BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

3 unknowns

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 418
Joined: Wed Jun 11, 2008 5:29 am
Thanked: 65 times

by bluementor » Tue Apr 28, 2009 2:04 am
x^2 - yz = 10 (eqn a)
y^2 + xz = 10 (eqn b)
z^2 + xy = 10 (eqn c)

x^2 + y^2 + z^2 = ?

(eqn a) - (eqn b):

x^2 - yz - y^2 - xz = 0
x^2 - y^2 = xz + yz
(x + y)(x - y) = z(x + y)
x - y = z (eqn 1)

Add equations a, b and c:

x^2 + y^2 + z^2 - yz + xz + xy = 30
x^2 + y^2 + z^2 - yz + xz + (10 - z^2) = 30 (xy substituted with equation c)
x^2 + y^2 + z^2 - yz + xz - z^2 = 20
x^2 + y^2 - yz + xz = 20
x^2 + y^2 + z(x - y) = 20
x^2 + y^2 + z(z) = 20 (insert equation 1)
x^2 + y^2 + z^2 = 20

Choose C

-BM-
Top
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

by sanju09 » Tue Apr 28, 2009 3:56 am
How do we know that (x + y) ≠ 0, BM? :)
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Master | Next Rank: 500 Posts
Posts: 418
Joined: Wed Jun 11, 2008 5:29 am
Thanked: 65 times

by bluementor » Tue Apr 28, 2009 1:17 pm
sanju09 wrote:How do we know that (x + y) ≠ 0, BM? :)
You are right, i didnt consider (x+y) = 0 in my solution.

However, with (x+y) = 0, can equations a, b and c all be satisfied? I cannot find a solution for x, y and z under this condition.

How would you solve this problem, sanju?

-BM-
Top
Post new topic Post Reply
• Page 1 of 1