Equations with square roots

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

Equations with square roots

by Brent@GMATPrepNow » Tue Jan 27, 2009 3:17 pm

What is the value of x?

(1) x – 2sqrt(3x) = -3
(2) x – sqrt(3x) – sqrt(5x) + sqrt(15) = 0

Please note that this is not an official GMAT question; it’s my attempt to create difficult (650+ level) GMAT-style questions for this forum.

Brent Hanneson - Creator of GMATPrepNow.com

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Source: Beat The GMAT — Data Sufficiency | Tue Jan 27, 2009 3:17 pm

gaggleofgirls: Master | Next Rank: 500 Posts; Posts: 138; Joined: Thu Jan 15, 2009 7:52 am; Location: Steamboat Springs, CO; Thanked: 15 times

by gaggleofgirls » Tue Jan 27, 2009 5:58 pm

Assume y = sqrtx

Then you can rewrite the equations to:

1) y^2-2*sqrt3*y = 3
y^2-2*sqrt3*y-3 = 0
(y-sqrt3)(y-sqrt3) = 0
y = sqrt3
x = sqrt3^2 = 3

You can back solve to the original here to check:
3 - 2(sqrt(3*3) = -3
3 - 2(sqrt9) = -3
3 - 2(3) = -3
3 - 6 = -3

1 is sufficient

2) y^2 - sqrt3*y - sqrt5*y - sqrt15 = 0
(y-sqrt3)(y-sqrt5) = 0
y=sqrt3 OR y = sqrt5
X = 3 or x = 5

Back solve just to prove it
3 - sqrt(3*3) - sqrt (3*5) + sqrt15 = 0
3 - 3 - sqrt15 + sqrt15 = 0
0 =0
AND
5 - sqrt(3*5) - sqrt(5*5) + sqrt15 = 0
5 - sqrt15 - 5 + sqrt15 = 0
0=0

2 insufficient.

Answer = A

-Carrie

That was evil and took very very long to solve. But thanks as it gives me one more way to look at square roots that might be very helpful on the test.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770