fastest solution...
Back to my books....
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by selango » Sun Jul 04, 2010 5:54 am
Jeremy,

There are lot of posts and materials available for algebra in BTG.Go through it and get familar with the topics.

Dont lose ur confidence.In this forum you can learn many things:)

go thru the below link,

https://www.platinumgmat.com/gmat_study_ ... _equations
--Anand--
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by jeremy8 » Sun Jul 04, 2010 12:58 pm
selango wrote:Jeremy,

There are lot of posts and materials available for algebra in BTG.Go through it and get familar with the topics.

Dont lose ur confidence.In this forum you can learn many things:)

go thru the below link,

https://www.platinumgmat.com/gmat_study_ ... _equations
Thanks Anand,

I'm definitely glad I found this forum; I think it might really save me.
I'll check the link and try to really master this factorization process.
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