GMAT Prep

Forum Index GMAT Math Data Sufficiency
Free GMAT Tutoring Sessions - Practice GMAT questions with a Grockit GMAT instructor. One week only - Feb 3 to 9. Sign up now!

Free $100 MBA Admissions Starter Kit - For February, purchase a GMAT course using a Beat The GMAT discount code and receive a free $100 MBA Admissions Starter Kit. Click here to learn more.
Post New Topic   Post Reply

atlantic
Really wants to Beat The GMAT!

Default Avatar

Joined: 27 Apr 2008
Posts: 132

Thanks given: 2
Thanked 7 times in 7 posts
Location: Portugal

Target GMAT Score: 650
Topic: GMAT Prep
PostSun Jun 29, 2008 10:18 am
Hi guys,

Your help is kindly requested for this one,

post OA latter
Attachments
This post contains an attachment. You must be logged in to download/view this file. Please login or register as a user.
Back to top
View user's profile Send private message
Ian Stewart
GMAT Instructor



Joined: 02 Jun 2008
Posts: 1541

Thanks given: 4
Thanked 410 times in 334 posts
Location: Toronto

GMAT Score: 780
PostSun Jun 29, 2008 1:03 pm
First, the question asks: is |x - z| + |x| = |z|. I find this easiest to think about if I understand what the equation says about distances. Remember that |a - b| is just the distance between a and b on the number line, and |a| is the distance from a to zero. So |x - z| + |x| = |z| just says "the distance between x and z plus the distance from x to zero is equal to the distance from z to zero". How can this happen? Draw a number line, try placing x and z in different orders and on either side of zero, and you can see that this can only happen in two ways:

z < x < 0
0 < x < z

So the question is just asking- can we be sure that one of the above inequalities is true?

Before looking at the statements, we know that zy < xy < 0. What does this tell us?

-Either y is negative, and both x and z are positive, or y is positive, and both x and z are negative.

-Because zy - xy < 0, y(z-x) <0. If y is negative, then z-x must be positive, and z > x. If y is positive, z-x must be negative, and z < x (and, conversely, if z < x, y must be positive).

Okay, that was the tough part. Let's look at the statements:
1) z < x

If z < x, we know that y must be positive. If y is positive, x and z are both negative. So we know that z < x <0, and the answer to the question must be yes.

2) y > 0

If y is positive, well, this is exactly the same situation as we had with Statement 1. So again, z < x < 0, and the answer to the question must be yes.

D.
_________________
private GMAT tutor
contact me via the tutor directory at www.gmatix.com
Back to top
View user's profile Send private message
Thanked by: nandistl, havocsummers
atlantic
Really wants to Beat The GMAT!

Default Avatar

Joined: 27 Apr 2008
Posts: 132

Thanks given: 2
Thanked 7 times in 7 posts
Location: Portugal

Target GMAT Score: 650
PostMon Jun 30, 2008 3:46 am
Thanks Ian. Your explanation was of great help.
Back to top
View user's profile Send private message
Display posts from previous:   

Post New Topic   Post Reply All times are GMT - 8 Hours
Page 1 of 1
 
Forum Index GMAT Math Data Sufficiency
Most Active Members in Last 30 Days
1. osirus0830 599 posts
2. bhumika.k.shah 557 posts
3. money9111 502 posts
4. ajith 462 posts
5. thephoenix 366 posts
See More Top Beat The GMAT Members
Most Active Experts in Last 30 Days
1. Stuart Kovinsky
Kaplan GMAT Teacher 		91 posts
2. Testluv
Kaplan GMAT Teacher 		80 posts
3. Brent Hanneson
Leap Education Teacher 		71 posts
4. bryantmichaels
Veritas GMAT Teacher 		61 posts
5. Stacey Koprince
Manhattan GMAT Teacher 		51 posts
See More Top Beat The GMAT Experts