3 unknowns

Expert replies

[email protected]: Master | Next Rank: 500 Posts; Posts: 117; Joined: Mon Oct 27, 2008 5:08 pm; Thanked: 1 times

by [email protected] » Mon Apr 27, 2009 9:23 am

If x^2-yz=10, y^2+xz=10, z^2 +xy=10, and z not=y, what is the value of x^2+y^2+z^2

10
15
20
25
30

C

is there an easy way to do this problem? shortcut?

Like this post

Source: Beat The GMAT — Problem Solving | Mon Apr 27, 2009 9:23 am

bluementor: 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-

Like this post

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; 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

Like this post

bluementor: 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-

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review