Value of X

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cartera: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Tue Jun 10, 2008 6:49 pm; Thanked: 2 times

Value of X

by cartera » Tue Nov 25, 2008 7:23 am

What is the value of X?

1. x^2+y^2=25
2. xy=12

OA E

Where Am I wrong?

x=12/y -------> (12/y)^2+y^2=25

144/y^2+y^2=25 --------> (y^4+144)/y^2=25 ------> y^4+144-25y^2=0

Sqrt [y^4+144-25y^2=0] --------> y^2-5y+12=0

Then the solution should be C

Quote

Source: Beat The GMAT — Data Sufficiency | Tue Nov 25, 2008 7:23 am

rohangupta83: Legendary Member; Posts: 541; Joined: Thu May 31, 2007 6:44 pm; Location: UK; Thanked: 21 times; Followed by:3 members; GMAT Score:680

Re: Value of X

by rohangupta83 » Tue Nov 25, 2008 8:21 am

cartera wrote:What is the value of X?

1. x^2+y^2=25
2. xy=12

OA E

Where Am I wrong?

x=12/y -------> (12/y)^2+y^2=25

144/y^2+y^2=25 --------> (y^4+144)/y^2=25 ------> y^4+144-25y^2=0

Fine till here

But you can't do the following

cartera wrote: Sqrt [y^4+144-25y^2=0] --------> y^2-5y+12=0

Then the solution should be C

If you want to solve the equation y^4+144-25y^2=0

substitute y^2 = z

you'll get z^2 -25z +144 = 0

solve for z

plug z into the equation y^2 = z

and then solve for x by using the equation xy=12

OR

when you had xy=12
you could've substituted for y i.e. y = 12/x and then the whole equation would've been in terms of x and not y

hope this helps..